NPTEL Video Lecture Topic List - Created by LinuXpert ... · NPTEL Video Course - Mathematics -...

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NPTEL Video Course - Mathematics - Elementary Numerical Analysis Subject Co-ordinator - Prof. Rekha P. Kulkarni Co-ordinating Institute - IIT - Bombay Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable Lecture 1 - Introduction Lecture 2 - Polynomial Approximation Lecture 3 - Interpolating Polynomials Lecture 4 - Properties of Divided Difference Lecture 5 - Error in the Interpolating polynomial Lecture 6 - Cubic Hermite Interpolation Lecture 7 - Piecewise Polynomial Approximation Lecture 8 - Cubic Spline Interpolation Lecture 9 - Tutorial 1 Lecture 10 - Numerical Integration Lecture 11 - Composite Numerical Integration Lecture 12 - Gauss 2-point Rule Lecture 13 - Gauss 2-point Rule Lecture 14 - Convergence of Gaussian Integration Lecture 15 - Tutorial 2 Lecture 16 - Numerical Differentiation Lecture 17 - Gauss Elimination Lecture 18 - L U decomposition Lecture 19 - Cholesky decomposition Lecture 20 - Gauss Elimination with partial pivoting Lecture 21 - Vector and Matrix Norms Lecture 22 - Perturbed Linear Systems Lecture 23 - Ill-conditioned Linear System Lecture 24 - Tutorial 3 Lecture 25 - Effect of Small Pivots Lecture 26 - Solution of Non-linear Equations Lecture 27 - Quadratic Convergence of Newton's Method Lecture 28 - Jacobi Method Lecture 29 - Gauss-Seidel Method NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------- Get Digi-MAT (Digital Media Access Terminal) For High-Speed Video Streaming of NPTEL and Educational Video Courses in LAN www.digimat.in

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Page 1: NPTEL Video Lecture Topic List - Created by LinuXpert ... · NPTEL Video Course - Mathematics - Measure and Integration Subject Co-ordinator - Prof. Inder K Rana Co-ordinating Institute

NPTEL Video Course - Mathematics - Elementary Numerical Analysis

Subject Co-ordinator - Prof. Rekha P. Kulkarni

Co-ordinating Institute - IIT - Bombay

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - IntroductionLecture 2 - Polynomial ApproximationLecture 3 - Interpolating PolynomialsLecture 4 - Properties of Divided DifferenceLecture 5 - Error in the Interpolating polynomialLecture 6 - Cubic Hermite InterpolationLecture 7 - Piecewise Polynomial ApproximationLecture 8 - Cubic Spline InterpolationLecture 9 - Tutorial 1Lecture 10 - Numerical IntegrationLecture 11 - Composite Numerical IntegrationLecture 12 - Gauss 2-point RuleLecture 13 - Gauss 2-point RuleLecture 14 - Convergence of Gaussian IntegrationLecture 15 - Tutorial 2Lecture 16 - Numerical DifferentiationLecture 17 - Gauss EliminationLecture 18 - L U decompositionLecture 19 - Cholesky decompositionLecture 20 - Gauss Elimination with partial pivotingLecture 21 - Vector and Matrix NormsLecture 22 - Perturbed Linear SystemsLecture 23 - Ill-conditioned Linear SystemLecture 24 - Tutorial 3Lecture 25 - Effect of Small PivotsLecture 26 - Solution of Non-linear EquationsLecture 27 - Quadratic Convergence of Newton's MethodLecture 28 - Jacobi MethodLecture 29 - Gauss-Seidel Method

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Lecture 30 - Tutorial 4Lecture 31 - Initial Value ProblemLecture 32 - Multi-step MethodsLecture 33 - Predictor-Corrector FormulaeLecture 34 - Boundary Value ProblemsLecture 35 - Eigenvalues and EigenvectorsLecture 36 - Spectral TheoremLecture 37 - Power MethodLecture 38 - Inverse Power MethodLecture 39 - Q R DecompositionLecture 40 - Q R Method

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Page 3: NPTEL Video Lecture Topic List - Created by LinuXpert ... · NPTEL Video Course - Mathematics - Measure and Integration Subject Co-ordinator - Prof. Inder K Rana Co-ordinating Institute

NPTEL Video Course - Mathematics - Measure and Integration

Subject Co-ordinator - Prof. Inder K Rana

Co-ordinating Institute - IIT - Bombay

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Introduction, Extended Real numbersLecture 2 - Algebra and Sigma Algebra of a subset of a setLecture 3 - Sigma Algebra generated by a classLecture 4 - Monotone ClassLecture 5 - Set functionLecture 6 - The Length function and its propertiesLecture 7 - Countably additive set functions on intervalsLecture 8 - Uniqueness Problem for MeasureLecture 9 - Extension of measureLecture 10 - Outer measure and its propertiesLecture 11 - Measurable setsLecture 12 - Lebesgue measure and its propertiesLecture 13 - Characterization of Lebesque measurable setsLecture 14 - Measurable functionsLecture 15 - Properties of measurable functionsLecture 16 - Measurable functions on measure spacesLecture 17 - Integral of non negative simple measurable functionsLecture 18 - Properties of non negative simple measurable functionsLecture 19 - Monotone convergence theorem & Fatou's LemmaLecture 20 - Properties of Integral functions & Dominated Convergence TheoremLecture 21 - Dominated Convergence Theorem and applicationsLecture 22 - Lebesgue Integral and its propertiesLecture 23 - Denseness of continuous functionLecture 24 - Product measures, an IntroductionLecture 25 - Construction of Product MeasureLecture 26 - Computation of Product Measure - ILecture 27 - Computation of Product Measure - IILecture 28 - Integration on Product spacesLecture 29 - Fubini's Theorems

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Lecture 30 - Lebesgue Measure and integral on R2Lecture 31 - Properties of Lebesgue Measure and integral on RnLecture 32 - Lebesgue integral on R2Lecture 33 - Integrating complex-valued functionsLecture 34 - Lp - spacesLecture 35 - L2(X,S,mue)Lecture 36 - Fundamental Theorem of calculas for Lebesgue Integral - ILecture 37 - Fundamental Theorem of calculus for Lebesgue Integral - IILecture 38 - Absolutely continuous measuresLecture 39 - Modes of convergenceLecture 40 - Convergence in Measure

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Page 5: NPTEL Video Lecture Topic List - Created by LinuXpert ... · NPTEL Video Course - Mathematics - Measure and Integration Subject Co-ordinator - Prof. Inder K Rana Co-ordinating Institute

NPTEL Video Course - Mathematics - Mathematics in India - From Vedic Period to Modern Times

Subject Co-ordinator - Prof. M.D. Srinivas, Prof. K. Ramasubramanian, Prof. M.S. Sriram

Co-ordinating Institute - Centre for Policy Studies, Chennai | IIT - Bombay | University of Madras, Chennai

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Indian MathematicsLecture 2 - Vedas and Sulbasutras - Part 1Lecture 3 - Vedas and Sulbasutras - Part 2Lecture 4 - Panini's AstadhyayiLecture 5 - Pingala's ChandahsastraLecture 6 - Decimal place value systemLecture 7 - Aryabhatiya of Aryabhata - Part 1Lecture 8 - Aryabhatiya of Aryabhata - Part 2Lecture 9 - Aryabhatiya of Aryabhata - Part 3Lecture 10 - Aryabhatiya of Aryabhata - Part 4 and Introduction to Jaina MathematicsLecture 11 - Brahmasphutasiddhanta of Brahmagupta - Part 1Lecture 12 - Brahmasphutasiddhanta of Brahmagupta - Part 2Lecture 13 - Brahmasphutasiddhanta of Brahmagupta - Part 3Lecture 14 - Brahmasphutasiddhanta of Brahmagupta - Part 4 and The Bakhshali ManuscriptLecture 15 - Mahaviras Ganitasarasangraha - Part 1Lecture 16 - Mahaviras Ganitasarasangraha - Part 2Lecture 17 - Mahaviras Ganitasarasangraha - Part 3Lecture 18 - Development of Combinatorics - Part 1Lecture 19 - Development of Combinatorics - Part 2Lecture 20 - Lilavati of Bhaskaracarya - Part 1Lecture 21 - Lilavati of Bhaskaracarya - Part 2Lecture 22 - Lilavati of Bhaskaracarya - Part 3Lecture 23 - Bijaganita of Bhaskaracarya - Part 1Lecture 24 - Bijaganita of Bhaskaracarya - Part 2Lecture 25 - Ganitakaumudi of Narayana Pandita - Part 1Lecture 26 - Ganitakaumudi of Narayana Pandita - Part 2Lecture 27 - Ganitakaumudi of Narayana Pandita - Part 3Lecture 28 - Magic Squares - Part 1Lecture 29 - Magic Squares - Part 2

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Lecture 30 - Development of Calculus in India - Part 1Lecture 31 - Development of Calculus in India - Part 2Lecture 32 - JyanayanamLecture 33 - Trigonometry and Spherical Trigonometry - Part 1Lecture 34 - Trigonometry and Spherical Trigonometry - Part 2Lecture 35 - Trigonometry and Spherical Trigonometry - Part 3Lecture 36 - Proofs in Indian Mathematics - Part 1Lecture 37 - Proofs in Indian Mathematics - Part 2Lecture 38 - Proofs in Indian Mathematics - Part 3Lecture 39 - Mathematics in Modern India - Part 1Lecture 40 - Mathematics in Modern India - Part 2

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Page 7: NPTEL Video Lecture Topic List - Created by LinuXpert ... · NPTEL Video Course - Mathematics - Measure and Integration Subject Co-ordinator - Prof. Inder K Rana Co-ordinating Institute

NPTEL Video Course - Mathematics - NOC:Measure Theory

Subject Co-ordinator - Prof. Inder K Rana

Co-ordinating Institute - IIT - Bombay

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - (1A) Introduction, Extended Real NumbersLecture 2 - (1B) Introduction, Extended Real NumbersLecture 3 - (2A) Algebra and Sigma Algebra of Subsets of a SetLecture 4 - (2B) Algebra and Sigma Algebra of Subsets of a SetLecture 5 - (3A) Sigma Algebra generated by a ClassLecture 6 - (3B) Sigma Algebra generated by a ClassLecture 7 - (4A) Monotone ClassLecture 8 - (4B) Monotone ClassLecture 9 - (5A) Set FunctionsLecture 10 - (5B) Set FunctionsLecture 11 - (6A) The Length Function and its PropertiesLecture 12 - (6B) The Length Function and its PropertiesLecture 13 - (7A) Countably Additive Set Functions on IntervalsLecture 14 - (7B) Countably Additive Set Functions on IntervalsLecture 15 - (8A) Uniqueness Problem for MeasureLecture 16 - (8B) Uniqueness Problem for MeasureLecture 17 - (9A) Extension of MeasureLecture 18 - (9B) Extension of MeasureLecture 19 - (10A) Outer Measure and its PropertiesLecture 20 - (10B) Outer Measure and its PropertiesLecture 21 - (11A) Measurable SetsLecture 22 - (11B) Measurable SetsLecture 23 - (12A) Lebesgue Measure and its PropertiesLecture 24 - (12B) Lebesgue Measure and its PropertiesLecture 25 - (13A) Characterization of Lebesgue Measurable SetsLecture 26 - (13B) Characterization of Lebesgue Measurable SetsLecture 27 - (14A) Measurable FunctionsLecture 28 - (14B) Measurable FunctionsLecture 29 - (15A) Properties of Measurable Functions

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Lecture 30 - (15B) Properties of Measurable FunctionsLecture 31 - (16A) Measurable Functions on Measure SpacesLecture 32 - (16B) Measurable Functions on Measure SpacesLecture 33 - (17A) Integral of Nonnegative Simple Measurable FunctionsLecture 34 - (17B) Integral of Nonnegative Simple Measurable FunctionsLecture 35 - (18A) Properties of Nonnegative Simple Measurable FunctionsLecture 36 - (18B) Properties of Nonnegative Simple Measurable FunctionsLecture 37 - (19A) Monotone Convergence Theorem and Fatou's LemmaLecture 38 - (19B) Monotone Convergence Theorem and Fatou's LemmaLecture 39 - (20A) Properties of Integrable Functions and Dominated Convergence TheoremLecture 40 - (20B) Properties of Integrable Functions and Dominated Convergence TheoremLecture 41 - (21A) Dominated Convergence Theorem and ApplicationsLecture 42 - (21B) Dominated Convergence Theorem and ApplicationsLecture 43 - (22A) Lebesgue Integral and its PropertiesLecture 44 - (22B) Lebesgue Integral and its PropertiesLecture 45 - (23A) Product Measure, an IntroductionLecture 46 - (23B) Product Measure, an IntroductionLecture 47 - (24A) Construction of Product MeasuresLecture 48 - (24B) Construction of Product MeasuresLecture 49 - (25A) Computation of Product Measure - ILecture 50 - (25B) Computation of Product Measure - ILecture 51 - (26A) Computation of Product Measure - IILecture 52 - (26B) Computation of Product Measure - IILecture 53 - (27A) Integration on Product SpacesLecture 54 - (27B) Integration on Product SpacesLecture 55 - (28A) Fubini's TheoremsLecture 56 - (28B) Fubini's TheoremsLecture 57 - (29A) Lebesgue Measure and Integral on R2Lecture 58 - (29B) Lebesgue Measure and Integral on R2Lecture 59 - (30A) Properties of Lebesgue Measure on R2Lecture 60 - (30B) Properties of Lebesgue Measure on R2Lecture 61 - (31A) Lebesgue Integral on R2Lecture 62 - (31B) Lebesgue Integral on R2

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Page 9: NPTEL Video Lecture Topic List - Created by LinuXpert ... · NPTEL Video Course - Mathematics - Measure and Integration Subject Co-ordinator - Prof. Inder K Rana Co-ordinating Institute

NPTEL Video Course - Mathematics - NOC:Calculus for Economics, Commerce and Management

Subject Co-ordinator - Prof.Inder Kumar Rana

Co-ordinating Institute - IIT - Bombay

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Introduction to the CourseLecture 2 - Concept of a Set, Ways of Representing SetsLecture 3 - Venn Diagrams, Operations on SetsLecture 4 - Operations on Sets, Cardinal Number, Real NumbersLecture 5 - Real Numbers, SequencesLecture 6 - Sequences, Convergent Sequences, Bounded SequencesLecture 7 - Limit Theorems, Sandwich Theorem, Monotone Sequences, Completeness of Real NumbersLecture 8 - Relations and FunctionsLecture 9 - Functions, Graph of a Functions, Function FormulasLecture 10 - Function Formulas, Linear ModelsLecture 11 - Linear Models, Elasticity, Linear Functions, Nonlinear Models, Quadratic FunctionsLecture 12 - Quadratic Functions, Quadratic Models, Power Function, Exponential FunctionLecture 13 - Exponential Function, Exponential Models, Logarithmic FunctionLecture 14 - Limit of a Function at a Point, Continuous FunctionsLecture 15 - Limit of a Function at a PointLecture 16 - Limit of a Function at a Point, Left and Right LimitsLecture 17 - Computing Limits, Continuous FunctionsLecture 18 - Applications of Continuous FunctionsLecture 19 - Applications of Continuous Functions, Marginal of a FunctionLecture 20 - Rate of Change, DifferentiationLecture 21 - Rules of DifferentiationLecture 22 - Derivatives of Some Functions, Marginal, ElasticityLecture 23 - Elasticity, Increasing and Decreasing Functions, Optimization, Mean Value TheoremLecture 24 - Mean Value Theorem, Marginal Analysis, Local Maxima and MinimaLecture 25 - Local Maxima and MinimaLecture 26 - Local Maxima and Minima, Continuity Test, First Derivative Test, Successive DifferentiationLecture 27 - Successive Differentiation, Second Derivative TestLecture 28 - Average and Marginal Product, Marginal of Revenue and Cost, Absolute Maximum and MinimumLecture 29 - Absolute Maximum and Minimum

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Lecture 30 - Monopoly Market, Revenue and ElasticityLecture 31 - Property of Marginals, Monopoly Market, Publisher v/s Author ProblemLecture 32 - Convex and Concave FunctionsLecture 33 - Derivative Tests for Convexity, Concavity and Points of Inflection, Higher Order Derivative ConditionsLecture 34 - Convex and Concave Functions, AsymptotesLecture 35 - Asymptotes, Curve SketchingLecture 36 - Functions of Two Variables, Visualizing Graph, Level Curves, Contour LinesLecture 37 - Partial Derivatives and Application to Marginal AnalysisLecture 38 - Marginals in Cobb-Douglas model, partial derivatives and elasticity, chain rulesLecture 39 - Chain Rules, Higher Order Partial Derivatives, Local Maxima and Minima, Critical PointsLecture 40 - Saddle Points, Derivative Tests, Absolute Maxima and MinimaLecture 41 - Some Examples, Constrained Maxima and Minima

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Page 11: NPTEL Video Lecture Topic List - Created by LinuXpert ... · NPTEL Video Course - Mathematics - Measure and Integration Subject Co-ordinator - Prof. Inder K Rana Co-ordinating Institute

NPTEL Video Course - Mathematics - NOC:Basic Linear Algebra

Subject Co-ordinator - Prof.Inder Kumar Rana

Co-ordinating Institute - IIT - Bombay

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Introduction - ILecture 2 - Introduction - IILecture 3 - Introduction - IIILecture 4 - Systems of Linear Equations - ILecture 5 - Systems of Linear Equations - IILecture 6 - Systems of Linear Equations - IIILecture 7 - Reduced Row Echelon Form and Rank - ILecture 8 - Reduced Row Echelon Form and Rank - IILecture 9 - Reduced Row Echelon Form and Rank - IIILecture 10 - Solvability of a Linear System, Linear Span, Basis - ILecture 11 - Solvability of a Linear System, Linear Span, Basis - IILecture 12 - Solvability of a Linear System, Linear Span, Basis - IIILecture 13 - Linear Span, Linear Independence and Basis - ILecture 14 - Linear Span, Linear Independence and Basis - IILecture 15 - Linear Span, Linear Independence and Basis - IIILecture 16 - Row Space, Column Space, Rank-Nullity Theorem - ILecture 17 - Row Space, Column Space, Rank-Nullity Theorem - IILecture 18 - Row Space, Column Space, Rank-Nullity Theorem - IIILecture 19 - Determinants and their Properties - ILecture 20 - Determinants and their Properties - IILecture 21 - Determinants and their Properties - IIILecture 22 - Linear Transformations - ILecture 23 - Linear Transformations - IILecture 24 - Linear Transformations - IIILecture 25 - Orthonormal Basis, Geometry in R^2 - ILecture 26 - Orthonormal Basis, Geometry in R^2 - IILecture 27 - Orthonormal Basis, Geometry in R^2 - IIILecture 28 - Isometries, Eigenvalues and Eigenvectors - ILecture 29 - Isometries, Eigenvalues and Eigenvectors - II

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Lecture 30 - Isometries, Eigenvalues and Eigenvectors - IIILecture 31 - Diagonalization and Real Symmetric Matrices - ILecture 32 - Diagonalization and Real Symmetric Matrices - IILecture 33 - Diagonalization and Real Symmetric Matrices - IIILecture 34 - Diagonalization and its Applications - ILecture 35 - Diagonalization and its Applications - IILecture 36 - Diagonalization and its Applications - IIILecture 37 - Abstract Vector Spaces - ILecture 38 - Abstract Vector Spaces - IILecture 39 - Abstract Vector Spaces - IIILecture 40 - Inner Product Spaces - ILecture 41 - Inner Product Spaces - II

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NPTEL Video Course - Mathematics - NOC:Commutative Algebra

Subject Co-ordinator - Prof. Dilip P. Patil

Co-ordinating Institute - IIT - Bombay

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Zariski Topology and K-SpectrumLecture 2 - Algebraic Varieties and Classical NullstelensatzLecture 3 - Motivation for Krulls DimensionLecture 4 - Chevalleys dimensionLecture 5 - Associated Prime Ideals of a ModuleLecture 6 - Support of a ModuleLecture 7 - Primary DecompositionLecture 8 - Primary Decomposition (Continued...)Lecture 9 - Uniqueness of Primary DecompositionLecture 10 - Modules of Finite LengthLecture 11 - Modules of Finite Length (Continued...)Lecture 12 - Introduction to Krullâ��s DimensionLecture 13 - Noether Normalization Lemma (Classical Version)Lecture 14 - Consequences of Noether Normalization LemmaLecture 15 - Nil Radical and Jacobson Radical of Finite type Algebras over a Field and digression of Integral ExtensionLecture 16 - Nagataâ��s version of NNLLecture 17 - Dimensions of Polynomial ring over Noetherian ringsLecture 18 - Dimension of Polynomial Algebra over arbitrary RingsLecture 19 - Dimension InequalitiesLecture 20 - Hilbertâ��s NullstelensatzLecture 21 - Computational rules for Poincar�© SeriesLecture 22 - Graded Rings, Modules and Poincar�© SeriesLecture 23 - Hilbert-Samuel PolynomialsLecture 24 - Hilbert-Samuel Polynomials (Continued...)Lecture 25 - Numerical Function of polynomial typeLecture 26 - Hilbert-Samuel Polynomial of a Local ringLecture 27 - Filtration on a ModuleLecture 28 - Artin-Rees LemmaLecture 29 - Dimension Theorem

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Lecture 30 - Dimension Theorem (Continued...)Lecture 31 - Consequences of Dimension TheoremLecture 32 - Generalized Krull�s Principal Ideal TheoremLecture 33 - Second proof of Krull�s Principal Ideal TheoremLecture 34 - The Spec FunctorLecture 35 - Prime ideals in Polynomial ringsLecture 36 - Characterization of Equidimensional Affine AlgebraLecture 37 - Connection between Regular local rings and associated graded ringsLecture 38 - Statement of the Jacobian Criterion for RegularityLecture 39 - Hilbert function for Affine AlgebraLecture 40 - Hilbert Serre TheoremLecture 41 - Jacobian Matrix and its RankLecture 42 - Jacobian Matrix and its Rank (Continued...)Lecture 43 - Proof of Jacobian CritrerionLecture 44 - Proof of Jacobian Critrerion (Continued...)Lecture 45 - Preparation for Homological DimensionLecture 46 - Complexes of Modules and HomologyLecture 47 - Projective ModulesLecture 48 - Homological Dimension and Projective moduleLecture 49 - Global DimensionLecture 50 - Homological characterization of Regular Local Rings (RLR)Lecture 51 - Homological characterization of Regular Local Rings (Continued...)Lecture 52 - Homological Characterization of Regular Local Rings (Continued...)Lecture 53 - Regular Local Rings are UFDLecture 54 - RLR-Prime ideals of height 1Lecture 55 - Discrete Valuation RingLecture 56 - Discrete Valuation Ring (Continued...)Lecture 57 - Dedekind DomainsLecture 58 - Fractionary Ideals and Dedekind DomainsLecture 59 - Characterization of Dedekind DomainLecture 60 - Dedekind Domains and prime factorization of ideals

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NPTEL Video Course - Mathematics - NOC:Galois Theory

Subject Co-ordinator - Prof. Dilip P. Patil

Co-ordinating Institute - IIT - Bombay

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Historical PerspectivesLecture 2 - Examples of FieldsLecture 3 - Polynomials and Basic propertiesLecture 4 - Polynomial RingsLecture 5 - Unit and Unit GroupsLecture 6 - Division with remainder and prime factorizationLecture 7 - Zeroes of PolynomialsLecture 8 - Polynomial functionsLecture 9 - Algebraically closed Fields and statement of FTALecture 10 - Gauss�s Theorem(Uniqueness of factorization)Lecture 11 - Digression on Rings homomorphism, AlgebrasLecture 12 - Kernel of homomorphisms and ideals in K[X],ZLecture 13 - Algebraic elementsLecture 14 - ExamplesLecture 15 - Minimal PolynomialsLecture 16 - Characterization of Algebraic elementsLecture 17 - Theorem of KroneckerLecture 18 - ExamplesLecture 19 - Digression on GroupsLecture 20 - Some examples and Characteristic of a RingLecture 21 - Finite subGroups of the Unit Group of a FieldLecture 22 - Construction of Finite FieldsLecture 23 - Digression on Group action - ILecture 24 - Automorphism Groups of a Field ExtensionLecture 25 - Dedekind-Artin TheoremLecture 26 - Galois ExtensionLecture 27 - Examples of Galois extensionLecture 28 - Examples of Automorphism GroupsLecture 29 - Digression on Linear Algebra

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Lecture 30 - Minimal and Characteristic Polynomials, Norms, Trace of elementsLecture 31 - Primitive Element Theorem for Galois ExtensionLecture 32 - Fundamental Theorem of Galois TheoryLecture 33 - Fundamental Theorem of Galois Theory (Continued...)Lecture 34 - Cyclotomic extensionsLecture 35 - Cyclotomic PolynomialsLecture 36 - Irreducibility of Cyclotomic Polynomials over QLecture 37 - Reducibility of Cyclotomic Polynomials over Finite FieldsLecture 38 - Galois Group of Cyclotomic PolynomialsLecture 39 - Extension over a fixed Field of a finite subGroup is Galois ExtensionLecture 40 - Digression on Group action - IILecture 41 - Correspondence of Normal SubGroups and Galois sub-extensionsLecture 42 - Correspondence of Normal SubGroups and Galois sub-extensions (Continued...)Lecture 43 - Inverse Galois problem for Abelian GroupsLecture 44 - Elementary Symmetric PolynomialsLecture 45 - Fundamental Theorem on Symmetric PolynomialsLecture 46 - Gal (K[X1,X2,�,Xn]/K[S1,S2,...,Sn])Lecture 47 - Digression on Symmetric and Alternating GroupLecture 48 - Discriminant of a PolynomialLecture 49 - Zeroes and EmbeddingsLecture 50 - Normal ExtensionsLecture 51 - Existence of Algebraic ClosureLecture 52 - Uniqueness of Algebraic ClosureLecture 53 - Proof of The Fundamental Theorem of AlgebraLecture 54 - Galois Group of a PolynomialLecture 55 - Perfect FieldsLecture 56 - EmbeddingsLecture 57 - Characterization of finite Separable extensionLecture 58 - Primitive Element TheoremLecture 59 - Equivalence of Galois extensions and Normal-Separable extensionsLecture 60 - Operation of Galois Group of Polynomial on the set of zeroesLecture 61 - DiscriminantsLecture 62 - Examples for further study

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NPTEL Video Course - Mathematics - Stochastic Processes

Subject Co-ordinator - Dr. S. Dharmaraja

Co-ordinating Institute - IIT - Delhi

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Introduction to Stochastic ProcessesLecture 2 - Introduction to Stochastic Processes (Continued.)Lecture 3 - Problems in Random Variables and DistributionsLecture 4 - Problems in Sequences of Random VariablesLecture 5 - Definition, Classification and ExamplesLecture 6 - Simple Stochastic ProcessesLecture 7 - Stationary ProcessesLecture 8 - Autoregressive ProcessesLecture 9 - Introduction, Definition and Transition Probability MatrixLecture 10 - Chapman-Kolmogrov EquationsLecture 11 - Classification of States and Limiting DistributionsLecture 12 - Limiting and Stationary DistributionsLecture 13 - Limiting Distributions, Ergodicity and Stationary DistributionsLecture 14 - Time Reversible Markov Chain, Application of Irreducible Markov Chain in Queueing ModelsLecture 15 - Reducible Markov ChainsLecture 16 - Definition, Kolmogrov Differential Equations and Infinitesimal Generator MatrixLecture 17 - Limiting and Stationary Distributions, Birth Death ProcessesLecture 18 - Poisson ProcessesLecture 19 - M/M/1 Queueing ModelLecture 20 - Simple Markovian Queueing ModelsLecture 21 - Queueing NetworksLecture 22 - Communication SystemsLecture 23 - Stochastic Petri NetsLecture 24 - Conditional Expectation and FiltrationLecture 25 - Definition and Simple ExamplesLecture 26 - Definition and PropertiesLecture 27 - Processes Derived from Brownian MotionLecture 28 - Stochastic Differential EquationsLecture 29 - Ito Integrals

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Lecture 30 - Ito Formula and its VariantsLecture 31 - Some Important SDE`s and Their SolutionsLecture 32 - Renewal Function and Renewal EquationLecture 33 - Generalized Renewal Processes and Renewal Limit TheoremsLecture 34 - Markov Renewal and Markov Regenerative ProcessesLecture 35 - Non Markovian QueuesLecture 36 - Non Markovian Queues Cont,,Lecture 37 - Application of Markov Regenerative ProcessesLecture 38 - Galton-Watson ProcessLecture 39 - Markovian Branching Process

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NPTEL Video Course - Mathematics - NOC:Stochastic Processes - 1

Subject Co-ordinator - Dr. S. Dharmaraja

Co-ordinating Institute - IIT - Delhi

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Introduction and motivation for studying stochastic processesLecture 2 - Probability space and conditional probabilityLecture 3 - Random variable and cumulative distributive functionLecture 4 - Discrete Uniform Distribution, Binomial Distribution, Geometric Distribution, Continuous Uniform Distribution, Exponential Distribution, Normal Distribution and Poisson DistributionLecture 5 - Joint Distribution of Random VariablesLecture 6 - Independent Random Variables, Covariance and Correlation Coefficient and Conditional DistributionLecture 7 - Conditional Expectation and Covariance MatrixLecture 8 - Generating Functions, Law of Large Numbers and Central Limit TheoremLecture 9 - Problems in Random variables and DistributionsLecture 10 - Problems in Random variables and Distributions (Continued...)Lecture 11 - Problems in Random variables and Distributions (Continued...)Lecture 12 - Problems in Random variables and Distributions (Continued...)Lecture 13 - Problems in Sequences of Random VariablesLecture 14 - Problems in Sequences of Random Variables (Continued...)Lecture 15 - Problems in Sequences of Random Variables (Continued...)Lecture 16 - Problems in Sequences of Random Variables (Continued...)Lecture 17 - Definition of Stochastic Processes, Parameter and State SpacesLecture 18 - Classification of Stochastic ProcessesLecture 19 - Examples of Classification of Stochastic ProcessesLecture 20 - Examples of Classification of Stochastic Processes (Continued...)Lecture 21 - Bernoulli ProcessLecture 22 - Poisson ProcessLecture 23 - Poisson Process (Continued...)Lecture 24 - Simple Random Walk and Population ProcessesLecture 25 - Introduction to Discrete time Markov ChainLecture 26 - Introduction to Discrete time Markov Chain (Continued...)Lecture 27 - Examples of Discrete time Markov ChainLecture 28 - Examples of Discrete time Markov Chain (Continued...)Lecture 29 - Introduction to Chapman-Kolmogorov equations

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Lecture 30 - State Transition Diagram and ExamplesLecture 31 - ExamplesLecture 32 - Introduction to Classification of States and PeriodicityLecture 33 - Closed set of States and Irreducible Markov ChainLecture 34 - First Passage time and Mean Recurrence TimeLecture 35 - Recurrent State and Transient StateLecture 36 - Introduction and example of Classification of statesLecture 37 - Example of Classification of states (Continued...)Lecture 38 - Example of Classification of states (Continued...)Lecture 39 - Example of Classification of states (Continued...)Lecture 40 - Introduction and Limiting DistributionLecture 41 - Example of Limiting Distribution and ErgodicityLecture 42 - Stationary Distribution and ExamplesLecture 43 - Examples of Stationary DistributionsLecture 44 - Time Reversible Markov Chain and ExamplesLecture 45 - Definition of Reducible Markov Chains and Types of Reducible Markov ChainsLecture 46 - Stationary Distributions and Types of Reducible Markov chainsLecture 47 - Type of Reducible Markov Chains (Continued...)Lecture 48 - Gambler's Ruin ProblemLecture 49 - Introduction to Continuous time Markov ChainLecture 50 - Waiting time DistributionLecture 51 - Chapman-Kolmogorov EquationLecture 52 - Infinitesimal Generator MatrixLecture 53 - Introduction and Example Of Continuous time Markov ChainLecture 54 - Limiting and Stationary DistributionsLecture 55 - Time reversible CTMC and Birth Death ProcessLecture 56 - Steady State Distributions, Pure Birth Process and Pure Death ProcessLecture 57 - Introduction to Poisson ProcessLecture 58 - Definition of Poisson ProcessLecture 59 - Superposition and Deposition of Poisson ProcessLecture 60 - Compound Poisson Process and ExamplesLecture 61 - Introduction to Queueing Systems and Kendall NotationsLecture 62 - M/M/1 Queueing ModelLecture 63 - Little's Law, Distribution of Waiting Time and Response TimeLecture 64 - Burke's Theorem and Simulation of M/M/1 queueing ModelLecture 65 - M/M/c Queueing ModelLecture 66 - M/M/1/N Queueing ModelLecture 67 - M/M/c/K Model, M/M/c/c Loss System, M/M/? Self Service SystemLecture 68 - Transient Solution of Finite Birth Death Process and Finite Source Markovian Queueing Model

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Lecture 69 - Queueing Networks Characteristics and Types of Queueing NetworksLecture 70 - Tandem Queueing NetworksLecture 71 - Stationary Distribution and Open Queueing NetworkLecture 72 - Jackson's Theorem, Closed Queueing Networks, Gordon and Newell ResultsLecture 73 - Wireless Handoff Performance Model and System DescriptionLecture 74 - Description of 3G Cellular Networks and Queueing ModelLecture 75 - Simulation of Queueing SystemsLecture 76 - Definition and Basic Components of Petri Net and Reachability AnalysisLecture 77 - Arc Extensions in Petri Net, Stochastic Petri Nets and examples

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Page 22: NPTEL Video Lecture Topic List - Created by LinuXpert ... · NPTEL Video Course - Mathematics - Measure and Integration Subject Co-ordinator - Prof. Inder K Rana Co-ordinating Institute

NPTEL Video Course - Mathematics - NOC:Stochastic Processes

Subject Co-ordinator - Dr. S. Dharmaraja

Co-ordinating Institute - IIT - Delhi

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Introduction and motivation for studying stochastic processesLecture 2 - Probability space and conditional probabilityLecture 3 - Random variable and cumulative distributive functionLecture 4 - Discrete Uniform Distribution, Binomial Distribution, Geometric Distribution, Continuous Uniform Distribution, Exponential Distribution, Normal Distribution and Poisson DistributionLecture 5 - Joint Distribution of Random VariablesLecture 6 - Independent Random Variables, Covariance and Correlation Coefficient and Conditional DistributionLecture 7 - Conditional Expectation and Covariance MatrixLecture 8 - Generating Functions, Law of Large Numbers and Central Limit TheoremLecture 9 - Problems in Random variables and DistributionsLecture 10 - Problems in Random variables and Distributions (Continued...)Lecture 11 - Problems in Random variables and Distributions (Continued...)Lecture 12 - Problems in Random variables and Distributions (Continued...)Lecture 13 - Problems in Sequences of Random VariablesLecture 14 - Problems in Sequences of Random Variables (Continued...)Lecture 15 - Problems in Sequences of Random Variables (Continued...)Lecture 16 - Problems in Sequences of Random Variables (Continued...)Lecture 17 - Definition of Stochastic Processes, Parameter and State SpacesLecture 18 - Classification of Stochastic ProcessesLecture 19 - Examples of Classification of Stochastic ProcessesLecture 20 - Examples of Classification of Stochastic Processes (Continued...)Lecture 21 - Bernoulli ProcessLecture 22 - Poisson ProcessLecture 23 - Poisson Process (Continued...)Lecture 24 - Simple Random Walk and Population ProcessesLecture 25 - Introduction to Discrete time Markov ChainLecture 26 - Introduction to Discrete time Markov Chain (Continued...)Lecture 27 - Examples of Discrete time Markov ChainLecture 28 - Examples of Discrete time Markov Chain (Continued...)Lecture 29 - Introduction to Chapman-Kolmogorov equations

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Page 23: NPTEL Video Lecture Topic List - Created by LinuXpert ... · NPTEL Video Course - Mathematics - Measure and Integration Subject Co-ordinator - Prof. Inder K Rana Co-ordinating Institute

Lecture 30 - State Transition Diagram and ExamplesLecture 31 - ExamplesLecture 32 - Introduction to Classification of States and PeriodicityLecture 33 - Closed set of States and Irreducible Markov ChainLecture 34 - First Passage time and Mean Recurrence TimeLecture 35 - Recurrent State and Transient StateLecture 36 - Introduction and example of Classification of statesLecture 37 - Example of Classification of states (Continued...)Lecture 38 - Example of Classification of states (Continued...)Lecture 39 - Example of Classification of states (Continued...)Lecture 40 - Introduction and Limiting DistributionLecture 41 - Example of Limiting Distribution and ErgodicityLecture 42 - Stationary Distribution and ExamplesLecture 43 - Examples of Stationary DistributionsLecture 44 - Time Reversible Markov Chain and ExamplesLecture 45 - Definition of Reducible Markov Chains and Types of Reducible Markov ChainsLecture 46 - Stationary Distributions and Types of Reducible Markov chainsLecture 47 - Type of Reducible Markov Chains (Continued...)Lecture 48 - Gambler's Ruin ProblemLecture 49 - Introduction to Continuous time Markov ChainLecture 50 - Waiting time DistributionLecture 51 - Chapman-Kolmogorov EquationLecture 52 - Infinitesimal Generator MatrixLecture 53 - Introduction and Example Of Continuous time Markov ChainLecture 54 - Limiting and Stationary DistributionsLecture 55 - Time reversible CTMC and Birth Death ProcessLecture 56 - Steady State Distributions, Pure Birth Process and Pure Death ProcessLecture 57 - Introduction to Poisson ProcessLecture 58 - Definition of Poisson ProcessLecture 59 - Superposition and Deposition of Poisson ProcessLecture 60 - Compound Poisson Process and ExamplesLecture 61 - Introduction to Queueing Systems and Kendall NotationsLecture 62 - M/M/1 Queueing ModelLecture 63 - Little's Law, Distribution of Waiting Time and Response TimeLecture 64 - Burke's Theorem and Simulation of M/M/1 queueing ModelLecture 65 - M/M/c Queueing ModelLecture 66 - M/M/1/N Queueing ModelLecture 67 - M/M/c/K Model, M/M/c/c Loss System, M/M/? Self Service SystemLecture 68 - Transient Solution of Finite Birth Death Process and Finite Source Markovian Queueing Model

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Lecture 69 - Queueing Networks Characteristics and Types of Queueing NetworksLecture 70 - Tandem Queueing NetworksLecture 71 - Stationary Distribution and Open Queueing NetworkLecture 72 - Jackson's Theorem, Closed Queueing Networks, Gordon and Newell ResultsLecture 73 - Wireless Handoff Performance Model and System DescriptionLecture 74 - Description of 3G Cellular Networks and Queueing ModelLecture 75 - Simulation of Queueing SystemsLecture 76 - Definition and Basic Components of Petri Net and Reachability AnalysisLecture 77 - Arc Extensions in Petri Net, Stochastic Petri Nets and examplesLecture 78 - Generalized Stochastic Petri NetLecture 79 - Generalized Stochastic Petri Net (Continued...)Lecture 80 - Conditional Expectation and ExamplesLecture 81 - Filtration in Discrete timeLecture 82 - Remarks of Conditional Expectation and AdaptabiltyLecture 83 - Definition and Examples of MartingaleLecture 84 - Examples of Martingale (Continued...)Lecture 85 - Examples of Martingale (Continued...)Lecture 86 - Doob's Martingale Process, Sub martingale and Super MartingaleLecture 87 - Definition of Brownian MotionLecture 88 - Definition of Brownian Motion (Continued...)Lecture 89 - Properties of Brownian MotionLecture 90 - Processes Derived from Brownian MotionLecture 91 - Processes Derived from Brownian Motion (Continued...)Lecture 92 - Processes Derived from Brownian Motion (Continued...)Lecture 93 - Stochastic Differential EquationsLecture 94 - Stochastic Differential Equations (Continued...)Lecture 95 - Stochastic Differential Equations (Continued...)Lecture 96 - Ito IntegralsLecture 97 - Ito Integrals (Continued...)Lecture 98 - Ito Integrals (Continued...)Lecture 99 - Renewal Function and Renewal EquationLecture 100 - Renewal Function and Renewal Equation (Continued...)Lecture 101 - Renewal Function and Renewal Equation (Continued...)Lecture 102 - Generalized Renewal Processes and Renewal Limit TheoremsLecture 103 - Generalized Renewal Processes and Renewal Limit Theorems (Continued...)Lecture 104 - Generalized Renewal Processes and Renewal Limit Theorems (Continued...)Lecture 105 - Markov Renewal and Markov Regenerative ProcessesLecture 106 - Markov Renewal and Markov Regenerative Processes (Continued...)Lecture 107 - Markov Renewal and Markov Regenerative Processes (Continued...)

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Lecture 108 - Markov Renewal and Markov Regenerative Processes (Continued...)Lecture 109 - Non Markovian QueuesLecture 110 - Non Markovian Queues (Continued...)Lecture 111 - Non Markovian Queues (Continued...)Lecture 112 - Stationary ProcessesLecture 113 - Stationary Processes (Continued...)Lecture 114 - Stationary Processes (Continued...)Lecture 115 - Stationary Processes (Continued...) and ErgodicityLecture 116 - G1/M/1 queueLecture 117 - G1/M/1 queue (Continued...)Lecture 118 - G1/M/1/N queue and examplesLecture 119 - Galton-Watson ProcessLecture 120 - Examples and TheoremsLecture 121 - Theorems and Examples (Continued...)Lecture 122 - Markov Branching ProcessLecture 123 - Markov Branching Process Theorems and PropertiesLecture 124 - Markov Branching Process Theorems and Properties (Continued...)

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NPTEL Video Course - Mathematics - NOC:Chaotic Dynamical Systems

Subject Co-ordinator - Dr. Anima Nagar

Co-ordinating Institute - IIT - Delhi

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - The beginningLecture 2 - Elementary ConceptsLecture 3 - Elementary Concepts (Continued...)Lecture 4 - More on orbitsLecture 5 - Peiods of Periodic PointsLecture 6 - Scrambled SetsLecture 7 - Sensitive Dependence on Initial ConditionsLecture 8 - A Population Dynamics ModelLecture 9 - BifurcationsLecture 10 - Nonlinear SystemsLecture 11 - Horseshoe AttractorLecture 12 - Dynamics of the Horseshoe AttractorLecture 13 - RecurrenceLecture 14 - Recurrence (Continued...)Lecture 15 - TransitivityLecture 16 - Devaney�s ChaosLecture 17 - Transitivity = Chaos on IntervalsLecture 18 - Stronger forms of TransitivityLecture 19 - Chaotic Properties of Mixing SystemsLecture 20 - Weakly Mixing and ChaosLecture 21 - Strongly Transitive SystemsLecture 22 - Strongly Transitive Systems (Continued...)Lecture 23 - Introduction to Symbolic DynamicsLecture 24 - Shift SpacesLecture 25 - Subshifts of Finite TypeLecture 26 - Subshifts of Finite Type (Continued...), Chatoic Dynamical SystemsLecture 27 - Measuring Chaos - Topological EntropyLecture 28 - Topological Entropy - Adler�s VersionLecture 29 - Bowen�s Definition of Topological Entropy

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Lecture 30 - Equivalance of the two definitions of Topological EntropyLecture 31 - Linear Systems in Two DimentionsLecture 32 - Asymptotic Properties of Orbits of Linear Transformation in IR2Lecture 33 - Hyperbolic Toral AutomorphismsLecture 34 - Chaos in Toral AutomorphismsLecture 35 - Chaotic Attractors of Henon Maps

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NPTEL Video Course - Mathematics - NOC:Introduction to Probability Theory and Stochastic Processes

Subject Co-ordinator - Dr. S. Dharmaraja

Co-ordinating Institute - IIT - Delhi

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Random experiment, sample space, axioms of probability, probability spaceLecture 2 - Random experiment, sample space, axioms of probability, probability space (Continued...)Lecture 3 - Random experiment, sample space, axioms of probability, probability space (Continued...)Lecture 4 - Conditional probability, independence of events.Lecture 5 - Multiplication rule, total probability rule, Bayes's theorem.Lecture 6 - Definition of Random Variable, Cumulative Distribution FunctionLecture 7 - Definition of Random Variable, Cumulative Distribution Function (Continued...)Lecture 8 - Definition of Random Variable, Cumulative Distribution Function (Continued...)Lecture 9 - Type of Random Variables, Probability Mass Function, Probability Density FunctionLecture 10 - Type of Random Variables, Probability Mass Function, Probability Density Function (Continued...)Lecture 11 - Distribution of Function of Random VariablesLecture 12 - Mean and VarianceLecture 13 - Mean and Variance (Continued...)Lecture 14 - Higher Order Moments and Moments InequalitiesLecture 15 - Higher Order Moments and Moments Inequalities (Continued...)Lecture 16 - Generating FunctionsLecture 17 - Generating Functions (Continued...)Lecture 18 - Common Discrete DistributionsLecture 19 - Common Discrete Distributions (Continued...)Lecture 20 - Common Continuous DistributionsLecture 21 - Common Continuous Distributions (Continued...)Lecture 22 - Applications of Random VariableLecture 23 - Applications of Random Variable (Continued...)Lecture 24 - Random vector and joint distributionLecture 25 - Joint probability mass functionLecture 26 - Joint probability density functionLecture 27 - Independent random variablesLecture 28 - Independent random variables (Continued...)Lecture 29 - Functions of several random variables

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Lecture 30 - Functions of several random variables (Continued...)Lecture 31 - Some important resultsLecture 32 - Order statisticsLecture 33 - Conditional distributionsLecture 34 - Random sumLecture 35 - Moments and CovarianceLecture 36 - Variance Covariance matrixLecture 37 - Multivariate Normal distributionLecture 38 - Probability generating function and Moment generating functionLecture 39 - Correlation coefficientLecture 40 - Conditional ExpectationLecture 41 - Conditional Expectation (Continued...)Lecture 42 - Modes of ConvergenceLecture 43 - Mode of Convergence (Continued...)Lecture 44 - Law of Large NumbersLecture 45 - Central Limit TheoremLecture 46 - Central Limit Theorem (Continued...)Lecture 47 - Motivation for Stochastic ProcessesLecture 48 - Definition of a Stochastic ProcessLecture 49 - Classification of Stochastic ProcessesLecture 50 - Examples of Stochastic ProcessLecture 51 - Examples Of Stochastic Process (Continued...)Lecture 52 - Bernoulli ProcessLecture 53 - Poisson ProcessLecture 54 - Poisson Process (Continued...)Lecture 55 - Simple Random WalkLecture 56 - Time Series and Related DefinitionsLecture 57 - Strict Sense Stationary ProcessLecture 58 - Wide Sense Stationary Process and ExamplesLecture 59 - Examples of Stationary Processes (Continued...)Lecture 60 - Discrete Time Markov Chain (DTMC)Lecture 61 - DTMC (Continued...)Lecture 62 - Examples of DTMCLecture 63 - Examples of DTMC (Continued...)Lecture 64 - Chapman-Kolmogorov equations and N-step transition matrixLecture 65 - Examples based on N-step transition matrixLecture 66 - Examples (Continued...)Lecture 67 - Classification of statesLecture 68 - Classification of states (Continued...)

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Lecture 69 - Calculation of N-Step - 9Lecture 70 - Calculation of N-Step - 10Lecture 71 - Limiting and Stationary distributionsLecture 72 - Limiting and Stationary distributions (Continued...)Lecture 73 - Continuous time Markov chain (CTMC)Lecture 74 - CTMC (Continued...)Lecture 75 - State transition diagram and Chapman-Kolmogorov equationLecture 76 - Infinitesimal generator and Kolmogorov differential equationsLecture 77 - Limiting distributionLecture 78 - Limiting and Stationary distributions - 1Lecture 79 - Birth death processLecture 80 - Birth death process (Continued...)Lecture 81 - Poisson process - 1Lecture 82 - Poisson process (Continued...)Lecture 83 - Poisson process (Continued...)Lecture 84 - Non-homogeneous and compound Poisson processLecture 85 - Introduction to Queueing Models and Kendall NotationLecture 86 - M/M/1 Queueing ModelLecture 87 - M/M/1 Queueing Model (Continued...)Lecture 88 - M/M/1 Queueing Model and Burke's TheoremLecture 89 - M/M/c Queueing ModelLecture 90 - M/M/c (Continued...) and M/M/1/N ModelLecture 91 - Other Markovian Queueing ModelsLecture 92 - Transient Solution of Finite Capacity Markovian Queues

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NPTEL Video Course - Mathematics - NOC:Statistical Inference

Subject Co-ordinator - Prof. Nilladri Chaterjee

Co-ordinating Institute - IIT - Delhi

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Statistical Inference - 1Lecture 2 - Statistical Inference - 2Lecture 3 - Statistical Inference - 3Lecture 4 - Statistical Inference - 4Lecture 5 - Statistical Inference - 5Lecture 6 - Statistical Inference - 6Lecture 7 - Statistical Inference - 7Lecture 8 - Statistical Inference - 8Lecture 9 - Statistical Inference - 9Lecture 10 - Statistical Inference - 10Lecture 11 - Statistical Inference - 11Lecture 12 - Statistical Inference - 12Lecture 13 - Statistical Inference - 13Lecture 14 - Statistical Inference - 14Lecture 15 - Statistical Inference - 15Lecture 16 - Stasistical Inference - 16Lecture 17 - Stasistical Inference - 17Lecture 18 - Statistical Inference - 18Lecture 19 - Stasistical Inference - 19Lecture 20 - Stasistical Inference - 20Lecture 21 - Stasistical Inference - 21

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NPTEL Video Course - Mathematics - NOC:Integral Transforms and their Applications

Subject Co-ordinator - Prof. Sarthok Sircar

Co-ordinating Institute - IIT - Delhi

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Introduction to Fourier Transforms - Part 1Lecture 2 - Introduction to Fourier Transforms - Part 2Lecture 3 - Introduction to Fourier Transforms - Part 3Lecture 4 - Properties of Fourier transforms, Shannon Sampling Theorem, Gibb's Phenomena - Part 1Lecture 5 - Properties of Fourier transforms, Shannon Sampling Theorem, Gibb's Phenomena - Part 2Lecture 6 - Properties of Fourier transforms, Shannon Sampling Theorem, Gibb's Phenomena - Part 3Lecture 7 - Applications of Fourier Transforms - Part 1Lecture 8 - Applications of Fourier Transforms - Part 2Lecture 9 - Applications of Fourier Transforms - Part 3Lecture 10 - Introduction to Laplace Transforms - Part 1Lecture 11 - Introduction to Laplace Transforms - Part 2Lecture 12 - Introduction to Laplace Transforms - Part 3Lecture 13 - Inverse Laplace Transform, Initial and Final Value Theorems - Part 1Lecture 14 - Inverse Laplace Transform, Initial and Final Value Theorems - Part 2Lecture 15 - Inverse Laplace Transform, Initial and Final Value Theorems - Part 3Lecture 16 - Applications of Laplace Transforms - Part 1Lecture 17 - Applications of Laplace Transforms - Part 2Lecture 18 - Applications of Laplace Transforms - Part 3Lecture 19 - Applications of Laplace Transforms (Continued) - Part 1Lecture 20 - Applications of Laplace Transforms (Continued) - Part 2Lecture 21 - Applications of Laplace Transforms (Continued) - Part 3Lecture 22 - Applications of Fourier-Laplace Transforms - Part 1Lecture 23 - Applications of Fourier-Laplace Transforms - Part 2Lecture 24 - Applications of Fourier-Laplace Transforms - Part 3Lecture 25 - Introduction to Hankel Transforms - Part 1Lecture 26 - Introduction to Hankel Transforms - Part 2Lecture 27 - Introduction to Hankel Transforms - Part 3Lecture 28 - Introduction to Mellin Transforms - Part 1Lecture 29 - Introduction to Mellin Transforms - Part 2

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Lecture 30 - Introduction to Mellin Transforms - Part 3Lecture 31 - Introduction to Hilbert Transforms - Part 1Lecture 32 - Introduction to Hilbert Transforms - Part 2Lecture 33 - Introduction to Hilbert Transforms - Part 3Lecture 34 - Applications of Hilbert Transfroms, Introduction to Stieltjes Transform - Part 1Lecture 35 - Applications of Hilbert Transfroms, Introduction to Stieltjes Transform - Part 2Lecture 36 - Applications of Hilbert Transfroms, Introduction to Stieltjes Transform - Part 3Lecture 37 - Applications of Stieltjes Transform, Generalized Stieltjes Transform - Part 1Lecture 38 - Applications of Stieltjes Transform, Generalized Stieltjes Transform - Part 2Lecture 39 - Applications of Stieltjes Transform, Generalized Stieltjes Transform - Part 3Lecture 40 - Introduction to Legendre Transform - Part 1Lecture 41 - Introduction to Legendre Transform - Part 2Lecture 42 - Introduction to Legendre Transform - Part 3Lecture 43 - Introduction to Z-transform - Part 1Lecture 44 - Introduction to Z-transform - Part 2Lecture 45 - Introduction to Z-transform - Part 3Lecture 46 - Inverse Z-transfrom, Applciations of Z-Transform - Part 1Lecture 47 - Inverse Z-transfrom, Applciations of Z-Transform - Part 2Lecture 48 - Inverse Z-transfrom, Applciations of Z-Transform - Part 3Lecture 49 - Introduction to Radon Transform - Part 1Lecture 50 - Introduction to Radon Transform - Part 2Lecture 51 - Introduction to Radon Transform - Part 3Lecture 52 - Inverse Radon Transform, Applications to Radon Transform - Part 1Lecture 53 - Inverse Radon Transform, Applications to Radon Transform - Part 2Lecture 54 - Inverse Radon Transform, Applications to Radon Transform - Part 3Lecture 55 - Introduction to Fractional Calculus - Part 1Lecture 56 - Introduction to Fractional Calculus - Part 2Lecture 57 - Introduction to Fractional Calculus - Part 3Lecture 58 - Fractional ODEs, Abel's Integral Equations - Part 1Lecture 59 - Fractional ODEs, Abel's Integral Equations - Part 2Lecture 60 - Fractional ODEs, Abel's Integral Equations - Part 3Lecture 61 - Fractional PDEs - Part 1Lecture 62 - Fractional PDEs - Part 2Lecture 63 - Fractional PDEs - Part 3Lecture 64 - Fractional ODEs and PDEs (Continued) - Part 1Lecture 65 - Fractional ODEs and PDEs (Continued) - Part 2Lecture 66 - Fractional ODEs and PDEs (Continued) - Part 3Lecture 67 - Introduction to Wavelet Transform - Part 1Lecture 68 - Introduction to Wavelet Transform - Part 2

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Lecture 69 - Introduction to Wavelet Transform - Part 3Lecture 70 - Discrete Haar, Shanon and Debauchies Wavelet - Part 1Lecture 71 - Discrete Haar, Shanon and Debauchies Wavelet - Part 2Lecture 72 - Discrete Haar, Shanon and Debauchies Wavelet - Part 3

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NPTEL Video Course - Mathematics - NOC:Introduction to Fuzzy Set Theory, Arithmetic and Logic

Subject Co-ordinator - Prof. Nilladri Chaterjee

Co-ordinating Institute - IIT - Delhi

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Fuzzy Sets Arithmetic and Logic - 1Lecture 2 - Fuzzy Sets Arithmetic and Logic - 2Lecture 3 - Fuzzy Sets Arithmetic and Logic - 3Lecture 4 - Fuzzy Sets Arithmetic and Logic - 4Lecture 5 - Fuzzy Sets Arithmetic and Logic - 5Lecture 6 - Fuzzy Sets Arithmetic and Logic - 6Lecture 7 - Fuzzy Sets Arithmetic and Logic - 7Lecture 8 - Fuzzy Sets Arithmetic and Logic - 8Lecture 9 - Fuzzy Sets Arithmetic and Logic - 9Lecture 10 - Fuzzy Sets Arithmetic and Logic - 10Lecture 11 - Fuzzy Sets Arithmetic and Logic - 11Lecture 12 - Fuzzy Sets Arithmetic and Logic - 12Lecture 13 - Fuzzy Sets Arithmetic and Logic - 13Lecture 14 - Fuzzy Sets Arithmetic and Logic - 14Lecture 15 - Fuzzy Sets Arithmetic and Logic - 15Lecture 16 - Fuzzy Sets Arithmetic and Logic - 16Lecture 17 - Fuzzy Sets Arithmetic and Logic - 17Lecture 18 - Fuzzy Sets Arithmetic and Logic - 18Lecture 19 - Fuzzy Sets Arithmetic and Logic - 19Lecture 20 - Fuzzy Sets Arithmetic and Logic - 20Lecture 21 - Fuzzy Sets Arithmetic and Logic - 21Lecture 22 - Fuzzy Sets Arithmetic and Logic - 22Lecture 23 - Fuzzy Sets Arithmetic and Logic - 23Lecture 24 - Fuzzy Sets Arithmetic and Logic - 24Lecture 25 - Fuzzy Sets Arithmetic and Logic - 25Lecture 26 - Fuzzy Sets Arithmetic and Logic - 26Lecture 27 - Fuzzy Sets Arithmetic and Logic - 27Lecture 28 - Fuzzy Sets Arithmetic and Logic - 28Lecture 29 - Fuzzy Sets Arithmetic and Logic - 29

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Lecture 30 - Fuzzy Sets Arithmetic and Logic - 30

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NPTEL Video Course - Mathematics - NOC:Introduction to Methods of Applied Mathematics

Subject Co-ordinator - Prof. Vivek Kumar Aggarwal

Co-ordinating Institute - IIT - Delhi

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Introduction to First Order Differential EquationsLecture 2 - Introduction to First Order Differential Equations (Continued...)Lecture 3 - Introduction to Second Order Linear Differential EquationsLecture 4 - Second Order Linear Differential Equations With Constant CoefficientsLecture 5 - Second Order Linear Differential Equations With Constant Coefficients (Continued...)Lecture 6 - Second Order Linear Differential Equations With Variable CoefficientsLecture 7 - Factorization of Second order Differential Operator and Euler Cauchy EquationLecture 8 - Power Series Solution of General Differential EquationLecture 9 - Green's functionLecture 10 - Method of Green's Function for Solving Initial Value and Boundary Value ProblemsLecture 11 - Adjoint Linear Differential OperatorLecture 12 - Adjoint Linear Differential Operator (Continued...)Lecture 13 - Sturm-Liouvile ProblemsLecture 14 - Laplace transformationLecture 15 - Laplace transformation (Continued...)Lecture 16 - Laplace Transform Method for Solving Ordinary Differential EquationsLecture 17 - Laplace Transform Applied to Differential Equations and ConvolutionLecture 18 - Fourier SeriesLecture 19 - Fourier Series (Continued...)Lecture 20 - Gibbs Phenomenon and Parseval's IdentityLecture 21 - Fourier Integral and Fourier TransformLecture 22 - Fourier Integral and Fourier Transform (Continued...)Lecture 23 - Fourier Transform Method for Solving Ordinary Differential EquationsLecture 24 - Frames, Riesz Bases and Orthonormal BasesLecture 25 - Frames, Riesz Bases and Orthonormal Bases (Continued...)Lecture 26 - Fourier Series and Fourier TransformLecture 27 - Time-Frequency Analysis and Gabor TransformLecture 28 - Window Fourier Transform and Multiresolution AnalysisLecture 29 - Construction of Scaling Functions and Wavelets Using Multiresolution Analysis

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Lecture 30 - Daubechies WaveletLecture 31 - Daubechies Wavelet (Continued...)Lecture 32 - Wavelet Transform and Shannon Wavelet

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NPTEL Video Course - Mathematics - Formal Languages and Automata Theory

Subject Co-ordinator - Dr. K.V. Krishna, Dr. Diganta Goswami

Co-ordinating Institute - IIT - Guwahati

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - IntroductionLecture 2 - Alphabet, Strings, LanguagesLecture 3 - Finite RepresentationLecture 4 - Grammars (CFG)Lecture 5 - Derivation TreesLecture 6 - Regular GrammarsLecture 7 - Finite AutomataLecture 8 - Nondeterministic Finite AutomataLecture 9 - NFA <=> DFALecture 10 - Myhill-Nerode TheoremLecture 11 - MinimizationLecture 12 - RE => FALecture 13 - FA => RELecture 14 - FA <=> RGLecture 15 - Variants of FALecture 16 - Closure Properties of RLLecture 17 - HomomorphismLecture 18 - Pumping LemmaLecture 19 - Simplification of CFGLecture 20 - Normal Forms of CFGLecture 21 - Properties of CFLsLecture 22 - Pushdown AutomataLecture 23 - PDA <=> CFGLecture 24 - Turing MachinesLecture 25 - Turing Computable FunctionsLecture 26 - Combining Turing MachinesLecture 27 - Multi InputLecture 28 - Turing Decidable LanguagesLecture 29 - Varients of Turing Machines

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Lecture 30 - Structured GrammarsLecture 31 - DecidabilityLecture 32 - Undecidability 1Lecture 33 - Undecidability 2Lecture 34 - Undecidability 3Lecture 35 - Time Bounded Turing MachinesLecture 36 - P and NPLecture 37 - NP-CompletenessLecture 38 - NP-Complete Problems 1Lecture 39 - NP-Complete Problems 2Lecture 40 - NP-Complete Problems 3Lecture 41 - Chomsky Hierarchy

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NPTEL Video Course - Mathematics - Complex Analysis

Subject Co-ordinator - Prof. P.A.S. Sree Krishna

Co-ordinating Institute - IIT - Guwahati

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - IntroductionLecture 2 - Introduction to Complex NumbersLecture 3 - de Moivre�s Formula and Stereographic ProjectionLecture 4 - Topology of the Complex Plane - Part-ILecture 5 - Topology of the Complex Plane - Part-IILecture 6 - Topology of the Complex Plane - Part-IIILecture 7 - Introduction to Complex FunctionsLecture 8 - Limits and ContinuityLecture 9 - DifferentiationLecture 10 - Cauchy-Riemann Equations and DifferentiabilityLecture 11 - Analytic functions; the exponential functionLecture 12 - Sine, Cosine and Harmonic functionsLecture 13 - Branches of Multifunctions; Hyperbolic FunctionsLecture 14 - Problem Solving Session ILecture 15 - Integration and ContoursLecture 16 - Contour IntegrationLecture 17 - Introduction to Cauchy�s TheoremLecture 18 - Cauchy�s Theorem for a RectangleLecture 19 - Cauchy�s theorem - Part-IILecture 20 - Cauchy�s Theorem - Part-IIILecture 21 - Cauchy�s Integral Formula and its ConsequencesLecture 22 - The First and Second Derivatives of Analytic FunctionsLecture 23 - Morera�s Theorem and Higher Order Derivatives of Analytic FunctionsLecture 24 - Problem Solving Session IILecture 25 - Introduction to Complex Power SeriesLecture 26 - Analyticity of Power SeriesLecture 27 - Taylor�s TheoremLecture 28 - Zeroes of Analytic FunctionsLecture 29 - Counting the Zeroes of Analytic Functions

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Lecture 30 - Open mapping theorem - Part-ILecture 31 - Open mapping theorem - Part-IILecture 32 - Properties of Mobius Transformations - Part-ILecture 33 - Properties of Mobius Transformations - Part-IILecture 34 - Problem Solving Session IIILecture 35 - Removable SingularitiesLecture 36 - Poles Classification of Isolated SingularitiesLecture 37 - Essential Singularity & Introduction to Laurent SeriesLecture 38 - Laurent�s TheoremLecture 39 - Residue Theorem and ApplicationsLecture 40 - Problem Solving Session IV

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NPTEL Video Course - Mathematics - NOC:Mathematical Finance

Subject Co-ordinator - Prof. Siddhartha Pratim Chakrabarty

Co-ordinating Institute - IIT - Guwahati

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Introduction to Financial Markets and BondsLecture 2 - Introduction to Stocks, Futures and Forwards and SwapsLecture 3 - Introduction to OptionsLecture 4 - Interest Rates and Present ValueLecture 5 - Present and Future Values, Annuities, Amortization and Bond YieldLecture 6 - Price Yield Curve and Term Structure of Interest RatesLecture 7 - Markowitz Theory, Return and Risk and Two Asset PortfolioLecture 8 - Minimum Variance Portfolio and Feasible SetLecture 9 - Multi Asset Portfolio, Minimum Variance Portfolio, Efficient Frontier and Minimum Variance LineLecture 10 - Minimum Variance Line (Continued), Market PortfolioLecture 11 - Capital Market Line, Capital Asset Pricing ModelLecture 12 - Performance AnalysisLecture 13 - No-Arbitrage Principle and Pricing of Forward ContractsLecture 14 - Futures, Options and Put-Call-ParityLecture 15 - Bounds on OptionsLecture 16 - Derivative Pricing in a Single Period Binomial ModelLecture 17 - Derivative Pricing in Multiperiod Binomial ModelLecture 18 - Derivative Pricing in Binomial Model and Path Dependent OptionsLecture 19 - Discrete Probability SpacesLecture 20 - Filtrations and Conditional ExpectationsLecture 21 - Properties of Conditional ExpectationsLecture 22 - Examples of Conditional Expectations, MartingalesLecture 23 - Risk-Neutral Pricing of European Derivatives in Binomial ModelLecture 24 - Actual and Risk-Neutral Probabilities, Markov Process, American OptionsLecture 25 - General Probability Spaces, Expectations, Change of MeasureLecture 26 - Filtrations, Independence, Conditional ExpectationsLecture 27 - Brownian Motion and its PropertiesLecture 28 - Itô Integral and its PropertiesLecture 29 - Itô Formula, Itô Processes

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Lecture 30 - Multivariable Stochastic Calculus, Stochastic Differential EquationsLecture 31 - Black-Scholes-Merton (BSM) Model, BSM Equation, BSM FormulaLecture 32 - Greeks, Put-Call Parity, Change of MeasureLecture 33 - Girsanov Theorem, Risk-Neutral Pricing of Derivatives, BSM FormulaLecture 34 - MRT and Hedging, Multidimensional Girsanov and MRTLecture 35 - Multidimensional BSM Model, Fundamental Theorems of Asset PricingLecture 36 - BSM Model with Dividend-Paying Stocks

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NPTEL Video Course - Mathematics - Applied Multivariate Analysis

Subject Co-ordinator - Dr. Sharmishtha Mitra

Co-ordinating Institute - IIT - Kanpur

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - PrologueLecture 2 - Basic concepts on multivariate distributionLecture 3 - Basic concepts on multivariate distributionLecture 4 - Multivariate normal distribution � ILecture 5 - Multivariate normal distribution � IILecture 6 - Multivariate normal distribution � IIILecture 7 - Some problems on multivariate distributions � ILecture 8 - Some problems on multivariate distributions � IILecture 9 - Random sampling from multivariate normal distribution and Wishart distribution - ILecture 10 - Random sampling from multivariate normal distribution and Wishart distribution - IILecture 11 - Random sampling from multivariate normal distribution and Wishart distribution - IIILecture 12 - Wishart distribution and it�s properties - ILecture 13 - Wishart distribution and it�s properties - IILecture 14 - Hotelling�s T2 distribution and it�s applicationsLecture 15 - Hotelling�s T2 distribution and various confidence intervals and regionsLecture 16 - Hotelling�s T2 distribution and Profile analysisLecture 17 - Profile analysis - ILecture 18 - Profile analysis - IILecture 19 - MANOVA - ILecture 20 - MANOVA - IILecture 21 - MANOVA - IIILecture 22 - MANOVA & Multiple Correlation CoefficientLecture 23 - Multiple Correlation CoefficientLecture 24 - Principal Component AnalysisLecture 25 - Principal Component AnalysisLecture 26 - Principal Component AnalysisLecture 27 - Cluster AnalysisLecture 28 - Cluster AnalysisLecture 29 - Cluster Analysis

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Lecture 30 - Cluster AnalysisLecture 31 - Discriminant Analysis and ClassificationLecture 32 - Discriminant Analysis and ClassificationLecture 33 - Discriminant Analysis and ClassificationLecture 34 - Discriminant Analysis and ClassificationLecture 35 - Discriminant Analysis and ClassificationLecture 36 - Discriminant Analysis and ClassificationLecture 37 - Discriminant Analysis and ClassificationLecture 38 - Factor_AnalysisLecture 39 - Factor_AnalysisLecture 40 - Factor_AnalysisLecture 41 - Cannonical Correlation AnalysisLecture 42 - Cannonical Correlation AnalysisLecture 43 - Cannonical Correlation AnalysisLecture 44 - Cannonical Correlation Analysis

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NPTEL Video Course - Mathematics - Calculus of Variations and Integral Equations

Subject Co-ordinator - Dr. Malay Banerjee, Prof. D. Bahuguna

Co-ordinating Institute - IIT - Kanpur

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Calculus of Variations and Integral EquationsLecture 2 - Calculus of Variations and Integral EquationsLecture 3 - Calculus of Variations and Integral EquationsLecture 4 - Calculus of Variations and Integral EquationsLecture 5 - Calculus of Variations and Integral EquationsLecture 6 - Calculus of Variations and Integral EquationsLecture 7 - Calculus of Variations and Integral EquationsLecture 8 - Calculus of Variations and Integral EquationsLecture 9 - Calculus of Variations and Integral EquationsLecture 10 - Calculus of Variations and Integral EquationsLecture 11 - Calculus of Variations and Integral EquationsLecture 12 - Calculus of Variations and Integral EquationsLecture 13 - Calculus of Variations and Integral EquationsLecture 14 - Calculus of Variations and Integral EquationsLecture 15 - Calculus of Variations and Integral EquationsLecture 16 - Calculus of Variations and Integral EquationsLecture 17 - Calculus of Variations and Integral EquationsLecture 18 - Calculus of Variations and Integral EquationsLecture 19 - Calculus of Variations and Integral EquationsLecture 20 - Calculus of Variations and Integral EquationsLecture 21 - Calculus of Variations and Integral EquationsLecture 22 - Calculus of Variations and Integral EquationsLecture 23 - Calculus of Variations and Integral EquationsLecture 24 - Calculus of Variations and Integral EquationsLecture 25 - Calculus of Variations and Integral EquationsLecture 26 - Calculus of Variations and Integral EquationsLecture 27 - Calculus of Variations and Integral EquationsLecture 28 - Calculus of Variations and Integral EquationsLecture 29 - Calculus of Variations and Integral Equations

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Lecture 30 - Calculus of Variations and Integral EquationsLecture 31 - Calculus of Variations and Integral EquationsLecture 32 - Calculus of Variations and Integral EquationsLecture 33 - Calculus of Variations and Integral EquationsLecture 34 - Calculus of Variations and Integral EquationsLecture 35 - Calculus of Variations and Integral EquationsLecture 36 - Calculus of Variations and Integral EquationsLecture 37 - Calculus of Variations and Integral EquationsLecture 38 - Calculus of Variations and Integral EquationsLecture 39 - Calculus of Variations and Integral EquationsLecture 40 - Calculus of Variations and Integral Equations

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NPTEL Video Course - Mathematics - Linear programming and Extensions

Subject Co-ordinator - Prof. Prabha Sharma

Co-ordinating Institute - IIT - Kanpur

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Introduction to Linear Programming ProblemsLecture 2 - Vector space, Linear independence and dependence, basisLecture 3 - Moving from one basic feasible solution to another, optimality criteriaLecture 4 - Basic feasible solutions, existence & derivationLecture 5 - Convex sets, dimension of a polyhedron, Faces, Example of a polytopeLecture 6 - Direction of a polyhedron, correspondence between bfs and extreme pointsLecture 7 - Representation theorem, LPP solution is a bfs, Assignment 1Lecture 8 - Development of the Simplex Algorithm, Unboundedness, Simplex TableauLecture 9 - Simplex Tableau & algorithm ,Cycling, Bland�s anti-cycling rules, Phase I & Phase IILecture 10 - Big-M method,Graphical solutions, adjacent extreme pts and adjacent bfsLecture 11 - Assignment 2, progress of Simplex algorithm on a polytope, bounded variable LPPLecture 12 - LPP Bounded variable, Revised Simplex algorithm, Duality theory, weak duality theoremLecture 13 - Weak duality theorem, economic interpretation of dual variables, Fundamental theorem of dualityLecture 14 - Examples of writing the dual, complementary slackness theoremLecture 15 - Complementary slackness conditions, Dual Simplex algorithm, Assignment 3Lecture 16 - Primal-dual algorithmLecture 17 - Problem in lecture 16, starting dual feasible solution, Shortest Path ProblemLecture 18 - Shortest Path Problem, Primal-dual method, exampleLecture 19 - Shortest Path Problem-complexity, interpretation of dual variables, post-optimality analysis-changes in the cost vectorLecture 20 - Assignment 4, postoptimality analysis, changes in b, adding a new constraint, changes in {aij} , Parametric analysisLecture 21 - Parametric LPP-Right hand side vectorLecture 22 - Parametric cost vector LPPLecture 23 - Parametric cost vector LPP, Introduction to Min-cost flow problemLecture 24 - Mini-cost flow problem-Transportation problemLecture 25 - Transportation problem degeneracy, cyclingLecture 26 - Sensitivity analysisLecture 27 - Sensitivity analysisLecture 28 - Bounded variable transportation problem, min-cost flow problemLecture 29 - Min-cost flow problem

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Lecture 30 - Starting feasible solution, Lexicographic method for preventing cycling ,strongly feasible solutionLecture 31 - Assignment 6, Shortest path problem, Shortest Path between any two nodes,Detection of negative cyclesLecture 32 - Min-cost-flow Sensitivity analysis Shortest path problem sensitivity analysisLecture 33 - Min-cost flow changes in arc capacities , Max-flow problem, assignment 7Lecture 34 - Problem 3 (assignment 7), Min-cut Max-flow theorem, Labelling algorithmLecture 35 - Max-flow - Critical capacity of an arc, starting solution for min-cost flow problemLecture 36 - Improved Max-flow algorithmLecture 37 - Critical Path Method (CPM)Lecture 38 - Programme Evaluation and Review Technique (PERT)Lecture 39 - Simplex Algorithm is not polynomial time- An exampleLecture 40 - Interior Point Methods

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NPTEL Video Course - Mathematics - Convex Optimization

Subject Co-ordinator - Dr. Joydeep Dutta

Co-ordinating Institute - IIT - Kanpur

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Convex OptimizationLecture 2 - Convex OptimizationLecture 3 - Convex OptimizationLecture 4 - Convex OptimizationLecture 5 - Convex OptimizationLecture 6 - Convex OptimizationLecture 7 - Convex OptimizationLecture 8 - Convex OptimizationLecture 9 - Convex OptimizationLecture 10 - Convex OptimizationLecture 11 - Convex OptimizationLecture 12 - Convex OptimizationLecture 13 - Convex OptimizationLecture 14 - Convex OptimizationLecture 15 - Convex OptimizationLecture 16 - Convex OptimizationLecture 17 - Convex OptimizationLecture 18 - Convex OptimizationLecture 19 - Convex OptimizationLecture 20 - Convex OptimizationLecture 21 - Convex OptimizationLecture 22 - Convex OptimizationLecture 23 - Convex OptimizationLecture 24 - Convex OptimizationLecture 25 - Convex OptimizationLecture 26 - Convex OptimizationLecture 27 - Convex OptimizationLecture 28 - Convex OptimizationLecture 29 - Convex Optimization

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Lecture 30 - Convex OptimizationLecture 31 - Convex OptimizationLecture 32 - Convex OptimizationLecture 33 - Convex OptimizationLecture 34 - Convex OptimizationLecture 35 - Convex OptimizationLecture 36 - Convex OptimizationLecture 37 - Convex OptimizationLecture 38 - Convex OptimizationLecture 39 - Convex OptimizationLecture 40 - Convex OptimizationLecture 41 - Convex OptimizationLecture 42 - Convex Optimization

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NPTEL Video Course - Mathematics - Foundations of Optimization

Subject Co-ordinator - Dr. Joydeep Dutta

Co-ordinating Institute - IIT - Kanpur

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - OptimizationLecture 2 - OptimizationLecture 3 - OptimizationLecture 4 - OptimizationLecture 5 - OptimizationLecture 6 - OptimizationLecture 7 - OptimizationLecture 8 - OptimizationLecture 9 - OptimizationLecture 10 - OptimizationLecture 11 - OptimizationLecture 12 - OptimizationLecture 13 - OptimizationLecture 14 - OptimizationLecture 15 - OptimizationLecture 16 - OptimizationLecture 17 - OptimizationLecture 18 - OptimizationLecture 19 - OptimizationLecture 20 - OptimizationLecture 21 - OptimizationLecture 22 - OptimizationLecture 23 - OptimizationLecture 24 - OptimizationLecture 25 - OptimizationLecture 26 - OptimizationLecture 27 - OptimizationLecture 28 - OptimizationLecture 29 - Optimization

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Lecture 30 - OptimizationLecture 31 - OptimizationLecture 32 - OptimizationLecture 33 - OptimizationLecture 34 - OptimizationLecture 35 - OptimizationLecture 36 - OptimizationLecture 37 - OptimizationLecture 38 - Optimization

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NPTEL Video Course - Mathematics - Probability Theory and Applications

Subject Co-ordinator - Prof. Prabha Sharma

Co-ordinating Institute - IIT - Kanpur

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Basic principles of countingLecture 2 - Sample space, events, axioms of probabilityLecture 3 - Conditional probability, Independence of eventsLecture 4 - Random variables, cumulative density function, expected valueLecture 5 - Discrete random variables and their distributionsLecture 6 - Discrete random variables and their distributionsLecture 7 - Discrete random variables and their distributionsLecture 8 - Continuous random variables and their distributionsLecture 9 - Continuous random variables and their distributionsLecture 10 - Continuous random variables and their distributionsLecture 11 - Function of random variables, Momement generating functionLecture 12 - Jointly distributed random variables, Independent r. v. and their sumsLecture 13 - Independent r. v. and their sumsLecture 14 - Chi � square r. v., sums of independent normal r. v., Conditional distrLecture 15 - Conditional disti, Joint distr. of functions of r. v., Order statisticsLecture 16 - Order statistics, Covariance and correlationLecture 17 - Covariance, Correlation, Cauchy- Schwarz inequalities, Conditional expectationLecture 18 - Conditional expectation, Best linear predictorLecture 19 - Inequalities and boundsLecture 20 - Convergence and limit theoremsLecture 21 - Central limit theoremLecture 22 - Applications of central limit theoremLecture 23 - Strong law of large numbers, Joint mgfLecture 24 - ConvolutionsLecture 25 - Stochastic processesLecture 26 - Transition and state probabilitiesLecture 27 - State prob., First passage and First return probLecture 28 - First passage and First return prob. Classification of statesLecture 29 - Random walk, periodic and null states

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Lecture 30 - Reducible Markov chainsLecture 31 - Time reversible Markov chainsLecture 32 - Poisson ProcessesLecture 33 - Inter-arrival times, Properties of Poisson processesLecture 34 - Queuing ModelsLecture 35 - Analysis of L, Lq ,W and Wq , M/M/S modelLecture 36 - M/M/S , M/M/I/K modelsLecture 37 - M/M/I/K and M/M/S/K modelsLecture 38 - Application to reliability theory failure lawLecture 39 - Exponential failure law, Weibull lawLecture 40 - Reliability of systems

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NPTEL Video Course - Mathematics - NOC:Basic Calculus for Engineers, Scientists and Economists

Subject Co-ordinator - Dr. Joydeep Dutta

Co-ordinating Institute - IIT - Kanpur

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - NumbersLecture 2 - Functions-1Lecture 3 - Sequence-1Lecture 4 - Sequence-2Lecture 5 - Limits and Continuity-1Lecture 6 - Limits and Continuity-2Lecture 7 - Limits And Continuity-3Lecture 8 - Derivative-1Lecture 9 - Derivative-2Lecture 10 - Maxima And MinimaLecture 11 - Mean-Value Theorem And Taylors Expansion-1Lecture 12 - Mean-Value Theorem And Taylors Expansion-2Lecture 13 - Integration-1Lecture 14 - Integration-2Lecture 15 - Integration By PartsLecture 16 - Definite IntegralLecture 17 - Riemann Integration-1Lecture 18 - Riemann Integration-2Lecture 19 - Functions Of Two Or More VariablesLecture 20 - Limits And Continuity Of Functions Of Two VariableLecture 21 - Differentiation Of Functions Of Two Variables-1Lecture 22 - Differentiation Of Functions Of Two Variables-2Lecture 23 - Unconstrained Minimization Of Funtions Of Two VariablesLecture 24 - Constrained Minimization And Lagrange Multiplier RulesLecture 25 - Infinite Series-1Lecture 26 - Infinite Series-2Lecture 27 - Infinite Series-3Lecture 28 - Multiple Integrals-1Lecture 29 - Multiple Integrals-2

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Lecture 30 - Multiple Integrals-3

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NPTEL Video Course - Mathematics - NOC:Probability and Stochastics for finance

Subject Co-ordinator - Dr. Joydeep Dutta

Co-ordinating Institute - IIT - Kanpur

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Basic ProbabilityLecture 2 - Interesting Problems In ProbabilityLecture 3 - Random variables, distribution function and independenceLecture 4 - Chebyshev inequality, Borel-Cantelli Lemmas and related issuesLecture 5 - Law of Large Number and Central Limit TheoremLecture 6 - Conditional Expectation - ILecture 7 - Conditional Expectation - IILecture 8 - MartingalesLecture 9 - Brownian Motion - ILecture 10 - Brownian Motion - IILecture 11 - Brownian Motion - IIILecture 12 - Ito Integral - ILecture 13 - Ito Integral - IILecture 14 - Ito Calculus - ILecture 15 - Ito Calculus - IILecture 16 - Ito Integral In Higher DimensionLecture 17 - Application to Ito Integral - ILecture 18 - Application to Ito Integral - IILecture 19 - Black Scholes Formula - ILecture 20 - Black Scholes Formula - II

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NPTEL Video Course - Mathematics - NOC:Differential Calculus in Several Variables

Subject Co-ordinator - Prof. Sudipta Dutta

Co-ordinating Institute - IIT - Kanpur

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Introduction to Several Variables and Notion Of distance in RnLecture 2 - Countinuity And CompactnessLecture 3 - Countinuity And ConnectdnessLecture 4 - DerivativesLecture 5 - Matrix Of Linear TransformationLecture 6 - Examples for Differentiable functionLecture 7 - Sufficient condition of differentiabilityLecture 8 - Chain RuleLecture 9 - Mean Value TheoremLecture 10 - Higher Order DerivativesLecture 11 - Taylor's FormulaLecture 12 - Maximum And MinimumLecture 13 - Second derivative test for maximum, minimum and saddle pointLecture 14 - We formalise the second derivative test discussed in Lecture 2 and do examplesLecture 15 - Specialisation to functions of two variablesLecture 16 - Implicit Function TheoremLecture 17 - Implicit Function Theorem -aLecture 18 - Application of IFTLecture 19 - Application of IFTLecture 20 - Application of IFTLecture 21 - Application of IFT

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NPTEL Video Course - Mathematics - NOC:Curves and Surfaces

Subject Co-ordinator - Prof. Sudipta Dutta

Co-ordinating Institute - IIT - Kanpur

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Level curves and locus, definition of parametric curves, tangent, arc length, arc length parametrisationLecture 2 - How much a curve is �curved�, signed unit normal and signed curvature, rigid motions, constant curvatureLecture 3 - Curves in R^3, principal normal and binormal, torsionLecture 4 - Frenet-Serret formulaLecture 5 - Simple closed curve and isoperimetric inequalityLecture 6 - Surfaces and parametric surfaces, examples, regular surface and non-example of regular surface, transition maps.Lecture 7 - Transition maps of smooth surfaces, smooth function between surfaces, diffeomorphismLecture 8 - ReparameterizationLecture 9 - Tangent, NormalLecture 10 - Orientable surfacesLecture 11 - Examples of SurfacesLecture 12 - First Fundamental FormLecture 13 - Conformal MappingLecture 14 - Curvature of SurfacesLecture 15 - Euler's TheoremLecture 16 - Regular Surfaces locally as Quadratic SurfacesLecture 17 - GeodesicsLecture 18 - Existence of Geodesics, Geodesics on Surfaces of revolutionLecture 19 - Geodesics on surfaces of revolution; Clairaut's TheoremLecture 20 - PseudosphereLecture 21 - Classification of Quadratic SurfaceLecture 22 - Surface Area and Equiareal Map

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NPTEL Video Course - Mathematics - NOC:Linear Regression Analysis and Forecasting

Subject Co-ordinator - Prof. Shalabh

Co-ordinating Institute - IIT - Kanpur

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Basic Fundamental Concepts Of ModellingLecture 2 - Regression Model - A Statistical ToolLecture 3 - Simple Linear Regression AnalysisLecture 4 - Estimation Of Parameters In Simple Linear Regression ModelLecture 5 - Estimation Of Parameters In Simple Linear Regression Model (Continued...)Lecture 6 - Estimation Of Parameters In Simple Linear Regression Model (Continued...)Lecture 7 - Maximum Likelihood Estimation of Parameters in Simple Linear Regression ModelLecture 8 - Testing of Hypotheis and Confidence Interval Estimation in Simple Linear Regression ModelLecture 9 - Testing of Hypotheis and Confidence Interval Estimation in Simple Linear Regression Model (Continued...)Lecture 10 - Software Implementation in Simple Linear Regression Model using MINITABLecture 11 - Multiple Linear Regression ModelLecture 12 - Estimation of Model Parameters in Multiple Linear Regression ModelLecture 13 - Estimation of Model Parameters in Multiple Linear Regression Model (Continued...)Lecture 14 - Standardized Regression Coefficients and Testing of HypothesisLecture 15 - Testing of Hypothesis (Continued...) and Goodness of Fit of the ModelLecture 16 - Diagnostics in Multiple Linear Regression ModelLecture 17 - Diagnostics in Multiple Linear Regression Model (Continued...)Lecture 18 - Diagnostics in Multiple Linear Regression Model (Continued...)Lecture 19 - Software Implementation of Multiple Linear Regression Model using MINITABLecture 20 - Software Implementation of Multiple Linear Regression Model using MINITAB (Continued...)Lecture 21 - Forecasting in Multiple Linear Regression ModelLecture 22 - Within Sample ForecastingLecture 23 - Outside Sample ForecastingLecture 24 - Software Implementation of Forecasting using MINITAB

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NPTEL Video Course - Mathematics - NOC:Introduction to R Software

Subject Co-ordinator - Prof. Shalabh

Co-ordinating Institute - IIT - Kanpur

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - How to Learn and Follow the CourseLecture 2 - Why R and Installation ProcedureLecture 3 - Introduction _Help_ Demo examples_ packages_ librariesLecture 4 - Introduction _Command line_ Data editor _ RstudioLecture 5 - Basics in CalculationsLecture 6 - Basics of Calculations _ Calculator _Built in Functions AssignmentsLecture 7 - Basics of Calculations _Functions _MatricesLecture 8 - Basics CalculationsLecture 9 - Basics CalculationsLecture 10 - Basics CalculationsLecture 11 - Basics CalculationsLecture 12 - Basics CalculationsLecture 13 - Basics CalculationsLecture 14 - Basics CalculationsLecture 15 - Data management - SequencesLecture 16 - Data management - sequencesLecture 17 - Data management - RepeatsLecture 18 - Data management - Sorting and OrderingLecture 19 - Data management - ListsLecture 20 - Data management - Lists (Continued...)Lecture 21 - Data management - Vector indexingLecture 22 - Data management - Vector Indexing (Continued...)Lecture 23 - Data management - FactorsLecture 24 - Data management - factors (Continued...)Lecture 25 - Strings - Display and Formatting, Print and Format FunctionsLecture 26 - Strings - Display and Formatting, Print and Format with ConcatenateLecture 27 - Strings - Display and Formatting, Paste FunctionLecture 28 - Strings - Display and Formatting, SplittingLecture 29 - Strings - Display and Formatting, Replacement_ Manipulations _Alphabets

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Lecture 30 - Strings - Display and Formatting, Replacement and Evaluation of StringsLecture 31 - Data framesLecture 32 - Data frames (Continued...)Lecture 33 - Data frames (Continued...)Lecture 34 - Data Handling - Importing CSV and Tabular Data FilesLecture 35 - Data Handling - Importing Data Files from Other SoftwareLecture 36 - Statistical Functions - Frequency and Partition valuesLecture 37 - Statistical Functions - Graphics and PlotsLecture 38 - Statistical Functions - Central Tendency and VariationLecture 39 - Statistical Functions - Boxplots, Skewness and KurtosisLecture 40 - Statistical Functions - Bivariate three dimensional plotLecture 41 - Statistical Functions - Correlation and Examples of ProgrammingLecture 42 - Examples of ProgrammingLecture 43 - Examples of More Programming

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NPTEL Video Course - Mathematics - NOC:Descriptive Statistics with R Software

Subject Co-ordinator - Prof. Shalabh

Co-ordinating Institute - IIT - Kanpur

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Introduction to R SoftwareLecture 2 - Basics and R as a CalculatorLecture 3 - Calculations with Data VectorsLecture 4 - Built-in Commands and Missing Data HandlingLecture 5 - Operations with MatricesLecture 6 - Objectives, Steps and Basic DefinitionsLecture 7 - Variables and Types of DataLecture 8 - Absolute Frequency, Relative Frequency and Frequency DistributionLecture 9 - Frequency Distribution and Cumulative Distribution FunctionLecture 10 - Bar DiagramsLecture 11 - Subdivided Bar Plots and Pie DiagramsLecture 12 - 3D Pie Diagram and HistogramLecture 13 - Kernel Density and Stem - Leaf PlotsLecture 14 - Arithmetic MeanLecture 15 - MedianLecture 16 - QuantilesLecture 17 - Mode, Geometric Mean and Harmonic MeanLecture 18 - Range, Interquartile Range and Quartile DeviationLecture 19 - Absolute Deviation and Absolute Mean DeviationLecture 20 - Mean Squared Error, Variance and Standard DeviationLecture 21 - Coefficient of Variation and BoxplotsLecture 22 - Raw and Central MomentsLecture 23 - Sheppard's Correction, Absolute Moments and Computation of MomentsLecture 24 - Skewness and KurtosisLecture 25 - Univariate and Bivariate Scatter PlotsLecture 26 - Smooth Scatter PlotsLecture 27 - Quantile- Quantile and Three Dimensional PlotsLecture 28 - Correlation CoefficientLecture 29 - Correlation Coefficient Using R Software

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Lecture 30 - Rank Correlation CoefficientLecture 31 - Measures of Association for Discrete and Counting Variables - Part 1Lecture 32 - Measures of Association for Discrete and Counting Variables - Part 2Lecture 33 - Least Squares Method - One VariableLecture 34 - Least Squares Method - R Commands and More than One Variables

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NPTEL Video Course - Mathematics - NOC:Calculus of Several Real Variables

Subject Co-ordinator - Dr. Joydeep Dutta

Co-ordinating Institute - IIT - Kanpur

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Vectors in plane and spaceLecture 2 - Inner product and distanceLecture 3 - Application to real world problemsLecture 4 - Matrices and determinantsLecture 5 - Cross product of two vectorsLecture 6 - Higher dimensional Euclidean spaceLecture 7 - Functions of more than one real-variableLecture 8 - Partial derivatives and ContinuityLecture 9 - Vector-valued maps and Jacobian matrixLecture 10 - Chain rule for partial derivativesLecture 11 - The Gradient Vector and Directional DerivativeLecture 12 - The Implicit Function TheoremLecture 13 - Higher Order Partial DerivativesLecture 14 - Taylor's Theorem in Higher DimensionLecture 15 - Maxima and Minima for Several VariablesLecture 16 - Second Derivative Test for Maximum and MinimumLecture 17 - Constrained Optimization and The Lagrange Multiplier RuleLecture 18 - Vector Valued Function and Classical MechanicsLecture 19 - Arc LengthLecture 20 - Vector FieldsLecture 21 - Multiple Integral - ILecture 22 - Multiple Integral - IILecture 23 - Multiple Integral - IIILecture 24 - Multiple Integral - IVLecture 25 - Cylindrical and Spherical CoordinatesLecture 26 - Multiple Integrals and MechanicsLecture 27 - Line Integral - ILecture 28 - Line Integral - IILecture 29 - Parametrized Surfaces

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Lecture 30 - Area of a surface IntegralLecture 31 - Area of parametrized surfaceLecture 32 - Surface IntegralsLecture 33 - Green's TheoremLecture 34 - Stoke's TheoremLecture 35 - Examples of Stoke's TheoremLecture 36 - Gauss Divergence TheoremLecture 37 - Facts about vector fields

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NPTEL Video Course - Mathematics - Advanced Engineering Mathematics

Subject Co-ordinator - Dr. P. Panigrahi, Prof. J. Kumar, Prof. P.D. Srivastava, Prof. Somesh Kumar

Co-ordinating Institute - IIT - Kharagpur

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Review Groups, Fields and MatricesLecture 2 - Vector Spaces, Subspaces, Linearly Dependent/Independent of VectorsLecture 3 - Basis, Dimension, Rank and Matrix InverseLecture 4 - Linear Transformation, Isomorphism and Matrix RepresentationLecture 5 - System of Linear Equations, Eigenvalues and EigenvectorsLecture 6 - Method to Find Eigenvalues and Eigenvectors, Diagonalization of MatricesLecture 7 - Jordan Canonical Form, Cayley Hamilton TheoremLecture 8 - Inner Product Spaces, Cauchy-Schwarz InequalityLecture 9 - Orthogonality, Gram-Schmidt Orthogonalization ProcessLecture 10 - Spectrum of special matrices,positive/negative definite matricesLecture 11 - Concept of Domain, Limit, Continuity and DifferentiabilityLecture 12 - Analytic Functions, C-R EquationsLecture 13 - Harmonic FunctionsLecture 14 - Line Integral in the ComplexLecture 15 - Cauchy Integral TheoremLecture 16 - Cauchy Integral Theorem (Continued.)Lecture 17 - Cauchy Integral FormulaLecture 18 - Power and Taylor's Series of Complex NumbersLecture 19 - Power and Taylor's Series of Complex Numbers (Continued.)Lecture 20 - Taylor's, Laurent Series of f(z) and SingularitiesLecture 21 - Classification of Singularities, Residue and Residue TheoremLecture 22 - Laplace Transform and its ExistenceLecture 23 - Properties of Laplace TransformLecture 24 - Evaluation of Laplace and Inverse Laplace TransformLecture 25 - Applications of Laplace Transform to Integral Equations and ODEsLecture 26 - Applications of Laplace Transform to PDEsLecture 27 - Fourier SeriesLecture 28 - Fourier Series (Continued.)Lecture 29 - Fourier Integral Representation of a Function

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Lecture 30 - Introduction to Fourier TransformLecture 31 - Applications of Fourier Transform to PDEsLecture 32 - Laws of Probability - ILecture 33 - Laws of Probability - IILecture 34 - Problems in ProbabilityLecture 35 - Random VariablesLecture 36 - Special Discrete DistributionsLecture 37 - Special Continuous DistributionsLecture 38 - Joint Distributions and Sampling DistributionsLecture 39 - Point EstimationLecture 40 - Interval EstimationLecture 41 - Basic Concepts of Testing of HypothesisLecture 42 - Tests for Normal Populations

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NPTEL Video Course - Mathematics - Functional Analysis

Subject Co-ordinator - Prof. P.D. Srivastava

Co-ordinating Institute - IIT - Kharagpur

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Metric Spaces with ExamplesLecture 2 - Holder Inequality and Minkowski InequalityLecture 3 - Various Concepts in a Metric SpaceLecture 4 - Separable Metrics Spaces with ExamplesLecture 5 - Convergence, Cauchy Sequence, CompletenessLecture 6 - Examples of Complete and Incomplete Metric SpacesLecture 7 - Completion of Metric Spaces + TutorialLecture 8 - Vector Spaces with ExamplesLecture 9 - Normed Spaces with ExamplesLecture 10 - Banach Spaces and Schauder BasicLecture 11 - Finite Dimensional Normed Spaces and SubspacesLecture 12 - Compactness of Metric/Normed SpacesLecture 13 - Linear Operators-definition and ExamplesLecture 14 - Bounded Linear Operators in a Normed SpaceLecture 15 - Bounded Linear Functionals in a Normed SpaceLecture 16 - Concept of Algebraic Dual and Reflexive SpaceLecture 17 - Dual Basis & Algebraic Reflexive SpaceLecture 18 - Dual Spaces with ExamplesLecture 19 - Tutorial - ILecture 20 - Tutorial - IILecture 21 - Inner Product & Hilbert SpaceLecture 22 - Further Properties of Inner Product SpacesLecture 23 - Projection Theorem, Orthonormal Sets and SequencesLecture 24 - Representation of Functionals on a Hilbert SpacesLecture 25 - Hilbert Adjoint OperatorLecture 26 - Self Adjoint, Unitary & Normal OperatorsLecture 27 - Tutorial - IIILecture 28 - Annihilator in an IPSLecture 29 - Total Orthonormal Sets And Sequences

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Lecture 30 - Partially Ordered Set and Zorns LemmaLecture 31 - Hahn Banach Theorem for Real Vector SpacesLecture 32 - Hahn Banach Theorem for Complex V.S. & Normed SpacesLecture 33 - Baires Category & Uniform Boundedness TheoremsLecture 34 - Open Mapping TheoremLecture 35 - Closed Graph TheoremLecture 36 - Adjoint OperatorLecture 37 - Strong and Weak ConvergenceLecture 38 - Convergence of Sequence of Operators and FunctionalsLecture 39 - LP - SpaceLecture 40 - LP - Space (Continued.)

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NPTEL Video Course - Mathematics - Numerical methods of Ordinary and Partial Differential Equations

Subject Co-ordinator - Dr. G.P. Raja Sekhar

Co-ordinating Institute - IIT - Kharagpur

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Motivation with few ExamplesLecture 2 - Single - Step Methods for IVPsLecture 3 - Analysis of Single Step MethodsLecture 4 - Runge - Kutta Methods for IVPsLecture 5 - Higher Order Methods/EquationsLecture 6 - Error - Stability - Convergence of Single Step MethodsLecture 7 - Tutorial - ILecture 8 - Tutorial - IILecture 9 - Multi-Step Methods (Explicit)Lecture 10 - Multi-Step Methods (Implicit)Lecture 11 - Convergence and Stability of multi step methodsLecture 12 - General methods for absolute stabilityLecture 13 - Stability Analysis of Multi Step MethodsLecture 14 - Predictor - Corrector MethodsLecture 15 - Some Comments on Multi - Step MethodsLecture 16 - Finite Difference Methods - Linear BVPsLecture 17 - Linear/Non - Linear Second Order BVPsLecture 18 - BVPS - Derivative Boundary ConditionsLecture 19 - Higher Order BVPsLecture 20 - Shooting Method BVPsLecture 21 - Tutorial - IIILecture 22 - Introduction to First Order PDELecture 23 - Introduction to Second Order PDELecture 24 - Finite Difference Approximations to Parabolic PDEsLecture 25 - Implicit Methods for Parabolic PDEsLecture 26 - Consistency, Stability and ConvergenceLecture 27 - Other Numerical Methods for Parabolic PDEsLecture 28 - Tutorial - IVLecture 29 - Matrix Stability Analysis of Finite Difference Scheme

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Lecture 30 - Fourier Series Stability Analysis of Finite Difference SchemeLecture 31 - Finite Difference Approximations to Elliptic PDEs - ILecture 32 - Finite Difference Approximations to Elliptic PDEs - IILecture 33 - Finite Difference Approximations to Elliptic PDEs - IIILecture 34 - Finite Difference Approximations to Elliptic PDEs - IVLecture 35 - Finite Difference Approximations to Hyperbolic PDEs - ILecture 36 - Finite Difference Approximations to Hyperbolic PDEs - IILecture 37 - Method of characteristics for Hyperbolic PDEs - ILecture 38 - Method of characterisitcs for Hyperbolic PDEs - IILecture 39 - Finite Difference Approximations to 1st order Hyperbolic PDEsLecture 40 - Summary, Appendices, Remarks

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NPTEL Video Course - Mathematics - Optimization

Subject Co-ordinator - Prof. A. Goswami, Dr. Debjani Chakraborty

Co-ordinating Institute - IIT - Kharagpur

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Optimization - IntroductionLecture 2 - Formulation of LPPLecture 3 - Geometry of LPP and Graphical Solution of LPPLecture 4 - Solution of LPPLecture 5 - Big - M MethodLecture 6 - Two - Phase MethodLecture 7 - Special Cases in Simple ApplicationsLecture 8 - Introduction to Duality TheoryLecture 9 - Dual Simplex MethodLecture 10 - Post Optimaility AnalysisLecture 11 - Integer Programming - ILecture 12 - Integer Programming - IILecture 13 - Introduction to Transportation ProblemsLecture 14 - Solving Various types of Transportation ProblemsLecture 15 - Assignment ProblemsLecture 16 - Project ManagementLecture 17 - Critical Path AnalysisLecture 18 - PERTLecture 19 - Shortest Path AlgorithmLecture 20 - Travelling Salesman ProblemLecture 21 - Classical optimization techniquesLecture 22 - Unconstarined multivariable optimizationLecture 23 - Nonlinear programming with equality constraintLecture 24 - Nonlinear programming KKT conditionsLecture 25 - Numerical optimizationLecture 26 - Numerical optimizationLecture 27 - Fibonacci MethodLecture 28 - Golden Section MethodsLecture 29 - Interpolation Methods

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Lecture 30 - Unconstarined optimization techniquesLecture 31 - Unconstarined optimization techniquesLecture 32 - Nonlinear programmingLecture 33 - Interior and Exterior penulty Function MethodLecture 34 - Separable Programming ProblemLecture 35 - Introduction to Geometric ProgrammingLecture 36 - Constrained Geometric Programming ProblemLecture 37 - Dynamic Programming ProblemLecture 38 - Dynamic Programming Problem (Continued.)Lecture 39 - Multi Objective Decision MakingLecture 40 - Multi attribute decision making

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NPTEL Video Course - Mathematics - Probability and Statistics

Subject Co-ordinator - Prof. Somesh Kumar

Co-ordinating Institute - IIT - Kharagpur

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Algebra of Sets - ILecture 2 - Algebra of Sets - IILecture 3 - Introduction to ProbabilityLecture 4 - Laws of Probability - ILecture 5 - Laws of Probability - IILecture 6 - Problems in ProbabilityLecture 7 - Random VariablesLecture 8 - Probability DistributionsLecture 9 - Characteristics of DistributionLecture 10 - Special Distributions - ILecture 11 - Special Distributions - IILecture 12 - Special Distributions - IIILecture 13 - Special Distributions - IVLecture 14 - Special Distributions - VLecture 15 - Special Distributions - VILecture 16 - Special Distributions - VIILecture 17 - Functions of a Random VariableLecture 18 - Joint Distributions - ILecture 19 - Joint Distributions - IILecture 20 - Joint Distributions - IIILecture 21 - Joint Distributions - IVLecture 22 - Transformations of Random VectorsLecture 23 - Sampling Distributions - ILecture 24 - Sampling Distributions - IILecture 25 - Descriptive Statistics - ILecture 26 - Descriptive Statistics - IILecture 27 - Estimation - ILecture 28 - Estimation - IILecture 29 - Estimation - III

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Lecture 30 - Estimation - IVLecture 31 - Estimation - VLecture 32 - Estimation - VILecture 33 - Testing of Hypothesis - ILecture 34 - Testing of Hypothesis - IILecture 35 - Testing of Hypothesis - IIILecture 36 - Testing of Hypothesis - IVLecture 37 - Testing of Hypothesis - VLecture 38 - Testing of Hypothesis - VILecture 39 - Testing of Hypothesis - VIILecture 40 - Testing of Hypothesis - VIII

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NPTEL Video Course - Mathematics - Regression Analysis

Subject Co-ordinator - Dr. Soumen Maity

Co-ordinating Institute - IIT - Kharagpur

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Simple Linear RegressionLecture 2 - Simple Linear Regression (Continued...1)Lecture 3 - Simple Linear Regression (Continued...2)Lecture 4 - Simple Linear Regression (Continued...3)Lecture 5 - Simple Linear Regression (Continued...4)Lecture 6 - Multiple Linear RegressionLecture 7 - Multiple Linear Regression (Continued...1)Lecture 8 - Multiple Linear Regression (Continued...2)Lecture 9 - Multiple Linear Regression (Continued...3)Lecture 10 - Selecting the BEST Regression modelLecture 11 - Selecting the BEST Regression model (Continued...1)Lecture 12 - Selecting the BEST Regression model (Continued...2)Lecture 13 - Selecting the BEST Regression model (Continued...3)Lecture 14 - MulticollinearityLecture 15 - Multicollinearity (Continued...1)Lecture 16 - Multicollinearity (Continued...2)Lecture 17 - Model Adequacy CheckingLecture 18 - Model Adequacy Checking (Continued...1)Lecture 19 - Model Adequacy Checking (Continued...2)Lecture 20 - Test for Influential ObservationsLecture 21 - Transformations and Weighting to correct model inadequaciesLecture 22 - Transformations and Weighting to correct model inadequacies (Continued...1)Lecture 23 - Transformations and Weighting to correct model inadequacies (Continued...2)Lecture 24 - Dummy VariablesLecture 25 - Dummy Variables (Continued...1)Lecture 26 - Dummy Variables (Continued...2)Lecture 27 - Polynomial Regression ModelsLecture 28 - Polynomial Regression Models (Continued...1)Lecture 29 - Polynomial Regression Models (Continued...2)

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Lecture 30 - Generalized Linear ModelsLecture 31 - Generalized Linear Models (Continued.)Lecture 32 - Non-Linear EstimationLecture 33 - Regression Models with Autocorrelated ErrorsLecture 34 - Regression Models with Autocorrelated Errors (Continued.)Lecture 35 - Measurement Errors & Calibration ProblemLecture 36 - Tutorial - ILecture 37 - Tutorial - IILecture 38 - Tutorial - IIILecture 39 - Tutorial - IVLecture 40 - Tutorial - V

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NPTEL Video Course - Mathematics - Statistical Inference

Subject Co-ordinator - Prof. Somesh Kumar

Co-ordinating Institute - IIT - Kharagpur

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Introduction and MotivationLecture 2 - Basic Concepts of Point Estimations - ILecture 3 - Basic Concepts of Point Estimations - IILecture 4 - Finding Estimators - ILecture 5 - Finding Estimators - IILecture 6 - Finding Estimators - IIILecture 7 - Properties of MLEsLecture 8 - Lower Bounds for Variance - ILecture 9 - Lower Bounds for Variance - IILecture 10 - Lower Bounds for Variance - IIILecture 11 - Lower Bounds for Variance - IVLecture 12 - SufficiencyLecture 13 - Sufficiency and InformationLecture 14 - Minimal Sufficiency, CompletenessLecture 15 - UMVU Estimation, AncillarityLecture 16 - Invariance - ILecture 17 - Invariance - IILecture 18 - Bayes and Minimax Estimation - ILecture 19 - Bayes and Minimax Estimation - IILecture 20 - Bayes and Minimax Estimation - IIILecture 21 - Testing of HypothesesLecture 22 - Neyman Pearson Fundamental LemmaLecture 23 - Applications of NP lemmaLecture 24 - UMP TestsLecture 25 - UMP Tests (Continued.)Lecture 26 - UMP Unbiased TestsLecture 27 - UMP Unbiased Tests (Continued.)Lecture 28 - UMP Unbiased TestsLecture 29 - Unbiased Tests for Normal Populations

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Lecture 30 - Unbiased Tests for Normal Populations (Continued.)Lecture 31 - Likelihood Ratio Tests - ILecture 32 - Likelihood Ratio Tests - IILecture 33 - Likelihood Ratio Tests - IIILecture 34 - Likelihood Ratio Tests - IVLecture 35 - Invariant TestsLecture 36 - Test for Goodness of FitLecture 37 - Sequential ProcedureLecture 38 - Sequential Procedure (Continued.)Lecture 39 - Confidence IntervalsLecture 40 - Confidence Intervals (Continued.)

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NPTEL Video Course - Mathematics - A Basic Course in Real Analysis

Subject Co-ordinator - Prof. P.D. Srivastava

Co-ordinating Institute - IIT - Kharagpur

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Rational Numbers and Rational CutsLecture 2 - Irrational numbers, Dedekind's TheoremLecture 3 - Continuum and ExercisesLecture 4 - Continuum and Exercises (Continued.)Lecture 5 - Cantor's Theory of Irrational NumbersLecture 6 - Cantor's Theory of Irrational Numbers (Continued.)Lecture 7 - Equivalence of Dedekind and Cantor's TheoryLecture 8 - Finite, Infinite, Countable and Uncountable Sets of Real NumbersLecture 9 - Types of Sets with Examples, Metric SpaceLecture 10 - Various properties of open set, closure of a setLecture 11 - Ordered set, Least upper bound, greatest lower bound of a setLecture 12 - Compact Sets and its propertiesLecture 13 - Weiersstrass Theorem, Heine Borel Theorem, Connected setLecture 14 - Tutorial - IILecture 15 - Concept of limit of a sequenceLecture 16 - Some Important limits, Ratio tests for sequences of Real NumbersLecture 17 - Cauchy theorems on limit of sequences with examplesLecture 18 - Fundamental theorems on limits, Bolzano-Weiersstrass TheoremLecture 19 - Theorems on Convergent and divergent sequencesLecture 20 - Cauchy sequence and its propertiesLecture 21 - Infinite series of real numbersLecture 22 - Comparison tests for series, Absolutely convergent and Conditional convergent seriesLecture 23 - Tests for absolutely convergent seriesLecture 24 - Raabe's test, limit of functions, Cluster pointLecture 25 - Some results on limit of functionsLecture 26 - Limit Theorems for functionsLecture 27 - Extension of limit concept (one sided limits)Lecture 28 - Continuity of FunctionsLecture 29 - Properties of Continuous Functions

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Lecture 30 - Boundedness Theorem, Max-Min Theorem and Bolzano's theoremLecture 31 - Uniform Continuity and Absolute ContinuityLecture 32 - Types of Discontinuities, Continuity and CompactnessLecture 33 - Continuity and Compactness (Continued.), ConnectednessLecture 34 - Differentiability of real valued function, Mean Value TheoremLecture 35 - Mean Value Theorem (Continued.)Lecture 36 - Application of MVT , Darboux Theorem, L Hospital RuleLecture 37 - L'Hospital Rule and Taylor's TheoremLecture 38 - Tutorial - IIILecture 39 - Riemann/Riemann Stieltjes IntegralLecture 40 - Existence of Reimann Stieltjes IntegralLecture 41 - Properties of Reimann Stieltjes IntegralLecture 42 - Properties of Reimann Stieltjes Integral (Continued.)Lecture 43 - Definite and Indefinite IntegralLecture 44 - Fundamental Theorems of Integral CalculusLecture 45 - Improper IntegralsLecture 46 - Convergence Test for Improper Integrals

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NPTEL Video Course - Mathematics - Statistical Methods for Scientists and Engineers

Subject Co-ordinator - Prof. Somesh Kumar

Co-ordinating Institute - IIT - Kharagpur

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Foundations of ProbabilityLecture 2 - Laws of ProbabilityLecture 3 - Random VariablesLecture 4 - Moments and Special DistributionsLecture 5 - Moments and Special Distributions (Continued...)Lecture 6 - Special Distributions (Continued...)Lecture 7 - Special Distributions (Continued...)Lecture 8 - Sampling DistributionsLecture 9 - Parametric Methods - ILecture 10 - Parametric Methods - IILecture 11 - Parametric Methods - IIILecture 12 - Parametric Methods - IVLecture 13 - Parametric Methods - VLecture 14 - Parametric Methods - VILecture 15 - Parametric Methods - VIILecture 16 - Multivariate Analysis - ILecture 17 - Multivariate Analysis - IILecture 18 - Multivariate Analysis - IIILecture 19 - Multivariate Analysis - IVLecture 20 - Multivariate Analysis - VLecture 21 - Multivariate Analysis - VILecture 22 - Multivariate Analysis - VIILecture 23 - Multivariate Analysis - VIIILecture 24 - Multivariate Analysis - IXLecture 25 - Multivariate Analysis - XLecture 26 - Multivariate Analysis - XILecture 27 - Multivariate Analysis - XIILecture 28 - Non parametric Methods - ILecture 29 - Non parametric Methods - II

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Lecture 30 - Non parametric Methods - IIILecture 31 - Non parametric Methods - IVLecture 32 - Nonparametric Methods - VLecture 33 - Nonparametric Methods - VILecture 34 - Nonparametric Methods - VIILecture 35 - Nonparametric Methods - VIIILecture 36 - Nonparametric Methods - IXLecture 37 - Nonparametric Methods - XLecture 38 - Nonparametric Methods - XILecture 39 - Nonparametric Methods - XIILecture 40 - Nonparametric Methods - XIII

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NPTEL Video Course - Mathematics - NOC:Probability and Statistics

Subject Co-ordinator - Prof. Somesh Kumar

Co-ordinating Institute - IIT - Kharagpur

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Sets, Classes, CollectionLecture 2 - Sequence of SetsLecture 3 - Ring, Field (Algebra)Lecture 4 - Sigma-Ring, Sigma-Field, Monotone ClassLecture 5 - Random Experiment, EventsLecture 6 - Definitions of ProbabilityLecture 7 - Properties of Probability Function - ILecture 8 - Properties of Probability Function - IILecture 9 - Conditional ProbabilityLecture 10 - Independence of EventsLecture 11 - Problems in Probability - ILecture 12 - Problems in Probability - IILecture 13 - Random VariablesLecture 14 - Probability Distribution of a Random Variable - ILecture 15 - Probability Distribution of a Random Variable - IILecture 16 - MomentsLecture 17 - Characteristics of Distributions - ILecture 18 - Characteristics of Distributions - IILecture 19 - Special Discrete Distributions - ILecture 20 - Special Discrete Distributions - IILecture 21 - Special Discrete Distributions - IIILecture 22 - Poisson Process - ILecture 23 - Poisson Process - IILecture 24 - Special Continuous Distributions - ILecture 25 - Special Continuous Distributions - IILecture 26 - Special Continuous Distributions - IIILecture 27 - Special Continuous Distributions - IVLecture 28 - Special Continuous Distributions - VLecture 29 - Normal Distribution

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Lecture 30 - Problems on Normal DistributionLecture 31 - Problems on Special Distributions - ILecture 32 - Problems on Special Distributions - IILecture 33 - Function of a random variable - ILecture 34 - Function of a random variable - IILecture 35 - Joint Distributions - ILecture 36 - Joint Distributions - IILecture 37 - Independence, Product MomentsLecture 38 - Linearity Property of Correlation and ExamplesLecture 39 - Bivariate Normal Distribution - ILecture 40 - Bivariate Normal Distribution - IILecture 41 - Additive Properties of Distributions - ILecture 42 - Additive Properties of Distributions - IILecture 43 - Transformation of Random VariablesLecture 44 - Distribution of Order StatisticsLecture 45 - Basic ConceptsLecture 46 - Chi-Square DistributionLecture 47 - Chi-Square Distribution (Continued...), t-DistributionLecture 48 - F-DistributionLecture 49 - Descriptive Statistics - ILecture 50 - Descriptive Statistics - IILecture 51 - Descriptive Statistics - IIILecture 52 - Descriptive Statistics - IVLecture 53 - Introduction to EstimationLecture 54 - Unbiased and Consistent EstimatorsLecture 55 - LSE, MMELecture 56 - Examples on MME, MLELecture 57 - Examples on MLE - ILecture 58 - Examples on MLE - II, MSELecture 59 - UMVUE, Sufficiency, CompletenessLecture 60 - Rao - Blackwell Theorem and Its ApplicationsLecture 61 - Confidence Intervals - ILecture 62 - Confidence Intervals - IILecture 63 - Confidence Intervals - IIILecture 64 - Confidence Intervals - IVLecture 65 - Basic DefinitionsLecture 66 - Two Types of ErrorsLecture 67 - Neyman-Pearson Fundamental LemmaLecture 68 - Applications of N-P Lemma - I

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Lecture 69 - Applications of N-P Lemma - IILecture 70 - Testing for Normal MeanLecture 71 - Testing for Normal VarianceLecture 72 - Large Sample Test for Variance and Two Sample ProblemLecture 73 - Paired t-TestLecture 74 - ExamplesLecture 75 - Testing Equality of ProportionsLecture 76 - Chi-Square Test for Goodness Fit - ILecture 77 - Chi-Square Test for Goodness Fit - IILecture 78 - Testing for Independence in rxc Contingency Table - ILecture 79 - Testing for Independence in rxc Contingency Table - II

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NPTEL Video Course - Mathematics - NOC:Applied Multivariate Statistical Modeling

Subject Co-ordinator - Dr. J. Maiti

Co-ordinating Institute - IIT - Kharagpur

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Introduction to multivariate statistical modeling - Part-ILecture 2 - Introduction to multivariate statistical modeling - Part-IILecture 3 - Univariate descriptive statisticsLecture 4 - Sampling DistributionLecture 5 - Estimation - Part-ILecture 6 - Estimation - Part-IILecture 7 - Hypothesis TestingLecture 8 - Introduction to multivariate statistical modeling - Part-ILecture 9 - Introduction to multivariate statistical modeling - Part-IILecture 10 - Multivariate Normal DistributionLecture 11 - Multivariate Normal Distribution (Continued...)Lecture 12 - ANOVA - Part-ILecture 13 - ANOVA - Part-IILecture 14 - Multivariate Analysis of Variance (MANOVA)Lecture 15 - Multivariate Analysis of Variance (MANOVA) (Continued...)Lecture 16 - Multiple Regression - IntroductionLecture 17 - MLR Sampling Distribution of Regression CoefficientsLecture 18 - MLR-Model Adequacy TestsLecture 19 - MLR - Test of AssumptionsLecture 20 - MLR - Model DiagnosticsLecture 21 - Principal Component Analysis (PCA)Lecture 22 - Principal Component Analysis (PCA)Lecture 23 - Factor AnalysisLecture 24 - Factor Analysis - Estimation and Model Adequacy TestingLecture 25 - Factor Analysis - Model Adequacy, Rotation, Factor Scores and Case StudyLecture 26 - Introduction to Structural Equation ModelingLecture 27 - SEM - Measurement ModelLecture 28 - SEM - Structural Model

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NPTEL Video Course - Mathematics - NOC:Partial Differential Equations (PDE) for Engineers: Solution by Separation of Variables

Subject Co-ordinator - Prof. S. De

Co-ordinating Institute - IIT - Kharagpur

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Introduction to PDELecture 2 - Classification of PDELecture 3 - Principle of Linear SuperpositionLecture 4 - Standard Eigen Value Problem and Special ODEsLecture 5 - Adjoint OperatorLecture 6 - Generalized Sturm - Louiville ProblemLecture 7 - Properties of Adjoint OperatorLecture 8 - Separation of VariablesLecture 9 - Solution of 3 Dimensional Parabolic ProblemLecture 10 - Solution of 4 Dimensional Parabolic problemLecture 11 - Solution of 4 Dimensional Parabolic Problem (Continued...)Lecture 12 - Solution of Elliptical PDELecture 13 - Solution of Hyperbolic PDELecture 14 - Orthogonality of Bessel Function and 2 Dimensional Cylindrical Coordinate SystemLecture 15 - Cylindrical Co-ordinate System - 3 Dimensional ProblemLecture 16 - Spherical Polar Coordinate SystemLecture 17 - Spherical Polar Coordinate System (Continued...)Lecture 18 - Example of Generalized 3 Dimensional ProblemLecture 19 - Example of Application Oriented ProblemsLecture 20 - Examples of Application Oriented Problems (Continued...)

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NPTEL Video Course - Mathematics - NOC:Introductory Course in Real Analysis

Subject Co-ordinator - Prof. P.D. Srivastava

Co-ordinating Institute - IIT - Kharagpur

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Countable and Uncountable setsLecture 2 - Properties of Countable and Uncountable setsLecture 3 - Examples of Countable and Uncountable setsLecture 4 - Concepts of Metric SpaceLecture 5 - Open ball, Closed ball, Limit point of a setLecture 6 - Tutorial-ILecture 7 - Some theorems on Open and Closed setsLecture 8 - Ordered set, Least upper bound, Greatest lower bound of a setLecture 9 - Ordered set, Least upper bound, Greatest lower bound of a set (Continued...)Lecture 10 - Compact SetLecture 11 - Properties of Compact setsLecture 12 - Tutorial-IILecture 13 - Heine Borel TheoremLecture 14 - Weierstrass TheoremLecture 15 - Cantor set and its propertiesLecture 16 - Derived set and Dense setLecture 17 - Limit of a sequence and monotone sequenceLecture 18 - Tutorial-IIILecture 19 - Some Important limits of sequencesLecture 20 - Ratio Test Cauchy�s theorems on limits of sequences of real numbersLecture 21 - Fundamental theorems on limitsLecture 22 - Some results on limits and Bolzano-Weierstrass TheoremLecture 23 - Criteria for convergent sequenceLecture 24 - Tutorial-IVLecture 25 - Criteria for Divergent SequenceLecture 26 - Cauchy SequenceLecture 27 - Cauchy Convergence Criteria for SequencesLecture 28 - Infinite Series of Real NumbersLecture 29 - Convergence Criteria for Series of Positive Real Numbers

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Lecture 30 - Tutorial-VLecture 31 - Comparison Test for SeriesLecture 32 - Absolutely and Conditionally Convergent SeriesLecture 33 - Rearrangement Theorem and Test for Convergence of SeriesLecture 34 - Ratio and Integral Test for Convergence of SeriesLecture 35 - Raabe's Test for Convergence of SeriesLecture 36 - Tutorial-VILecture 37 - Limit of Functions and Cluster PointLecture 38 - Limit of Functions (Continued...)Lecture 39 - Divergence Criteria for LimitLecture 40 - Various Properties of Limit of FunctionsLecture 41 - Left and Right Hand Limits for FunctionsLecture 42 - Tutorial-VIILecture 43 - Limit of Functions at InfinityLecture 44 - Continuous Functions (Cauchy's Definition)Lecture 45 - Continuous Functions (Heine's Definition)Lecture 46 - Properties of Continuous FunctionsLecture 47 - Properties of Continuous Functions (Continued...)Lecture 48 - Tutorial-VIIILecture 49 - Boundness Theorem and Max-Min TheoremLecture 50 - Location of Root and Bolzano's TheoremLecture 51 - Uniform Continuity and Related TheoremsLecture 52 - Absolute Continuity and Related TheoremsLecture 53 - Types of DiscontinuitiesLecture 54 - Tutorial-IXLecture 55 - Types of Discontinuities (Continued...)Lecture 56 - Relation between Continuity and Compact SetsLecture 57 - Differentiability of Real Valued FunctionsLecture 58 - Local Max. - Min. Cauchy's and Lagrange's Mean Value TheoremLecture 59 - Rolle's Mean Value Theorems and Its ApplicationsLecture 60 - Tutorial-XLecture 61Lecture 62Lecture 63Lecture 64Lecture 65Lecture 66Lecture 67Lecture 68

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Lecture 69Lecture 70Lecture 71Lecture 72Lecture 73

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NPTEL Video Course - Mathematics - NOC:Modeling Transport Phenomena of Microparticles

Subject Co-ordinator - Dr. G.P. Raja Sekhar, Prof. Somnath Bhattacharyya

Co-ordinating Institute - IIT - Kharagpur

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Preliminary conceptsLecture 2 - Cauchy�s equation of motion and Navier-Stokes equationsLecture 3 - Reduced forms of Navier-Stokes equations and Boundary conditionsLecture 4 - Exact solutions of Navier-Stokes equations in particular casesLecture 5 - Dimensional Analysis � Non-dimensionalization of Navier-Stokes�s equationsLecture 6 - Stream function formulation of Navier-Stokes equationsLecture 7 - Stokes flow past a cylinderLecture 8 - Stokes flow past a sphereLecture 9 - Elementary Lubrication TheoryLecture 10 - Hydrodynamics of Squeeze flowLecture 11 - Solution of arbitrary Stokes flowsLecture 12 - Mechanics of Swimming MicroorganismsLecture 13 - Viscous flow past a spherical dropLecture 14 - Migration of a viscous drop under Marangoni effectsLecture 15 - Singularities of Stokes flowsLecture 16 - Introduction to porous mediaLecture 17 - Flow through porous media � elementary geometriesLecture 18 - Flow through composite porous channelsLecture 19 - Modeling transport of particles inside capillariesLecture 20 - Modeling transport of microparticles � some applicationsLecture 21 - Introduction to ElctrokieticsLecture 22 - Basics on ElectrostaticsLecture 23 - Transport Equations for Electrokinetics, Part-ILecture 24 - Transport Equations for Electrokinetics, Part-IILecture 25 - Electric Double LayerLecture 26 - Electroosmotic flow (EOF) of ionized fluidLecture 27 - EOF in micro-channelLecture 28 - Non-linear EOF, Overlapping Debye LayerLecture 29 - Two-dimensional EOF

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Lecture 30 - EOF near heterogeneous surface potentialLecture 31 - Electroosmosis in hydrophobic surfaceLecture 32 - Numerical Methods for Boundary Value Problems (BVP)Lecture 33 - Numerical Methods for nonlinear BVPLecture 34 - Numerical Methods for coupled set of BVPLecture 35 - Numerical Methods for PDEsLecture 36 - Numerical Methods for transport equations, Part-ILecture 37 - Numerical Methods for transport equations, Part-IILecture 38 - Electrophoresis of charged colloids, Part-ILecture 39 - Electrophoresis of charged colloids, Part-IILecture 40 - Gel Electrophoresis

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NPTEL Video Course - Mathematics - NOC:Constrained and Unconstrained Optimization

Subject Co-ordinator - Dr. Debjani Chakraborty, Prof. A. Goswami

Co-ordinating Institute - IIT - Kharagpur

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Introduction to OptimizationLecture 2 - Assumptions and Mathematical Modeling of LPPLecture 3 - Geometrey of LPPLecture 4 - Graphical Solution of LPP - ILecture 5 - Graphical Solution of LPP - IILecture 6 - Solution of LPPLecture 7 - Simplex MethodLecture 8 - Introduction to BIG-M MethodLecture 9 - Algorithm of BIG-M MethodLecture 10 - Problems on BIG-M MethodLecture 11 - Two Phase MethodLecture 12 - Two Phase MethodLecture 13 - Special Cases of LPPLecture 14 - Degeneracy in LPPLecture 15 - Sensitivity Analysis - ILecture 16 - Sensitivity Analysis - IILecture 17 - Problems on Sensitivity AnalysisLecture 18 - Introduction to Duality Theory - ILecture 19 - Introduction to Duality Theory - IILecture 20 - Dual Simplex MethodLecture 21 - Examples on Dual Simplex MethodLecture 22 - Interger Linear ProgrammingLecture 23 - Interger Linear ProgrammingLecture 24 - IPPLecture 25 - Mixed Integer Programming ProblemLecture 26Lecture 27Lecture 28Lecture 29

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Lecture 30Lecture 31 - Introduction to Nonlinear programmingLecture 32 - Graphical Solution of NLPLecture 33 - Types of NLPLecture 34 - One dimentional unconstrained optimizationLecture 35 - Unconstrained OptimizationLecture 36 - Region Elimination Technique - 1Lecture 37 - Region Elimination Technique - 2Lecture 38 - Region Elimination Technique - 3Lecture 39 - Unconstrained OptimizationLecture 40 - Unconstrained OptimizationLecture 41 - Multivariate Unconstrained Optimization - 1Lecture 42 - Multivariate Unconstrained Optimization - 2Lecture 43 - Unconstrained OptimizationLecture 44 - NLP with Equality Constrained - 1Lecture 45 - NLP with Equality Constrained - 2Lecture 46 - Constrained NLP - 1Lecture 47 - Constrained NLP - 2Lecture 48 - Constrained OptimizationLecture 49 - Constrained OptimizationLecture 50 - KKTLecture 51 - Constrained OptimizationLecture 52 - Constrained OptimizationLecture 53 - Feasible DirectionLecture 54 - Penalty and barrier methodLecture 55 - Penalty methodLecture 56 - Penalty and barrier methodLecture 57 - Penalty and barrier methodLecture 58 - Dynamic programmingLecture 59 - Multi-Objective decision makingLecture 60 - Multi-Attribute decision making

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NPTEL Video Course - Mathematics - NOC:Matrix Solver

Subject Co-ordinator - Prof. Somnath Roy

Co-ordinating Institute - IIT - Kharagpur

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Introduction to Matrix Algebra - ILecture 2 - Introduction to Matrix Algebra - IILecture 3 - System of Linear EquationsLecture 4 - Determinant of a MatrixLecture 5 - Determinant of a Matrix (Continued...)Lecture 6 - Gauss EliminationLecture 7 - Gauss Elimination (Continued...)Lecture 8 - LU DecompositionLecture 9 - Gauss-Jordon MethodLecture 10 - Representation of Physical Systems as Matrix EquationsLecture 11 - Tridiagonal Matrix AlgorithmLecture 12 - Equations with Singular MatricesLecture 13 - Introduction to Vector SpaceLecture 14 - Vector SubspaceLecture 15 - Column Space and Nullspace of a MatrixLecture 16 - Finding Null Space of a MatrixLecture 17 - Solving Ax=b when A is SingularLecture 18 - Linear Independence and Spanning of a SubspaceLecture 19 - Basis and Dimension of a Vector SpaceLecture 20 - Four Fundamental Subspaces of a MatrixLecture 21 - Left and right inverse of a matrixLecture 22 - Orthogonality between the subspacesLecture 23 - Best estimateLecture 24 - Projection operation and linear transformationLecture 25 - Creating orthogonal basis vectorsLecture 26 - Gram-Schmidt and modified Gram-Schmidt algorithmsLecture 27 - Comparing GS and modified GSLecture 28 - Introduction to eigenvalues and eigenvectorsLecture 29 - Eigenvlues and eigenvectors for real symmetric matrix

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Lecture 30 - Positive definiteness of a matrixLecture 31 - Positive definiteness of a matrix (Continued...)Lecture 32 - Basic Iterative MethodsLecture 33 - Basic Iterative MethodsLecture 34 - Convergence Rate and Convergence Factor for Iterative MethodsLecture 35 - Numerical Experiments on ConvergenceLecture 36 - Steepest Descent MethodLecture 37 - Steepest Descent MethodLecture 38 - Steepest Descent MethodLecture 39 - Introduction to General Projection MethodsLecture 40 - Residue Norm and Minimum Residual AlgorithmLecture 41 - Developing computer programs for basic iterative methodsLecture 42 - Developing computer programs for projection based methodsLecture 43 - Introduction to Krylov subspace methodsLecture 44 - Krylov subspace methods for linear systemsLecture 45 - Iterative methods for solving linear systems using Krylov subspace methodsLecture 46 - Conjugate gradient methodsLecture 47 - Conjugate gradient methods (Continued...)Lecture 48 - Conjugate gradient methods (Continued...) and Introduction to GMRESLecture 49 - GMRES (Continued...)Lecture 50 - Lanczos Biorthogonalization and BCG AlgorithmLecture 51 - Numerical issues in BICG and polynomial based formulationLecture 52 - Conjugate gradient squared and Biconjugate gradient stabilizedLecture 53 - Line relaxation methodLecture 54 - Block relaxation methodLecture 55 - Domain Decomposition and Parallel ComputingLecture 56 - PreconditionersLecture 57 - Preconditioned conjugate gradientLecture 58 - Preconditioned GMRESLecture 59 - Multigrid methods - ILecture 60 - Multigrid methods - II

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NPTEL Video Course - Mathematics - NOC:Introduction to Abstract and Linear Algebra

Subject Co-ordinator - Prof.Sourav Mukhopadhyay

Co-ordinating Institute - IIT - Kharagpur

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Set TheoryLecture 2 - Set OperationsLecture 3 - Set Operations (Continued...)Lecture 4 - Set of setsLecture 5 - Binary relationLecture 6 - Equivalence relationLecture 7 - MappingLecture 8 - PermutationLecture 9 - Binary CompositionLecture 10 - GroupoidLecture 11 - GroupLecture 12 - Order of an elementLecture 13 - SubgroupLecture 14 - Cyclic GroupLecture 15 - Subgroup OperationsLecture 16 - Left CosetsLecture 17 - Right CosetsLecture 18 - Normal SubgroupLecture 19 - RingsLecture 20 - FieldLecture 21 - Vector SpacesLecture 22 - Sub-SpacesLecture 23 - Linear SpanLecture 24 - Basis of a Vector SpaceLecture 25 - Dimension of a Vector spaceLecture 26 - Complement of subspaceLecture 27 - Linear TransformationLecture 28 - Linear Transformation (Continued...)Lecture 29 - More on linear mapping

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Lecture 30 - Linear SpaceLecture 31 - Rank of a matrixLecture 32 - Rank of a matrix (Continued...)Lecture 33 - System of linear equationsLecture 34 - Row rank and Column rankLecture 35 - Eigen value of a matrixLecture 36 - Eigen VectorLecture 37 - Geometric multiplicityLecture 38 - More on eigen valueLecture 39 - Similar matricesLecture 40 - Diagonalisable

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NPTEL Video Course - Mathematics - NOC:Engineering Mathematics-I

Subject Co-ordinator - Prof. Jitendra Kumar

Co-ordinating Institute - IIT - Kharagpur

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Rolle�s TheoremLecture 2 - Mean Value TheoremsLecture 3 - Indeterminate Forms - Part 1Lecture 4 - Indeterminate Forms - Part 2Lecture 5 - Taylor Polynomial and Taylor SeriesLecture 6 - Limit of Functions of Two VariablesLecture 7 - Evaluation of Limit of Functions of Two VariablesLecture 8 - Continuity of Functions of Two VariablesLecture 9 - Partial Derivatives of Functions of Two VariablesLecture 10 - Partial Derivatives of Higher OrderLecture 11 - Derivative and DifferentiabilityLecture 12 - Differentiability of Functions of Two VariablesLecture 13 - Differentiability of Functions of Two Variables (Continued...)Lecture 14 - Differentiability of Functions of Two Variables (Continued...)Lecture 15 - Composite and Homogeneous FunctionsLecture 16 - Taylor�s Theorem for Functions of Two VariablesLecture 17 - Maxima and Minima of Functions of Two VariablesLecture 18 - Maxima and Minima of Functions of Two Variables (Continued...)Lecture 19 - Maxima and Minima of Functions of Two Variables (Continued...)Lecture 20 - Constrained Maxima and MinimaLecture 21 - Improper IntegralsLecture 22 - Improper Integrals (Continued...)Lecture 23 - Improper Integrals (Continued...)Lecture 24 - Improper Integrals (Continued...)Lecture 25 - Beta and Gamma FunctionLecture 26 - Beta and Gamma Function (Continued...)Lecture 27 - Differentiation Under Integral SignLecture 28 - Double IntegralsLecture 29 - Double Integrals (Continued...)

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Lecture 30 - Double Integrals (Continued...)Lecture 31 - Integral Calculus Double Integrals in Polar FormLecture 32 - Integral Calculus Double IntegralsLecture 33 - Integral Calculus Double IntegralsLecture 34 - Integral Calculus Triple IntegralsLecture 35 - Integral Calculus Triple Integrals (Continued...)Lecture 36 - System of Linear EquationsLecture 37 - System of Linear Equations Gauss EliminationLecture 38 - System of Linear Equations Gauss Elimination (Continued...)Lecture 39 - Linear Algebra - Vector SpacesLecture 40 - Linear Independence of VectorsLecture 41 - Vector Spaces Spanning SetLecture 42 - Vector Spaces Basis and DimensionLecture 43 - Rank of a MatrixLecture 44 - Linear TransformationsLecture 45 - Linear Transformations (Continued....)Lecture 46 - Eigenvalues and EigenvectorsLecture 47 - Eigenvalues and Eigenvectors (Continued...)Lecture 48 - Eigenvalues and Eigenvectors (Continued...)Lecture 49 - Eigenvalues and Eigenvectors (Continued...)Lecture 50 - Eigenvalues and EigenvectorsLecture 51 - Differential Equations - IntroductionLecture 52 - First Order Differential EquationsLecture 53 - Exact Differential EquationsLecture 54 - Exact Differential Equations (Continued...)Lecture 55 - First Order Linear Differential EquationsLecture 56 - Higher Order Linear Differential EquationsLecture 57 - Solution of Higher Order Homogeneous Linear EquationsLecture 58 - Solution of Higher Order Non-Homogeneous Linear EquationsLecture 59 - Solution of Higher Order Non-Homogeneous Linear Equations (Continued...)Lecture 60 - Cauchy-Euler Equations

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NPTEL Video Course - Mathematics - NOC:Integral and Vector Calculus

Subject Co-ordinator - Prof. Hari Shankar Mahato

Co-ordinating Institute - IIT - Kharagpur

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Partition, Riemann intergrability and One exampleLecture 2 - Partition, Riemann intergrability and One example (Continued...)Lecture 3 - Condition of integrabilityLecture 4 - Theorems on Riemann integrationsLecture 5 - ExamplesLecture 6 - Examples (Continued...)Lecture 7 - Reduction formulaLecture 8 - Reduction formula (Continued...)Lecture 9 - Improper IntegralLecture 10 - Improper Integral (Continued...)Lecture 11 - Improper Integral (Continued...)Lecture 12 - Improper Integral (Continued...)Lecture 13 - Introduction to Beta and Gamma FunctionLecture 14 - Beta and Gamma FunctionLecture 15 - Differentiation under Integral SignLecture 16 - Differentiation under Integral Sign (Continued...)Lecture 17 - Double IntegralLecture 18 - Double Integral over a Region ELecture 19 - Examples of Integral over a Region ELecture 20 - Change of variables in a Double IntegralLecture 21 - Change of order of IntegrationLecture 22 - Triple IntegralLecture 23 - Triple Integral (Continued...)Lecture 24 - Area of Plane RegionLecture 25 - Area of Plane Region (Continued...)Lecture 26 - RectificationLecture 27 - Rectification (Continued...)Lecture 28 - Surface IntegralLecture 29 - Surface Integral (Continued...)

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Lecture 30 - Surface Integral (Continued...)Lecture 31 - Volume Integral, Gauss Divergence TheoremLecture 32 - Vector CalculusLecture 33 - Limit, Continuity, DifferentiabilityLecture 34 - Successive DifferentiationLecture 35 - Integration of Vector FunctionLecture 36 - Gradient of a FunctionLecture 37 - Divergence and CurlLecture 38 - Divergence and Curl ExamplesLecture 39 - Divergence and Curl important IdentitiesLecture 40 - Level Surface Relevant TheoremsLecture 41 - Directional Derivative (Concept and Few Results)Lecture 42 - Directional Derivative (Concept and Few Results) (Continued...)Lecture 43 - Directional Derivatives, Level SurfacesLecture 44 - Application to MechanicsLecture 45 - Equation of Tangent, Unit Tangent VectorLecture 46 - Unit Normal, Unit binormal, Equation of Normal PlaneLecture 47 - Introduction and Derivation of Serret-Frenet Formula, few resultsLecture 48 - Example on binormal, normal tangent, Serret-Frenet FormulaLecture 49 - Osculating Plane, Rectifying plane, Normal planeLecture 50 - Application to Mechanics, Velocity, speed, accelerationLecture 51 - Angular Momentum, Newton's LawLecture 52 - Example on derivation of equation of motion of particleLecture 53 - Line IntegralLecture 54 - Surface integralLecture 55 - Surface integral (Continued...)Lecture 56 - Green's Theorem and ExampleLecture 57 - Volume integral, Gauss theoremLecture 58 - Gauss divergence theoremLecture 59 - Stoke's TheoremLecture 60 - Overview of Course

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NPTEL Video Course - Mathematics - NOC:Transform Calculus and its applications in Differential Equations

Subject Co-ordinator - Prof. A. Goswami

Co-ordinating Institute - IIT - Kharagpur

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Introduction to Integral Transform and Laplace TransformLecture 2 - Existence of Laplace TransformLecture 3 - Shifting Properties of Laplace TransformLecture 4 - Laplace Transform of Derivatives and Integration of a Function - ILecture 5 - Laplace Transform of Derivatives and Integration of a Function - IILecture 6 - Explanation of properties of Laplace Transform using ExamplesLecture 7 - Laplace Transform of Periodic FunctionLecture 8 - Laplace Transform of some special FunctionsLecture 9 - Error Function, Dirac Delta Function and their Laplace TransformLecture 10 - Bessel Function and its Laplace TransformLecture 11 - Introduction to Inverse Laplace TransformLecture 12 - Properties of Inverse Laplace TransformLecture 13 - Convolution and its ApplicationsLecture 14 - Evaluation of Integrals using Laplace TransformLecture 15 - Solution of Ordinary Differential Equations with constant coefficients using Laplace TransformLecture 16 - Solution of Ordinary Differential Equations with variable coefficients using Laplace TransformLecture 17 - Solution of Simultaneous Ordinary Differential Equations using Laplace TransformLecture 18 - Introduction to Integral Equation and its Solution ProcessLecture 19 - Introduction to Fourier SeriesLecture 20 - Fourier Series for Even and Odd FunctionsLecture 21 - Fourier Series of Functions having arbitrary period - ILecture 22 - Fourier Series of Functions having arbitrary period - IILecture 23 - Half Range Fourier SeriesLecture 24 - Parseval's Theorem and its ApplicationsLecture 25 - Complex form of Fourier SeriesLecture 26 - Fourier Integral RepresentationLecture 27 - Introduction to Fourier TransformLecture 28 - Derivation of Fourier Cosine Transform and Fourier Sine Transform of FunctionsLecture 29 - Evaluation of Fourier Transform of various functions

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Lecture 30 - Linearity Property and Shifting Properties of Fourier TransformLecture 31 - Change of Scale and Modulation Properties of Fourier TransformLecture 32 - Fourier Transform of Derivative and Integral of a FunctionLecture 33 - Applications of Properties of Fourier Transform - ILecture 34 - Applications of Properties of Fourier Transform - IILecture 35 - Fourier Transform of Convolution of two functionsLecture 36 - Parseval's Identity and its ApplicationLecture 37 - Evaluation of Definite Integrals using Properties of Fourier TransformLecture 38 - Fourier Transform of Dirac Delta FunctionLecture 39 - Representation of a function as Fourier IntegralLecture 40 - Applications of Fourier Transform to Ordinary Differential Equations - ILecture 41 - Applications of Fourier Transform to Ordinary Differential Equations - IILecture 42 - Solution of Integral Equations using Fourier TransformLecture 43 - Introduction to Partial Differential EquationsLecture 44 - Solution of Partial Differential Equations using Laplace TransformLecture 45 - Solution of Heat Equation and Wave Equation using Laplace TransformLecture 46 - Criteria for choosing Fourier Transform, Fourier Sine Transform, Fourier Cosine Transform in solving Partial Differential EquationsLecture 47 - Solution of Partial Differential Equations using Fourier Cosine Transform and Fourier Sine TransformLecture 48 - Solution of Partial Differential Equations using Fourier Transform - ILecture 49 - Solution of Partial Differential Equations using Fourier Transform - IILecture 50 - Solving problems on Partial Differential Equations using Transform TechniquesLecture 51 - Introduction to Finite Fourier TransformLecture 52 - Solution of Boundary Value Problems using Finite Fourier Transform - ILecture 53 - Solution of Boundary Value Problems using Finite Fourier Transform - IILecture 54 - Introduction to Mellin TransformLecture 55 - Properties of Mellin TransformLecture 56 - Examples of Mellin Transform - ILecture 57 - Examples of Mellin Transform - IILecture 58 - Introduction to Z-TransformLecture 59 - Properties of Z-TransformLecture 60 - Evaluation of Z-Transform of some functions

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NPTEL Video Course - Mathematics - NOC:Statistical Inference (2019)

Subject Co-ordinator - Prof. Somesh Kumar

Co-ordinating Institute - IIT - Kharagpur

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Introduction and Motivation - ILecture 2 - Introduction and Motivation - IILecture 3 - Basic Concepts of Point Estimations - ILecture 4 - Basic Concepts of Point Estimations - IILecture 5 - Basic Concepts of Point Estimations - IIILecture 6 - Basic Concepts of Point Estimations - IVLecture 7 - Finding Estimators - ILecture 8 - Finding Estimators - IILecture 9 - Finding Estimators - IIILecture 10 - Finding Estimators - IVLecture 11 - Finding Estimators - VLecture 12 - Finding Estimators - VILecture 13 - Properties of MLEs - ILecture 14 - Properties of MLEs - IILecture 15 - Lower Bounds for Variance - ILecture 16 - Lower Bounds for Variance - IILecture 17 - Lower Bounds for Variance - IIILecture 18 - Lower Bounds for Variance - IVLecture 19 - Lower Bounds for Variance - VLecture 20 - Lower Bounds for Variance - VILecture 21 - Lower Bounds for Variance - VIILecture 22 - Lower Bounds for Variance - VIIILecture 23 - Sufficiency - ILecture 24 - Sufficiency - IILecture 25 - Sufficiency and Information - ILecture 26 - Sufficiency and Information - IILecture 27 - Minimal Sufficiency, Completeness - ILecture 28 - Minimal Sufficiency, Completeness - IILecture 29 - UMVU Estimation, Ancillarity - I

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Lecture 30 - UMVU Estimation, Ancillarity - IILecture 31 - Testing of HypothesesLecture 32 - Testing of HypothesesLecture 33 - Neyman Pearson Fundamental Lemma - ILecture 34 - Neyman Pearson Fundamental Lemma - IILecture 35 - Application of NP-Lemma - ILecture 36 - Application of NP-Lemma - IILecture 37 - UMP Tests - ILecture 38 - UMP Tests - IILecture 39 - UMP Tests - IIILecture 40 - UMP Tests - IVLecture 41 - UMP Unbiased Tests - ILecture 42 - UMP Unbiased Tests - IILecture 43 - UMP Unbiased Tests - IIILecture 44 - UMP Unbiased Tests - IVLecture 45 - Applications of UMP Unbiased Tests - ILecture 46 - Applications of UMP Unbiased Tests - IILecture 47 - Unbiased Test for Normal Populations - ILecture 48 - Unbiased Test for Normal Populations - IILecture 49 - Unbiased Test for Normal Populations - IIILecture 50 - Unbiased Test for Normal Populations - IVLecture 51 - Likelihood Ratio Tests - ILecture 52 - Likelihood Ratio Tests - IILecture 53 - Likelihood Ratio Tests - IIILecture 54 - Likelihood Ratio Tests - IVLecture 55 - Likelihood Ratio Tests - VLecture 56 - Likelihood Ratio Tests - VILecture 57 - Likelihood Ratio Tests - VIILecture 58 - Likelihood Ratio Tests - VIIILecture 59 - Test for Goodness of Fit - ILecture 60 - Test for Goodness of Fit - IILecture 61 - Interval Estimation - ILecture 62 - Interval Estimation - IILecture 63 - Interval Estimation - IIILecture 64 - Interval Estimation - IV

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NPTEL Video Course - Mathematics - NOC:Mathematical Methods for Boundary Value Problems

Subject Co-ordinator - Prof. Somnath Bhattacharyya

Co-ordinating Institute - IIT - Kharagpur

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Strum-Liouville Problems, Linear BVPLecture 2 - Strum-Liouville Problems, Linear BVP (Continued...)Lecture 3 - Solution of BVPs by Eigen function expansionLecture 4 - Solution of BVPs by Eigen function expansion (Continued...)Lecture 5 - Solutions of linear parabolic, hyperbolic and elliptic PDEs with finite domain by Eigen function expansionsLecture 6 - Solutions of linear parabolic, hyperbolic and elliptic PDEs with finite domain by Eigen function expansions (Continued...)Lecture 7 - Green's Function for BVP and Dirichlet ProblemLecture 8 - Green's Function for BVP and Dirichlet Problem (Continued...)Lecture 9 - Numerical Techniques for IVP; Shooting Method for BVPLecture 10 - Numerical Techniques for IVP; Shooting Method for BVP (Continued...)Lecture 11 - Finite difference methods for linear BVP; Thomas AlgorithmLecture 12 - Finite difference methods for linear BVP; Thomas Algorithm (Continued...)Lecture 13 - Finite difference method for Higher-order BVP; Block tri-diagonal SystemLecture 14 - Finite difference method for Higher-order BVP; Block tri-diagonal System (Continued...)Lecture 15 - Iterative methods for nonlinear BVP; Control volume formulationLecture 16 - Iterative methods for nonlinear BVP; Control volume formulation (Continued...)Lecture 17 - Implicit scheme; Truncation error; Crank-Nicolson schemeLecture 18 - Implicit scheme; Truncation error; Crank-Nicolson scheme (Continued...)Lecture 19 - Stability analysis of numerical schemesLecture 20 - Alternating-Direction-Implicit Scheme; Successive-Over-Relaxation technique for Poisson equations

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NPTEL Video Course - Mathematics - An Introduction to Riemann Surfaces and Algebraic Curves: Complex 1-Tori and Elliptic Curves

Subject Co-ordinator - Dr. T.E. Venkata Balaji

Co-ordinating Institute - IIT - Madras

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - The Idea of a Riemann SurfaceLecture 2 - Simple Examples of Riemann SurfacesLecture 3 - Maximal Atlases and Holomorphic Maps of Riemann SurfacesLecture 4 - A Riemann Surface Structure on a CylinderLecture 5 - A Riemann Surface Structure on a TorusLecture 6 - Riemann Surface Structures on Cylinders and Tori via Covering SpacesLecture 7 - Moebius Transformations Make up Fundamental Groups of Riemann SurfacesLecture 8 - Homotopy and the First Fundamental GroupLecture 9 - A First Classification of Riemann SurfacesLecture 10 - The Importance of the Path-lifting PropertyLecture 11 - Fundamental groups as Fibres of the Universal covering SpaceLecture 12 - The Monodromy ActionLecture 13 - The Universal covering as a Hausdorff Topological SpaceLecture 14 - The Construction of the Universal Covering MapLecture 15 - Completion of the Construction of the Universal CoveringLecture 16 - Completion of the Construction of the Universal CoveringLecture 17 - The Riemann Surface Structure on the Topological Covering of a Riemann SurfaceLecture 18 - Riemann Surfaces with Universal Covering the Plane or the SphereLecture 19 - Classifying Complex CylindersLecture 20 - Characterizing Moebius Transformations with a Single Fixed PointLecture 21 - Characterizing Moebius Transformations with Two Fixed PointsLecture 22 - Torsion-freeness of the Fundamental Group of a Riemann SurfaceLecture 23 - Characterizing Riemann Surface Structures on Quotients of the Upper Half-Plane with Abelian Fundamental GroupsLecture 24 - Classifying Annuli up to Holomorphic IsomorphismLecture 25 - Orbits of the Integral Unimodular Group in the Upper Half-PlaneLecture 26 - Galois Coverings are precisely Quotients by Properly Discontinuous Free ActionsLecture 27 - Local Actions at the Region of Discontinuity of a Kleinian Subgroup of Moebius Transformations

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Lecture 28 - Quotients by Kleinian Subgroups give rise to Riemann SurfacesLecture 29 - The Unimodular Group is KleinianLecture 30 - The Necessity of Elliptic Functions for the Classification of Complex ToriLecture 31 - The Uniqueness Property of the Weierstrass Phe-function associated to a Lattice in the PlaneLecture 32 - The First Order Degree Two Cubic Ordinary Differential Equation satisfied by the Weierstrass Phe-functionLecture 33 - The Values of the Weierstrass Phe-function at the Zeros of its Derivative are nonvanishing Analytic Functions on the Upper Half-PlaneLecture 34 - The Construction of a Modular Form of Weight Two on the Upper Half-PlaneLecture 35 - The Fundamental Functional Equations satisfied by the Modular Form of Weight Two on the Upper Half-PlaneLecture 36 - The Weight Two Modular Form assumes Real Values on the Imaginary Axis in the Upper Half-planeLecture 37 - The Weight Two Modular Form Vanishes at InfinityLecture 38 - The Weight Two Modular Form Decays Exponentially in a Neighbourhood of InfinityLecture 39 - A Suitable Restriction of the Weight Two Modular Form is a Holomorphic Conformal Isomorphism onto the Upper Half-PlaneLecture 40 - The J-Invariant of a Complex Torus (or) of an Algebraic Elliptic CurveLecture 41 - A Fundamental Region in the Upper Half-Plane for the Elliptic Modular J-InvariantLecture 42 - The Fundamental Region in the Upper Half-Plane for the Unimodular GroupLecture 43 - A Region in the Upper Half-Plane Meeting Each Unimodular Orbit Exactly OnceLecture 44 - Moduli of Elliptic CurvesLecture 45 - Punctured Complex Tori are Elliptic Algebraic Affine Plane Cubic Curves in Complex 2-SpaceLecture 46 - The Natural Riemann Surface Structure on an Algebraic Affine Nonsingular Plane CurveLecture 47 - Complex Projective 2-Space as a Compact Complex Manifold of Dimension TwoLecture 48 - Complex Tori are the same as Elliptic Algebraic Projective Curves

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NPTEL Video Course - Mathematics - Linear Algebra

Subject Co-ordinator - Dr. K.C. Sivakumar

Co-ordinating Institute - IIT - Madras

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Introduction to the Course ContentsLecture 2 - Linear EquationsLecture 3a - Equivalent Systems of Linear Equations ILecture 3b - Equivalent Systems of Linear Equations IILecture 4 - Row-reduced Echelon MatricesLecture 5 - Row-reduced Echelon Matrices and Non-homogeneous EquationsLecture 6 - Elementary Matrices, Homogeneous Equations and Non-homogeneous EquationsLecture 7 - Invertible matrices, Homogeneous Equations Non-homogeneous EquationsLecture 8 - Vector spacesLecture 9 - Elementary Properties in Vector Spaces. SubspacesLecture 10 - Subspaces (Continued...), Spanning Sets, Linear Independence, DependenceLecture 11 - Basis for a vector spaceLecture 12 - Dimension of a vector spaceLecture 13 - Dimensions of Sums of SubspacesLecture 14 - Linear TransformationsLecture 15 - The Null Space and the Range Space of a Linear TransformationLecture 16 - The Rank-Nullity-Dimension Theorem. Isomorphisms Between Vector SpacesLecture 17 - Isomorphic Vector Spaces, Equality of the Row-rank and the Column-rank - ILecture 18 - Equality of the Row-rank and the Column-rank - IILecture 19 - The Matrix of a Linear TransformationLecture 20 - Matrix for the Composition and the Inverse. Similarity TransformationLecture 21 - Linear Functionals. The Dual Space. Dual Basis - ILecture 22 - Dual Basis II. Subspace Annihilators - ILecture 23 - Subspace Annihilators - IILecture 24 - The Double Dual. The Double AnnihilatorLecture 25 - The Transpose of a Linear Transformation. Matrices of a Linear Transformation and its TransposeLecture 26 - Eigenvalues and Eigenvectors of Linear OperatorsLecture 27 - Diagonalization of Linear Operators. A CharacterizationLecture 28 - The Minimal Polynomial

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Lecture 29 - The Cayley-Hamilton TheoremLecture 30 - Invariant SubspacesLecture 31 - Triangulability, Diagonalization in Terms of the Minimal PolynomialLecture 32 - Independent Subspaces and Projection OperatorsLecture 33 - Direct Sum Decompositions and Projection Operators - ILecture 34 - Direct Sum Decompositions and Projection Operators - IILecture 35 - The Primary Decomposition Theorem and Jordan DecompositionLecture 36 - Cyclic Subspaces and AnnihilatorsLecture 37 - The Cyclic Decomposition Theorem - ILecture 38 - The Cyclic Decomposition Theorem - II. The Rational FormLecture 39 - Inner Product SpacesLecture 40 - Norms on Vector spaces. The Gram-Schmidt Procedure ILecture 41 - The Gram-Schmidt Procedure II. The QR DecompositionLecture 42 - Bessel's Inequality, Parseval's Indentity, Best ApproximationLecture 43 - Best ApproximationLecture 44 - Orthogonal Complementary Subspaces, Orthogonal ProjectionsLecture 45 - Projection Theorem. Linear FunctionalsLecture 46 - The Adjoint OperatorLecture 47 - Properties of the Adjoint Operation. Inner Product Space IsomorphismLecture 48 - Unitary OperatorsLecture 49 - Unitary operators - II. Self-Adjoint Operators - I.Lecture 50 - Self-Adjoint Operators - II - Spectral TheoremLecture 51 - Normal Operators - Spectral Theorem

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NPTEL Video Course - Mathematics - Mathematical Logic

Subject Co-ordinator - Prof. Arindama Singh

Co-ordinating Institute - IIT - Madras

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Sets and StringsLecture 2 - Syntax of Propositional LogicLecture 3 - Unique ParsingLecture 4 - Semantics of PLLecture 5 - Consequences and EquivalencesLecture 6 - Five results about PLLecture 7 - Calculations and Informal ProofsLecture 8 - More Informal ProofsLecture 9 - Normal formsLecture 10 - SAT and 3SATLecture 11 - Horn-SAT and ResolutionLecture 12 - ResolutionLecture 13 - Adequacy of ResolutionLecture 14 - Adequacy and Resolution StrategiesLecture 15 - Propositional Calculus (PC)Lecture 16 - Some Results about PCLecture 17 - Arguing with ProofsLecture 18 - Adequacy of PCLecture 19 - Compactness & Analytic TableauLecture 20 - Examples of Tableau ProofsLecture 21 - Adequacy of TableauxLecture 22 - Syntax of First order Logic (FL)Lecture 23 - Symbolization & Scope of QuantifiersLecture 24 - Hurdles in giving MeaningLecture 25 - Semantics of FLLecture 26 - Relevance LemmaLecture 27 - Validity, Satisfiability & EquivalenceLecture 28 - Six Results about FLLecture 29 - Laws, Calculation & Informal Proof

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Lecture 30 - Quantifier Laws and ConsequencesLecture 31 - More Proofs and Prenex FormLecture 32 - Prenex Form ConversionLecture 33 - Skolem FormLecture 34 - Syntatic InterpretationLecture 35 - Herbrand's TheoremLecture 36 - Most General UnifiersLecture 37 - Resolution RulesLecture 38 - Resolution ExamplesLecture 39 - Ariomatic System FCLecture 40 - FC and Semidecidability of FLLecture 41 - Analytic Tableau for FLLecture 42 - Godels Incompleteness Theorems

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NPTEL Video Course - Mathematics - Real Analysis

Subject Co-ordinator - Prof. S.H. Kulkarni

Co-ordinating Institute - IIT - Madras

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - IntroductionLecture 2 - Functions and RelationsLecture 3 - Finite and Infinite SetsLecture 4 - Countable SetsLecture 5 - Uncountable Sets, Cardinal NumberLecture 6 - Real Number SystemLecture 7 - LUB AxiomLecture 8 - Sequences of Real NumbersLecture 9 - Sequences of Real Numbers - (Continued.)Lecture 10 - Sequences of Real Numbers - (Continued.)Lecture 11 - Infinite Series of Real NumbersLecture 12 - Series of nonnegative Real NumbersLecture 13 - Conditional ConvergenceLecture 14 - Metric SpacesLecture 15 - Metric SpacesLecture 16 - Balls and SpheresLecture 17 - Open SetsLecture 18 - Closure Points, Limit Points and isolated PointsLecture 19 - Closed setsLecture 20 - Sequences in Metric SpacesLecture 21 - CompletenessLecture 22 - Baire Category TheoremLecture 23 - Limit and Continuity of a Function defined on a Metric spaceLecture 24 - Continuous Functions on a Metric SpaceLecture 25 - Uniform ContinuityLecture 26 - ConnectednessLecture 27 - Connected SetsLecture 28 - CompactnessLecture 29 - Compactness (Continued.)

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Lecture 30 - Characterizations of Compact SetsLecture 31 - Continuous Functions on Compact SetsLecture 32 - Types of DiscontinuityLecture 33 - DifferentiationLecture 34 - Mean Value TheoremsLecture 35 - Mean Value Theorems (Continued.)Lecture 36 - Taylor's TheoremLecture 37 - Differentiation of Vector Valued FunctionsLecture 38 - IntegrationLecture 39 - IntegrabilityLecture 40 - Integrable FunctionsLecture 41 - Integrable Functions (Continued.)Lecture 42 - Integration as a Limit of SumLecture 43 - Integration and DifferentiationLecture 44 - Integration of Vector Valued FunctionsLecture 45 - More Theorems on IntegralsLecture 46 - Sequences and Series of FunctionsLecture 47 - Uniform ConvergenceLecture 48 - Uniform Convergence and IntegrationLecture 49 - Uniform Convergence and DifferentiationLecture 50 - Construction of Everywhere Continuous Nowhere Differentiable FunctionLecture 51 - Approximation of a Continuous Function by PolynomialsLecture 52 - Equicontinuous family of Functions

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NPTEL Video Course - Mathematics - Dynamic Data Assimilation: An Introduction

Subject Co-ordinator - Prof. S. Lakshmivarahan

Co-ordinating Institute - IIT - Madras

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - An OverviewLecture 2 - Data Mining, Data assimilation and predictionLecture 3 - A classification of forecast errorsLecture 4 - Finite Dimensional Vector SpaceLecture 5 - MatricesLecture 6 - Matrices (Continued...)Lecture 7 - Multi-variate CalculusLecture 8 - Optimization in Finite Dimensional Vector spacesLecture 9 - Deterministic, Static, linear Inverse (well-posed) ProblemsLecture 10 - Deterministic, Static, Linear Inverse (Ill-posed) ProblemsLecture 11 - A Geometric View � ProjectionsLecture 12 - Deterministic, Static, nonlinear Inverse ProblemsLecture 13 - On-line Least SquaresLecture 14 - Examples of static inverse problemsLecture 15 - Interlude and a Way ForwardLecture 16 - Matrix Decomposition AlgorithmsLecture 17 - Matrix Decomposition Algorithms (Continued...)Lecture 18 - Minimization algorithmsLecture 19 - Minimization algorithms (Continued...)Lecture 20 - Inverse problems in deterministicLecture 21 - Inverse problems in deterministic (Continued...)Lecture 22 - Forward sensitivity methodLecture 23 - Relation between FSM and 4DVARLecture 24 - Statistical EstimationLecture 25 - Statistical Least SquaresLecture 26 - Maximum Likelihood MethodLecture 27 - Bayesian EstimationLecture 28 - From Gauss to Kalman-Linear Minimum Variance EstimationLecture 29 - Initialization Classical Method

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Lecture 30 - Optimal interpolationsLecture 31 - A Bayesian Formation-3D-VAR methodsLecture 32 - Linear Stochastic Dynamics - Kalman FilterLecture 33 - Linear Stochastic Dynamics - Kalman Filter (Continued...)Lecture 34 - Linear Stochastic Dynamics - Kalman Filter (Continued...)Lecture 35 - Covariance Square Root FilterLecture 36 - Nonlinear FilteringLecture 37 - Ensemble Reduced Rank FilterLecture 38 - Basic nudging methodsLecture 39 - Deterministic predictabilityLecture 40 - Predictability A stochastic view and Summary

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NPTEL Video Course - Mathematics - NOC:An Invitation to Mathematics

Subject Co-ordinator - Prof. Sankaran Vishwanath

Co-ordinating Institute - Institute of Mathematical Sciences

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - IntroductionLecture 2 - Long divisionLecture 3 - Applications of Long divisionLecture 4 - Lagrange interpolationLecture 5 - The 0-1 idea in other contexts - dot and cross productLecture 6 - Taylors formulaLecture 7 - The Chebyshev polynomialsLecture 8 - Counting number of monomials - several variablesLecture 9 - Permutations, combinations and the binomial theoremLecture 10 - Combinations with repetition, and counting monomialsLecture 11 - Combinations with restrictions, recurrence relationsLecture 12 - Fibonacci numbers; an identity and a bijective proofLecture 13 - Permutations and cycle typeLecture 14 - The sign of a permutation, composition of permutationsLecture 15 - Rules for drawing tangle diagramsLecture 16 - Signs and cycle decompositionsLecture 17 - Sorting lists of numbers, and crossings in tangle diagramsLecture 18 - Real and integer valued polynomialsLecture 19 - Integer valued polynomials revisitedLecture 20 - Functions on the real line, continuityLecture 21 - The intermediate value propertyLecture 22 - Visualizing functionsLecture 23 - Functions on the plane, Rigid motionsLecture 24 - More examples of functions on the plane, dilationsLecture 25 - Composition of functionsLecture 26 - Affine and Linear transformationsLecture 27 - Length and Area dilation, the derivativeLecture 28 - Examples-ILecture 29 - Examples-II

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Lecture 30 - Linear equations, Lagrange interpolation revisitedLecture 31 - Completed Matrices in combinatoricsLecture 32 - Polynomials acting on matricesLecture 33 - Divisibility, prime numbersLecture 34 - Congruences, Modular arithmeticLecture 35 - The Chinese remainder theoremLecture 36 - The Euclidean algorithm, the 0-1 idea and the Chinese remainder theorem

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NPTEL Video Course - Mathematics - Advanced Complex Analysis

Subject Co-ordinator - Dr. T.E. Venkata Balaji

Co-ordinating Institute - IIT - Madras

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Fundamental Theorems Connected with Zeros of Analytic FunctionsLecture 2 - The Argument (Counting) Principle, Rouche's Theorem and The Fundamental Theorem of AlgebraLecture 3 - Morera's Theorem and Normal Limits of Analytic FunctionsLecture 4 - Hurwitz's Theorem and Normal Limits of Univalent FunctionsLecture 5 - Local Constancy of Multiplicities of Assumed ValuesLecture 6 - The Open Mapping TheoremLecture 7 - Introduction to the Inverse Function TheoremLecture 8 - Completion of the Proof of the Inverse Function TheoremLecture 9 - Univalent Analytic Functions have never-zero Derivatives and are Analytic IsomorphismsLecture 10 - Introduction to the Implicit Function TheoremLecture 11 - Proof of the Implicit Function TheoremLecture 12 - Proof of the Implicit Function TheoremLecture 13 - Doing Complex Analysis on a Real SurfaceLecture 14 - F(z,w)=0 is naturally a Riemann SurfaceLecture 15 - Constructing the Riemann Surface for the Complex LogarithmLecture 16 - Constructing the Riemann Surface for the m-th root functionLecture 17 - The Riemann Surface for the functional inverse of an analytic mapping at a critical pointLecture 18 - The Algebraic nature of the functional inverses of an analytic mapping at a critical pointLecture 19 - The Idea of a Direct Analytic Continuation or an Analytic ExtensionLecture 20 - General or Indirect Analytic Continuation and the Lipschitz Nature of the Radius of ConvergenceLecture 21 - Analytic Continuation Along Paths via Power Series Part ALecture 22 - Analytic Continuation Along Paths via Power Series Part BLecture 23 - Continuity of Coefficients occurring in Families of Power Series defining Analytic Continuations along PathsLecture 24 - Analytic Continuability along PathsLecture 25 - Maximal Domains of Direct and Indirect Analytic ContinuationLecture 26 - Deducing the Second (Simply Connected) Version of the Monodromy Theorem from the First (Homotopy) VersionLecture 27 - Existence and Uniqueness of Analytic Continuations on Nearby PathsLecture 28 - Proof of the First (Homotopy) Version of the Monodromy TheoremLecture 29 - Proof of the Algebraic Nature of Analytic Branches of the Functional Inverse of an Analytic Function at a Critical Point

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Lecture 30 - The Mean-Value Property, Harmonic Functions and the Maximum PrincipleLecture 31 - Proofs of Maximum Principles and Introduction to Schwarz LemmaLecture 32 - Proof of Schwarz Lemma and Uniqueness of Riemann MappingsLecture 33 - Reducing Existence of Riemann Mappings to Hyperbolic Geometry of Sub-domains of the Unit DiscLecture 34 - Differential or Infinitesimal Schwarzs Lemma, Picks Lemma, Hyperbolic Arclengths, Metric and Geodesics on the Unit DiscLecture 35 - Differential or Infinitesimal Schwarzs Lemma, Picks Lemma, Hyperbolic Arclengths, Metric and Geodesics on the Unit DiscLecture 36 - Hyperbolic Geodesics for the Hyperbolic Metric on the Unit DiscLecture 37 - Schwarz-Pick Lemma for the Hyperbolic Metric on the Unit DiscLecture 38 - Arzela-Ascoli TheoremLecture 39 - Completion of the Proof of the Arzela-Ascoli Theorem and Introduction to Montels TheoremLecture 40 - The Proof of Montels TheoremLecture 41 - The Candidate for a Riemann MappingLecture 42 - Completion of Proof of The Riemann Mapping TheoremLecture 43 - Completion of Proof of The Riemann Mapping Theorem

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NPTEL Video Course - Mathematics - NOC:Discrete Mathematics

Subject Co-ordinator - Prof. Sourav Chakraborty

Co-ordinating Institute - IIT - Madras

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Course IntroductionLecture 2 - Sets, Relations and FunctionsLecture 3 - Propositional Logic and Predicate LogicLecture 4 - Propositional Logic and Predicate Logic (Part 2)Lecture 5 - Elementary Number TheoryLecture 6 - Formal ProofsLecture 7 - Direct ProofsLecture 8 - Case StudyLecture 9 - Case Study (Part 2)Lecture 10 - Sets, Relations, Function and LogicLecture 11 - Proof by Contradiction (Part 1)Lecture 12 - Proof by Contradiction (Part 2)Lecture 13 - Proof by ContrapositionLecture 14 - Proof by Counter ExampleLecture 15 - Mathematical Induction (Part 1)Lecture 16 - Mathematical Induction (Part 2)Lecture 17 - Mathematical Induction (Part 3)Lecture 18 - Mathematical Induction (Part 4)Lecture 19 - Mathematical Induction (Part 5)Lecture 20 - Mathematical Induction (Part 6)Lecture 21 - Mathematical Induction (Part 7)Lecture 22 - Mathematical Induction (Part 8)Lecture 23 - Introduction to Graph TheoryLecture 24 - Handshake ProblemLecture 25 - Tournament ProblemLecture 26 - Tournament Problem (Part 2)Lecture 27 - Ramsey ProblemLecture 28 - Ramsey Problem (Part 2)Lecture 29 - Properties of Graphs

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Lecture 30 - Problem 1Lecture 31 - Problem 2Lecture 32 - Problem 3 & 4Lecture 33 - Counting for SelectionLecture 34 - Counting for DistributionLecture 35 - Counting for Distribution (Part 2)Lecture 36 - Some Counting ProblemsLecture 37 - Counting using Recurrence RelationsLecture 38 - Counting using Recurrence Relations (Part 2)Lecture 39 - Solving Recurrence Relations (Part 1)Lecture 40 - Solving Recurrence Relations (Part 2)Lecture 41 - Asymptotic Relations (Part 1)Lecture 42 - Asymptotic Relations (Part 2)Lecture 43 - Asymptotic Relations (Part 3)Lecture 44 - Asymptotic Relations (Part 4)Lecture 45 - Generating Functions (Part 1)Lecture 46 - Generating Functions (Part 2)Lecture 47 - Generating Functions (Part 3)Lecture 48 - Generating Functions (Part 4)Lecture 49 - Proof TechniquesLecture 50 - ModelingLecture 51 - Combinatorics

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Page 128: NPTEL Video Lecture Topic List - Created by LinuXpert ... · NPTEL Video Course - Mathematics - Measure and Integration Subject Co-ordinator - Prof. Inder K Rana Co-ordinating Institute

NPTEL Video Course - Mathematics - Advanced Complex Analysis - Part 2

Subject Co-ordinator - Dr. T.E. Venkata Balaji

Co-ordinating Institute - IIT - Madras

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Properties of the Image of an Analytic Function - Introduction to the Picard TheoremsLecture 2 - Recalling Singularities of Analytic Functions - Non-isolated and Isolated Removable, Pole and Essential SingularitiesLecture 3 - Recalling Riemann's Theorem on Removable SingularitiesLecture 4 - Casorati-Weierstrass Theorem; Dealing with the Point at Infinity -- Riemann Sphere and Riemann Stereographic ProjectionLecture 5 - Neighborhood of Infinity, Limit at Infinity and Infinity as an Isolated SingularityLecture 6 - Studying Infinity - Formulating Epsilon-Delta Definitions for Infinite Limits and Limits at InfinityLecture 7 - When is a function analytic at infinity ?Lecture 8 - Laurent Expansion at Infinity and Riemann\'s Removable Singularities Theorem for the Point at InfinityLecture 9 - The Generalized Liouville Theorem - Little Brother of Little Picard and Analogue of Casorati-Weierstrass; Failure of Cauchy\'s Theorem at InfinityLecture 10 - Morera\'s Theorem at Infinity, Infinity as a Pole and Behaviour at Infinity of Rational and Meromorphic FunctionsLecture 11 - Residue at Infinity and Introduction to the Residue Theorem for the Extended Complex Plane - Residue Theorem for the Point at InfinityLecture 12 - Proofs of Two Avatars of the Residue Theorem for the Extended Complex Plane and Applications of the Residue at InfinityLecture 13 - Infinity as an Essential Singularity and Transcendental Entire FunctionsLecture 14 - Meromorphic Functions on the Extended Complex Plane are Precisely Quotients of PolynomialsLecture 15 - The Ubiquity of Meromorphic Functions - The Nerves of the Geometric Network Bridging Algebra, Analysis and TopologyLecture 16 - Continuity of Meromorphic Functions at Poles and Topologies of Spaces of FunctionsLecture 17 - Why Normal Convergence, but Not Globally Uniform Convergence, is the Inevitable in Complex AnalysisLecture 18 - Measuring Distances to Infinity, the Function Infinity and Normal Convergence of Holomorphic Functions in the Spherical MetricLecture 19 - The Invariance Under Inversion of the Spherical Metric on the Extended Complex PlaneLecture 20 - Introduction to Hurwitz\'s Theorem for Normal Convergence of Holomorphic Functions in the Spherical MetricLecture 21 - Completion of Proof of Hurwitz\'s Theorem for Normal Limits of Analytic Functions in the Spherical MetricLecture 22 - Hurwitz\'s Theorem for Normal Limits of Meromorphic Functions in the Spherical MetricLecture 23 - What could the Derivative of a Meromorphic Function Relative to the Spherical Metric Possibly Be ?Lecture 24 - Defining the Spherical Derivative of a Meromorphic FunctionLecture 25 - Well-definedness of the Spherical Derivative of a Meromorphic Function at a Pole and Inversion-invariance of the Spherical DerivativeLecture 26 - Topological Preliminaries - Translating Compactness into BoundednessLecture 27 - Introduction to the Arzela-Ascoli Theorem - Passing from abstract Compactness to verifiable EquicontinuityLecture 28 - Proof of the Arzela-Ascoli Theorem for Functions - Abstract Compactness Implies EquicontinuityLecture 29 - Proof of the Arzela-Ascoli Theorem for Functions - Equicontinuity Implies Compactness

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Lecture 30 - Introduction to the Montel Theorem - the Holomorphic Avatar of the Arzela-Ascoli Theorem & Why you get Equicontinuity for FreeLecture 31 - Completion of Proof of the Montel Theorem - the Holomorphic Avatar of the Arzela-Ascoli TheoremLecture 32 - Introduction to Marty\'s Theorem - the Meromorphic Avatar of the Montel & Arzela-Ascoli TheoremsLecture 33 - Proof of one direction of Marty\'s Theorem - the Meromorphic Avatar of the Montel & Arzela-Ascoli Theorems - Normal Uniform Boundedness of Spherical Derivatives Implies Normal Sequential CompactnessLecture 34 - Proof of the other direction of Marty\'s Theorem - the Meromorphic Avatar of the Montel & Arzela-Ascoli Theorems - Normal Sequential Compactness Implies Normal Uniform Boundedness of Spherical DerivativesLecture 35 - Normal Convergence at Infinity and Hurwitz\'s Theorems for Normal Limits of Analytic and Meromorphic Functions at InfinityLecture 36 - Normal Sequential Compactness, Normal Uniform Boundedness and Montel\'s & Marty\'s Theorems at InfinityLecture 37 - Local Analysis of Normality and the Zooming Process - Motivation for Zalcman\'s LemmaLecture 38 - Characterizing Normality at a Point by the Zooming Process and the Motivation for Zalcman\'s LemmaLecture 39 - Local Analysis of Normality and the Zooming Process - Motivation for Zalcman\'s LemmaLecture 40 - Montel\'s Deep Theorem - The Fundamental Criterion for Normality or Fundamental Normality Test based on Omission of ValuesLecture 41 - Proofs of the Great and Little Picard TheoremsLecture 42 - Royden\'s Theorem on Normality Based On Growth Of DerivativesLecture 43 - Schottky\'s Theorem - Uniform Boundedness from a Point to a Neighbourhood & Problem Solving Session

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NPTEL Video Course - Mathematics - Basic Algebraic Geometry : Varieties, Morphisms, Local Rings, Function Fields and Nonsingularity

Subject Co-ordinator - Dr. T.E. Venkata Balaji

Co-ordinating Institute - IIT - Madras

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - What is Algebraic Geometry?Lecture 2 - The Zariski Topology and Affine SpaceLecture 3 - Going back and forth between subsets and idealsLecture 4 - Irreducibility in the Zariski TopologyLecture 5 - Irreducible Closed Subsets Correspond to Ideals Whose Radicals are PrimeLecture 6 - Understanding the Zariski Topology on the Affine Line; The Noetherian property in Topology and in AlgebraLecture 7 - Basic Algebraic GeometryLecture 8 - Topological Dimension, Krull Dimension and Heights of Prime IdealsLecture 9 - The Ring of Polynomial Functions on an Affine VarietyLecture 10 - Geometric Hypersurfaces are Precisely Algebraic HypersurfacesLecture 11 - Why Should We Study Affine Coordinate Rings of Functions on Affine Varieties ?Lecture 12 - Capturing an Affine Variety Topologically From the Maximal Spectrum of its Ring of FunctionsLecture 13 - Analyzing Open Sets and Basic Open Sets for the Zariski TopologyLecture 14 - The Ring of Functions on a Basic Open Set in the Zariski TopologyLecture 15 - Quasi-Compactness in the Zariski Topology; Regularity of a Function at a point of an Affine VarietyLecture 16 - What is a Global Regular Function on a Quasi-Affine Variety?Lecture 17 - Characterizing Affine Varieties; Defining Morphisms between Affine or Quasi-Affine VarietiesLecture 18 - Translating Morphisms into Affines as k-Algebra maps and the Grand Hilbert NullstellensatzLecture 19 - Morphisms into an Affine Correspond to k-Algebra Homomorphisms from its Coordinate Ring of FunctionsLecture 20 - The Coordinate Ring of an Affine Variety Determines the Affine Variety and is Intrinsic to itLecture 21 - Automorphisms of Affine Spaces and of Polynomial Rings - The Jacobian Conjecture; The Punctured Plane is Not AffineLecture 22 - The Various Avatars of Projective n-spaceLecture 23 - Gluing (n+1) copies of Affine n-Space to Produce Projective n-space in Topology, Manifold Theory and Algebraic Geometry; The Key to the Definition of a Homogeneous IdealLecture 24 - Translating Projective Geometry into Graded Rings and Homogeneous IdealsLecture 25 - Expanding the Category of Varieties to Include Projective and Quasi-Projective VarietiesLecture 26 - Translating Homogeneous Localisation into Geometry and BackLecture 27 - Adding a Variable is Undone by Homogenous Localization - What is the Geometric Significance of this Algebraic Fact ?Lecture 28 - Doing Calculus Without Limits in Geometry ?Lecture 29 - The Birth of Local Rings in Geometry and in Algebra

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Lecture 30 - The Formula for the Local Ring at a Point of a Projective Variety Or Playing with Localisations, Quotients, Homogenisation and Dehomogenisation !Lecture 31 - The Field of Rational Functions or Function Field of a Variety - The Local Ring at the Generic PointLecture 32 - Fields of Rational Functions or Function Fields of Affine and Projective Varieties and their Relationships with DimensionsLecture 33 - Global Regular Functions on Projective Varieties are Simply the ConstantsLecture 34 - The d-Uple Embedding and the Non-Intrinsic Nature of the Homogeneous Coordinate Ring of a Projective VarietyLecture 35 - The Importance of Local Rings - A Morphism is an Isomorphism if it is a Homeomorphism and Induces Isomorphisms at the Level of Local RingsLecture 36 - The Importance of Local Rings - A Rational Function in Every Local Ring is Globally RegularLecture 37 - Geometric Meaning of Isomorphism of Local Rings - Local Rings are Almost GlobalLecture 38 - Local Ring Isomorphism,Equals Function Field Isomorphism, Equals BirationalityLecture 39 - Why Local Rings Provide Calculus Without Limits for Algebraic Geometry Pun Intended!Lecture 40 - How Local Rings Detect Smoothness or Nonsingularity in Algebraic GeometryLecture 41 - Any Variety is a Smooth Manifold with or without Non-Smooth BoundaryLecture 42 - Any Variety is a Smooth Hypersurface On an Open Dense Subset

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NPTEL Video Course - Mathematics - NOC:Introduction to Commutative Algebra

Subject Co-ordinator - Prof. A.V.Jayanthan

Co-ordinating Institute - IIT - Madras

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Review of Ring TheoryLecture 2 - Review of Ring Theory (Continued...)Lecture 3 - Ideals in commutative ringsLecture 4 - Operations on idealsLecture 5 - Properties of prime idealsLecture 6 - Colon and Radical of idealsLecture 7 - Radicals, extension and contraction of idealsLecture 8 - Modules and homomorphismsLecture 9 - Isomorphism theorems and Operations on modulesLecture 10 - Operations on modules (Continued...)Lecture 11 - Module homomorphism and determinant trickLecture 12 - Nakayama�s lemma and exact sequencesLecture 13 - Exact sequences (Continued...)Lecture 14 - Homomorphisms and Tensor productsLecture 15 - Properties of tensor productsLecture 16 - Properties of tensor products (Continued...)Lecture 17 - Tensor product of AlgebrasLecture 18 - LocalizationLecture 19 - Localization (Continued...)Lecture 20 - Local propertiesLecture 21 - Further properties of localizationLecture 22 - Intergral dependenceLecture 23 - Integral extensionsLecture 24 - Lying over and Going-up theoremsLecture 25 - Going-down theoremLecture 26 - Going-down theorem (Continued...)Lecture 27 - Chain conditionsLecture 28 - Noetherian and Artinian modulesLecture 29 - Properties of Noetherian and Artinian modules, Composition Series

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Lecture 30 - Further properties of Noetherian and Artinian modules and ringsLecture 31 - Hilbert basis theorem and Primary decompositionLecture 32 - Primary decomposition (Continued...)Lecture 33 - Uniqueness of primary decompositionLecture 34 - 2nd Uniqueness theorem, Artinian ringsLecture 35 - Properties of Artinian ringsLecture 36 - Structure Theorem of Artinian ringsLecture 37 - Noether NormalizationLecture 38 - Hilberts Nullstellensatz

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NPTEL Video Course - Mathematics - NOC:Differential Equations

Subject Co-ordinator - Prof. Srinivasa Manam

Co-ordinating Institute - IIT - Madras

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Introduction to Ordinary Differential Equations (ODE)Lecture 2 - Methods for First Order ODE's - Homogeneous EquationsLecture 3 - Methods for First order ODE's - Exact EquationsLecture 4 - Methods for First Order ODE's - Exact Equations (Continued...)Lecture 5 - Methods for First order ODE's - Reducible to Exact EquationsLecture 6 - Methods for First order ODE's - Reducible to Exact Equations (Continued...)Lecture 7 - Non-Exact Equations - Finding Integrating FactorsLecture 8 - Linear First Order ODE and Bernoulli's EquationLecture 9 - Introduction to Second order ODE'sLecture 10 - Properties of solutions of second order homogeneous ODE'sLecture 11 - Abel's formula to find the other solutionLecture 12 - Abel's formula - DemonstrationLecture 13 - Second Order ODE's with constant coefficientsLecture 14 - Euler - Cauchy equationLecture 15 - Non homogeneous ODEs Variation of ParametersLecture 16 - Method of undetermined coefficientsLecture 17 - Demonstration of Method of undetermined coefficientsLecture 18 - Power Series and its propertiesLecture 19 - Power Series Solutions to Second Order ODE'sLecture 20 - Power Series Solutions (Continued...)Lecture 21 - Legendre Differential EquationLecture 22 - Legendre PolynomialsLecture 23 - Properties of Legendre PolynomialsLecture 24 - Power series solutions around a regular singular pointLecture 25 - Frobenius method of solutionsLecture 26 - Frobenius method of solutions (Continued...)Lecture 27 - Examples on Frobenius methodLecture 28 - Bessel differential equationLecture 29 - Frobenius solutions for Bessel Equation

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Lecture 30 - Properties of Bessel functionsLecture 31 - Properties of Bessel functions (Continued...)Lecture 32 - Introduction to Sturm-Liouville theoryLecture 33 - Sturm-Liouville ProblemsLecture 34 - Regular Sturm-Liouville problemLecture 35 - Periodic and singular Sturm-Liouville ProblemsLecture 36 - Generalized Fourier seriesLecture 37 - Examples of Sturm-Liouville systemsLecture 38 - Examples of Sturm-Liouville systems (Continued...)Lecture 39 - Examples of regular Sturm-Liouville systemsLecture 40 - Second order linear PDEsLecture 41 - Classification of second order linear PDEsLecture 42 - Reduction to canonical form for equations with constant coefficientsLecture 43 - Reduction to canonical form for equations with variable coefficientsLecture 44 - Reduction to Normal form-More examplesLecture 45 - D'Alembert solution for wave equationLecture 46 - Uniqueness of solutions for wave equationLecture 47 - Vibration of a semi-infinite stringLecture 48 - Vibration of a finite stringLecture 49 - Finite length string vibrationsLecture 50 - Finite length string vibrations (Continued...)Lecture 51 - Non-homogeneous wave equationLecture 52 - Vibration of a circular drumLecture 53 - Solutions of heat equation-PropertiesLecture 54 - Temperature in an infinite rodLecture 55 - Temperature in a semi-infinite rodLecture 56 - Non-homogeneous heat equationLecture 57 - Temperature in a finite rodLecture 58 - Temperature in a finite rod with insulated endsLecture 59 - Laplace equation over a rectangleLecture 60 - Laplace equation over a rectangle with flux boundary conditionsLecture 61 - Laplace equation over circular domainsLecture 62 - Laplace equation over circular SectorsLecture 63 - Uniqueness of the boundary value problems for Laplace equationLecture 64 - Conclusions

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NPTEL Video Course - Mathematics - NOC:Numerical Analysis

Subject Co-ordinator - Prof. R. Usha

Co-ordinating Institute - IIT - Madras

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Lesson 1 - Introduction, MotivationLecture 2 - Lesson 2 - Part 1 - Mathematical Preliminaries, Polynomial Interpolation - 1Lecture 3 - Lesson 2 - Part 2 - Mathematical Preliminaries, Polynomial Interpolation - 1Lecture 4 - Lesson 3 - Part 1 - Polynomial Interpolation - 2Lecture 5 - Lesson 3 - Part 2 - Polynomial Interpolation - 2Lecture 6 - Lesson 4 - Polynomial Interpolation - 3Lecture 7 - Lagrange Interpolation Polynomial, Error In Interpolation - 1Lecture 8 - Lagrange Interpolation Polynomial, Error In Interpolation - 1Lecture 9 - Error In Interpolation - 2Lecture 10 - Error In Interpolation - 2Lecture 11 - Divide Difference Interpolation PolynomialLecture 12 - Properties Of Divided Difference, Introduction To Inverse InterpolationLecture 13 - Properties Of Divided Difference, Introduction To Inverse InterpolationLecture 14 - Inverse Interpolation, Remarks on Polynomial InterpolationLecture 15 - Numerical Differentiation - 1 Taylor Series MethodLecture 16 - Numerical Differentiation - 2 Method Of Undetermined CoefficientsLecture 17 - Numerical Differentiation - 2 Polynomial Interpolation MethodLecture 18 - Numerical Differentiation - 3 Operator Method Numerical Integration - 1Lecture 19 - Numerical Integration - 2 Error in Trapezoidal Rule Simpson's RuleLecture 20 - Numerical Integration - 3 Error in Simpson's Rule Composite in Trapezoidal Rule, ErrorLecture 21 - Numerical Integration - 4 Composite Simpsons Rule , Error Method of Undetermined CoefficientsLecture 22 - Numerical Integration - 5 Gaussian Quadrature (Two-Point Method)Lecture 23 - Numerical Integrature - 5 Gaussian Quadrature (Three-Point Method) Adaptive QuadratureLecture 24 - Numerical Solution of Ordinary Differential Equation (ODE) - 1Lecture 25 - Numerical Solution Of ODE-2 Stability , Single-Step Methods - 1 Taylor Series MethodLecture 26 - Numerical Solution Of ODE-3 Examples of Taylor Series Method Euler's MethodLecture 27 - Numerical Solution Of ODE-4 Runge-Kutta MethodsLecture 28 - Numerical Solution Of ODE-5 Example For RK-Method Of Order 2 Modified Euler's MethodLecture 29 - Numerical Solution Of Ordinary Differential Equations - 6 Predictor-Corrector Methods (Adam-Moulton)

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Lecture 30 - Numerical Solution Of Ordinary Differential Equations - 7Lecture 31 - Numerical Solution Of Ordinary Differential Equations - 8Lecture 32 - Numerical Solution of Ordinary Differential Equations - 9Lecture 33 - Numerical Solution of Ordinary Differential Equations - 10Lecture 34 - Numerical Solution of Ordinary Differential Equations - 11Lecture 35 - Root Finding Methods - 1 The Bisection Method - 1Lecture 36 - Root Finding Methods - 2 The Bisection Method - 2Lecture 37 - Root Finding Methods - 3 Newton-Raphson Method - 1Lecture 38 - Root Finding Methods - 4 Newton-Raphson Method - 2Lecture 39 - Root Finding Methods - 5 Secant Method, Method Of false PositionLecture 40 - Root Finding Methods - 6 Fixed Point Methods - 1Lecture 41 - Root Finding Methods - 7 Fixed Point Methods - 2Lecture 42 - Root Finding Methods - 8 Fixed Point Iteration Methods - 3Lecture 43 - Root Finding Methods - 9 Practice ProblemsLecture 44 - Solution Of Linear Systems Of Equations - 1Lecture 45 - Solution Of Linear Systems Of Equations - 2Lecture 46 - Solution Of Linear Systems Of Equations - 3Lecture 47 - Solution Of Linear Systems Of Equations - 4Lecture 48 - Solution Of Linear Systems Of Equations - 5Lecture 49 - Solution Of Linear Systems Of Equations - 6Lecture 50 - Solution Of Linear Systems Of Equations - 7Lecture 51 - Solution Of Linear Systems Of Equations - 8 Iterative Method - 1Lecture 52 - Solution Of Linear Systems Of Equations - 8 Iterative Method - 2Lecture 53 - Matrix Eigenvalue Problems - 2 Power Method - 2Lecture 54 - Practice Problems

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NPTEL Video Course - Mathematics - NOC:Graph Theory

Subject Co-ordinator - Dr. Soumen Maity

Co-ordinating Institute - IISER - Pune

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Basic ConceptsLecture 2 - Basic Concepts - 1Lecture 3 - Eulerian and Hamiltonian GraphLecture 4 - Eulerian and Hamiltonian Graph - 1Lecture 5 - Bipartite GraphLecture 6 - Bipartite GraphLecture 7 - Diameter of a graph; Isomorphic graphsLecture 8 - Diameter of a graph; Isomorphic graphsLecture 9 - Minimum Spanning TreeLecture 10 - Minimum Spanning Trees (Continued...)Lecture 11 - Minimum Spanning Trees (Continued...)Lecture 12 - Minimum Spanning Trees (Continued...)Lecture 13 - Maximum Matching in Bipartite GraphLecture 14 - Maximum Matching in Bipartite Graph - 1Lecture 15 - Hall's Theorem and Konig's TheoremLecture 16 - Hall's Theorem and Konig's Theorem - 1Lecture 17 - Independent Set and Edge CoverLecture 18 - Independent Set and Edge Cover - 1Lecture 19 - Matching in General GraphsLecture 20 - Proof of Halls TheoremLecture 21 - Stable MatchingLecture 22 - Gale-Shapley AlgorithmLecture 23 - Graph ConnectivityLecture 24 - Graph Connectivity - 1Lecture 25 - 2-Connected GraphsLecture 26 - 2-Connected Graphs - 1Lecture 27 - Subdivision of an edge; 2-edge-connected graphsLecture 28 - Problems Related to Graphs ConnectivityLecture 29 - Flow Network

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Lecture 30 - Residual Network and Augmenting PathLecture 31 - Augmenting Path AlgorithmLecture 32 - Max-Flow and Min-CutLecture 33 - Max-Flow and Min-Cut TheoremLecture 34 - Vertex ColouringLecture 35 - Chromatic Number and Max. DegreeLecture 36 - Edge ColouringLecture 37 - Planar Graphs and Euler's FormulaLecture 38 - Characterization Of Planar GraphsLecture 39 - Colouring of Planar Graphs

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NPTEL Video Course - Mathematics - NOC:Transform Techniques for Engineers

Subject Co-ordinator - Prof. Srinivasa Manam

Co-ordinating Institute - IIT - Madras

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Introduction to Fourier seriesLecture 2 - Fourier series - Examples Lecture 3 - Complex Fourier series Lecture 4 - Conditions for the Convergence of Fourier Series Lecture 5 - Conditions for the Convergence of Fourier Series (Continued...)Lecture 6 - Use of Delta function in the Fourier series convergenceLecture 7 - More Examples on Fourier Series of a Periodic SignalLecture 8 - Gibb's Phenomenon in the Computation of Fourier SeriesLecture 9 - Properties of Fourier Transform of a Periodic SignalLecture 10 - Properties of Fourier transform (Continued...)Lecture 11 - Parseval's Identity and Recap of Fourier seriesLecture 12 - Fourier integral theorem-an informal proofLecture 13 - Definition of Fourier transformsLecture 14 - Fourier transform of a Heavyside functionLecture 15 - Use of Fourier transforms to evaluate some integralsLecture 16 - Evaluation of an integral- Recall of complex function theoryLecture 17 - Properties of Fourier transforms of non-periodic signalsLecture 18 - More properties of Fourier transformsLecture 19 - Fourier integral theorem - proofLecture 20 - Application of Fourier transform to ODE'sLecture 21 - Application of Fourier transforms to differential and integral equationsLecture 22 - Evaluation of integrals by Fourier transformsLecture 23 - D'Alembert's solution by Fourier transformLecture 24 - Solution of Heat equation by Fourier transformLecture 25 - Solution of Heat and Laplace equations by Fourier transformLecture 26 - Introduction to Laplace transformLecture 27 - Laplace transform of elementary functionsLecture 28 - Properties of Laplace transformsLecture 29 - Properties of Laplace transforms (Continued...)

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Lecture 30 - Methods of finding inverse Laplace transformLecture 31 - Heavyside expansion theoremLecture 32 - Review of complex function theoryLecture 33 - Inverse Laplace transform by contour integrationLecture 34 - Application of Laplace transforms - ODEs'Lecture 35 - Solutions of initial or boundary value problems for ODEs'Lecture 36 - Solving first order PDE's by Laplace transformLecture 37 - Solution of wave equation by Laplace transformLecture 38 - Solving hyperbolic equations by Laplace transformLecture 39 - Solving heat equation by Laplace transformLecture 40 - Initial boundary value problems for heat equationsLecture 41 - Solution of Integral Equations by Laplace TransformLecture 42 - Evaluation of Integrals by Laplace TransformLecture 43 - Introduction to Z-TransformsLecture 44 - Properties of Z-TransformsLecture 45 - Inverse Z-transformsLecture 46 - Solution of difference equations by Z-transformsLecture 47 - Evaluation of infinite sums by Z-transformsLecture 48 - conclusions

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NPTEL Video Course - Mathematics - NOC:Introduction to Probability and Statistics

Subject Co-ordinator - Prof. G. Srinivasan

Co-ordinating Institute - IIT - Madras

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Introduction to probability and StatisticsLecture 2 - Types of dataLecture 3 - Categorical dataLecture 4 - Describing Categorical dataLecture 5 - Describing Categorical data (Continued...)Lecture 6 - Describing numerical dataLecture 7 - Describing numerical data (Continued...)Lecture 8 - Exercises, Association between categorical variablesLecture 9 - Association between categorical variables (Continued...)Lecture 10 - Association between numerical variablesLecture 11 - Association between numerical variables (Continued...)Lecture 12 - ProbabilityLecture 13 - Rules of ProbabilityLecture 14 - Rules of Probability (Continued...)Lecture 15 - Conditional ProbabilityLecture 16 - Random variablesLecture 17 - Random variables - concepts and exercisesLecture 18 - Association between Random variablesLecture 19 - Binomial DistributionLecture 20 - Normal distributionLecture 21 - Additional Examples

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NPTEL Video Course - Mathematics - NOC:Introduction to Abstract Group Theory

Subject Co-ordinator - Prof. Krishna Hanumanthu

Co-ordinating Institute - IIT - Madras

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Motivational examples of groupsLecture 2 - Definition of a group and examplesLecture 3 - More examples of groupsLecture 4 - Basic properties of groups and multiplication tablesLecture 5 - Problems - 1Lecture 6 - Problems - 2Lecture 7 - Problems - 3Lecture 8 - SubgroupsLecture 9 - Types of groupsLecture 10 - Group homomorphisms and examplesLecture 11 - Properties of homomorphismsLecture 12 - Group isomorphismsLecture 13 - Normal subgroupsLecture 14 - Equivalence relationsLecture 15 - Problems - 4Lecture 16 - Cosets and Lagrange's theoremLecture 17 - S_3 revisitedLecture 18 - Problems - 5Lecture 19 - Quotient groupsLecture 20 - Examples of quotient groupsLecture 21 - First isomorphism theoremLecture 22 - Examples and Second isomorphism theoremLecture 23 - Third isomorphism theoremLecture 24 - Cauchy's theoremLecture 25 - Problems - 6Lecture 26 - Symmetric groups - ILecture 27 - Symmetric Groups - IILecture 28 - Symmetric groups - IIILecture 29 - Symmetric groups - IV

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Lecture 30 - Odd and even permutations - ILecture 31 - Odd and even permutations - IILecture 32 - Alternating groupsLecture 33 - Group actionsLecture 34 - Examples of group actionsLecture 35 - Orbits and stabilizersLecture 36 - Counting formulaLecture 37 - Cayley's theoremLecture 38 - Problems - 7Lecture 39 - Problems - 8 and Class equationLecture 40 - Group actions on subsetsLecture 41 - Sylow Theorem - ILecture 42 - Sylow Theorem - IILecture 43 - Sylow Theorem - IIILecture 44 - Problems - 9Lecture 45 - Problems - 10

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NPTEL Video Course - Mathematics - NOC:Groups: Motion, Symmetry and Puzzles

Subject Co-ordinator - Prof. Amit Kulshrestha

Co-ordinating Institute - IIT - Madras

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Permutation, symmetry and groupsLecture 2 - Groups acting on a set/an objectLecture 3 - More on group actionsLecture 4 - Groups and parityLecture 5 - Parity and puzzlesLecture 6 - Generators and relationsLecture 7 - Cosets, quotients and homomorphismsLecture 8 - Cayley graphs of groupsLecture 9 - Platonic solidsLecture 10 - Symmetries of plane and wallpapersLecture 11 - Introduction to GAPLecture 12 - GAP through Rubik's cubeLecture 13 - Representing abstract groupsLecture 14 - A quick introduction to group representationsLecture 15 - Rotations and quaternionsLecture 16 - Rotational symmetries of platonic solidsLecture 17 - Finite subgroups of SO(3)

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NPTEL Video Course - Mathematics - NOC:Introduction to Rings and Fields

Subject Co-ordinator - Prof. Krishna Hanumanthu

Co-ordinating Institute - IIT - Madras

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Introduction, main definitionsLecture 2 - Examples of ringsLecture 3 - More examplesLecture 4 - Polynomial Rings - 1Lecture 5 - Polynomial Rings - 2Lecture 6 - HomomorphismsLecture 7 - Kernels, idealsLecture 8 - Problems - 1Lecture 9 - Problems - 2Lecture 10 - Problems - 3Lecture 11 - Quotient RingsLecture 12 - First isomorphism and correspondence theoremsLecture 13 - Examples of correspondence theoremLecture 14 - Prime idealsLecture 15 - Maximal ideals, integral domainsLecture 16 - Existence of maximal idealsLecture 17 - Problems - 4Lecture 18 - Problems - 5Lecture 19 - Problems - 6Lecture 20 - Field of fractions, Noetherian rings - 1Lecture 21 - Noetherian rings - 2Lecture 22 - Hilbert Basis TheoremLecture 23 - Irreducible, prime elementsLecture 24 - Irreducible, prime elements, GCDLecture 25 - Principal Ideal DomainsLecture 26 - Unique Factorization Domains - 1Lecture 27 - Unique Factorization Domains - 2Lecture 28 - Gauss LemmaLecture 29 - Z[X] is a UFD

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Lecture 30 - Eisenstein criterion and Problems - 7Lecture 31 - Problems - 8Lecture 32 - Problems - 9Lecture 33 - Field extensions - 1Lecture 34 - Field extensions - 2Lecture 35 - Degree of a field extension - 1Lecture 36 - Degree of a field extension - 2Lecture 37 - Algebraic elements form a fieldLecture 38 - Field homomorphismsLecture 39 - Splitting fieldsLecture 40 - Finite fields - 1Lecture 41 - Finite fields - 2Lecture 42 - Finite fields - 3Lecture 43 - Problems - 10Lecture 44 - Problems - 11

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NPTEL Video Course - Mathematics - Discrete Mathematics

Subject Co-ordinator - Dr. Aditi Gangopadhyay, Dr. Sugata Gangopadhyay, Dr. Tanuja Srivastava

Co-ordinating Institute - IIT - Roorkee

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Introduction to the theory of setsLecture 2 - Set operation and laws of set operationLecture 3 - The principle of inclusion and exclusionLecture 4 - Application of the principle of inclusion and exclusionLecture 5 - Fundamentals of logicLecture 6 - Logical InferencesLecture 7 - Methods of proof of an implicationLecture 8 - First order logic (1)Lecture 9 - First order logic (2)Lecture 10 - Rules of influence for quantified propositionsLecture 11 - Mathematical Induction (1)Lecture 12 - Mathematical Induction (2)Lecture 13 - Sample space, eventsLecture 14 - Probability, conditional probabilityLecture 15 - Independent events, Bayes theoremLecture 16 - Information and mutual informationLecture 17 - Basic definitionLecture 18 - Isomorphism and sub graphsLecture 19 - Walks, paths and circuits operations on graphsLecture 20 - Euler graphs, Hamiltonian circuitsLecture 21 - Shortest path problemLecture 22 - Planar graphsLecture 23 - Basic definitionLecture 24 - Properties of relationsLecture 25 - Graph of relationsLecture 26 - Matrix of relationLecture 27 - Closure of relaton (1)Lecture 28 - Closure of relaton (2)Lecture 29 - Warshall's algorithm

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Lecture 30 - Partially ordered relationLecture 31 - Partially ordered setsLecture 32 - LatticesLecture 33 - Boolean algebraLecture 34 - Boolean function (1)Lecture 35 - Boolean function (2)Lecture 36 - Discrete numeric functionLecture 37 - Generating functionLecture 38 - Introduction to recurrence relationsLecture 39 - Second order recurrence relation with constant coefficients (1)Lecture 40 - Second order recurrence relation with constant coefficients (2)Lecture 41 - Application of recurrence relation

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NPTEL Video Course - Mathematics - NOC:Mathematical Methods and its Applications

Subject Co-ordinator - Prof. P.N. Agarwal, S. K. Gupta

Co-ordinating Institute - IIT - Roorkee

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Introduction to linear differential equationsLecture 2 - Linear dependence, independence and Wronskian of functionsLecture 3 - Solution of second-order homogenous linear differential equations with constant coefficients - ILecture 4 - Solution of second-order homogenous linear differential equations with constant coefficients - IILecture 5 - Method of undetermined coefficientsLecture 6 - Methods for finding Particular Integral for second-order linear differential equations with constant coefficients - ILecture 7 - Methods for finding Particular Integral for second-order linear differential equations with constant coefficients - IILecture 8 - Methods for finding Particular Integral for second-order linear differential equations with constant coefficients - IIILecture 9 - Euler-Cauchy equationsLecture 10 - Method of reduction for second-order linear differential equationsLecture 11 - Method of variation of parametersLecture 12 - Solution of second order differential equations by changing dependent variableLecture 13 - Solution of second order differential equations by changing independent variableLecture 14 - Solution of higher-order homogenous linear differential equations with constant coefficientsLecture 15 - Methods for finding Particular Integral for higher-order linear differential equationsLecture 16 - Formulation of Partial differential equationsLecture 17 - Solution of Lagrange�s equation - ILecture 18 - Solution of Lagrange�s equation - IILecture 19 - Solution of first order nonlinear equations - ILecture 20 - Solution of first order nonlinear equations - IILecture 21 - Solution of first order nonlinear equations - IIILecture 22 - Solution of first order nonlinear equations - IVLecture 23 - Introduction to Laplace transformsLecture 24 - Laplace transforms of some standard functionsLecture 25 - Existence theorem for Laplace transformsLecture 26 - Properties of Laplace transforms - ILecture 27 - Properties of Laplace transforms - IILecture 28 - Properties of Laplace transforms - IIILecture 29 - Properties of Laplace transforms - IV

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Lecture 30 - Convolution theorem for Laplace transforms - ILecture 31 - Convolution theorem for Laplace transforms - IILecture 32 - Initial and final value theorems for Laplace transformsLecture 33 - Laplace transforms of periodic functionsLecture 34 - Laplace transforms of Heaviside unit step functionLecture 35 - Laplace transforms of Dirac delta functionLecture 36 - Applications of Laplace transforms - ILecture 37 - Applications of Laplace transforms - IILecture 38 - Applications of Laplace transforms - IIILecture 39 - Z�transform and inverse Z-transform of elementary functionsLecture 40 - Properties of Z-transforms - ILecture 41 - Properties of Z-transforms - IILecture 42 - Initial and final value theorem for Z-transformsLecture 43 - Convolution theorem for Z-transformsLecture 44 - Applications of Z-transforms - ILecture 45 - Applications of Z-transforms - IILecture 46 - Applications of Z-transforms - IIILecture 47 - Fourier series and its convergence - ILecture 48 - Fourier series and its convergence - IILecture 49 - Fourier series of even and odd functionsLecture 50 - Fourier half-range seriesLecture 51 - Parsevel�s IdentityLecture 52 - Complex form of Fourier seriesLecture 53 - Fourier integralsLecture 54 - Fourier sine and cosine integralsLecture 55 - Fourier transformsLecture 56 - Fourier sine and cosine transformsLecture 57 - Convolution theorem for Fourier transformsLecture 58 - Applications of Fourier transforms to BVP - ILecture 59 - Applications of Fourier transforms to BVP - IILecture 60 - Applications of Fourier transforms to BVP - III

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NPTEL Video Course - Mathematics - NOC:Integral Equations, Calculus of Variations and its Applications

Subject Co-ordinator - Prof.D. N Pandey, Prof. P.N. Agarwal

Co-ordinating Institute - IIT - Roorkee

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Definition and classification of linear integral equationsLecture 2 - Conversion of IVP into integral equationsLecture 3 - Conversion of BVP into an integral equationsLecture 4 - Conversion of integral equations into differential equationsLecture 5 - Integro-differential equationsLecture 6 - Fredholm integral equation with separable kernelLecture 7 - Fredholm integral equation with separable kernelLecture 8 - Solution of integral equations by successive substitutionsLecture 9 - Solution of integral equations by successive approximationsLecture 10 - Solution of integral equations by successive approximationsLecture 11 - Fredholm integral equations with symmetric kernelsLecture 12 - Fredholm integral equations with symmetric kernelsLecture 13 - Fredholm integral equations with symmetric kernelsLecture 14 - Construction of Green function - ILecture 15 - Construction of Green function - IILecture 16 - Green function for self adjoint linear differential equationsLecture 17 - Green function for non-homogeneous boundary value problemLecture 18 - Fredholm alternative theorem - ILecture 19 - Fredholm alternative theorem - IILecture 20 - Fredholm method of solutionsLecture 21 - Classical Fredholm theoryLecture 22 - Classical Fredholm theoryLecture 23 - Classical Fredholm theoryLecture 24 - Method of successive approximationsLecture 25 - Neumann series and resolvent kernels - ILecture 26 - Neumann series and resolvent kernels - IILecture 27 - Equations with convolution type kernels - ILecture 28 - Equations with convolution type kernels - IILecture 29 - Singular integral equations - I

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Lecture 30 - Singular integral equations - IILecture 31 - Cauchy type integral equations - ILecture 32 - Cauchy type integral equations - IILecture 33 - Cauchy type integral equations - IIILecture 34 - Cauchy type integral equations - IVLecture 35 - Cauchy type integral equations - VLecture 36 - Solution of integral equations using Fourier transformLecture 37 - Solution of integral equations using Hilbert transform - ILecture 38 - Solution of integral equations using Hilbert transform - IILecture 39 - Calculus of variationsLecture 40 - Calculus of variationsLecture 41 - Calculus of variationsLecture 42 - Calculus of variationsLecture 43 - Euler equationLecture 44 - Euler equationLecture 45 - Brachistochrone problem and Euler equation - ILecture 46 - Euler's equation - IILecture 47 - Functions of several independent variablesLecture 48 - Variational problems in parametric formLecture 49 - Variational problems of general typeLecture 50 - Variational derivative and invariance of Euler's equationLecture 51 - Invariance of Euler's equation and isoperimetric problem - ILecture 52 - Isoperimetric problem - IILecture 53 - Variational problem involving a conditional extremum - ILecture 54 - Variational problem involving a conditional extremum - IILecture 55 - Variational problems with moving boundaries - ILecture 56 - Variational problems with moving boundaries - IILecture 57 - Variational problems with moving boundaries - IIILecture 58 - Variational problems with moving boundaries; One sided variationLecture 59 - Variational problem with a movable boundary for a functional dependent on two functionsLecture 60 - Hamilton's principle

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NPTEL Video Course - Mathematics - NOC:Nonlinear Programming

Subject Co-ordinator - S. K. Gupta

Co-ordinating Institute - IIT - Roorkee

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Convex Sets and FunctionsLecture 2 - Properties of Convex Functions - ILecture 3 - Properties of Convex Functions - IILecture 4 - Properties of Convex Functions- IIILecture 5 - Convex Programming ProblemsLecture 6 - KKT optimality conditionsLecture 7 - Quadratic Programming Problems - ILecture 8 - Quadratic Programming Problems - IILecture 9 - Separable Programming - ILecture 10 - Separable Programming - IILecture 11 - Geometric Programming - ILecture 12 - Geometric Programming - IILecture 13 - Geometric Programming - IIILecture 14 - Dynamic Programming - ILecture 15 - Dynamic Programming - IILecture 16 - Dynamic programming approach to find shortest path in any networkLecture 17 - Dynamic Programming - IVLecture 18 - Search Techniques - ILecture 19 - Search Techniques - IILecture 20 - Search Techniques - III

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NPTEL Video Course - Mathematics - NOC:Numerical Methods

Subject Co-ordinator - Prof. Sanjeev Kumar, Prof. Ameeya Kumar Nayak

Co-ordinating Institute - IIT - Roorkee

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Introduction to error analysis and linear systemsLecture 2 - Gaussian elimination with Partial pivotingLecture 3 - LU decompositionLecture 4 - Jacobi and Gauss Seidel methodsLecture 5 - Iterative methods-IILecture 6 - Introduction to Non-linear equations and Bisection methodLecture 7 - Regula Falsi and Secant methodsLecture 8 - Newton-Raphson methodLecture 9 - Fixed point iteration methodLecture 10 - System of Nonlinear equationsLecture 11 - Introduction to Eigenvalues and EigenvectorsLecture 12 - Similarity Transformations and Gershgorin TheoremLecture 13 - Jacobi's Method for Computing EigenvaluesLecture 14 - Power MethodLecture 15 - Inverse Power MethodLecture 16 - Interpolation - Part I (Introduction to Interpolation)Lecture 17 - Interpolation - Part II ( Some basic operators and their properties)Lecture 18 - Interpolation - Part III (Newton�s Forward/ Backward difference and derivation of general error)Lecture 19 - Interpolation - Part IV (Error in approximating a function by a polynomial using Newton�s Forward and Backward difference formula)Lecture 20 - Interpolation - Part V (Solving problems using Newton's Forward and Backward difference formula)Lecture 21 - Interpolation - Part VI (Central difference formula)Lecture 22 - Interpolation - Part VII (Lagrange interpolation formula with examples)Lecture 23 - Interpolation - Part VIII (Divided difference interpolation with examples)Lecture 24 - Interpolation - Part IX (Hermite's interpolation with examples)Lecture 25 - Numerical differentiation - Part I (Introduction to numerical differentiation by interpolation formula)Lecture 26 - Numerical differentiation - Part II (Numerical differentiation based on Lagrange�s interpolation with examples)Lecture 27 - Numerical differentiation - Part III (Numerical differentiation based on Divided difference formula with examples)Lecture 28 - Numerical differentiation - Part IV (Maxima and minima of a tabulated function and differentiation errors)Lecture 29 - Numerical differentiation - Part V (Differentiation based on finite difference operators)

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Lecture 30 - Numerical differentiation - Part VI (Method of undetermined coefficients and Derivatives with unequal intervals)Lecture 31 - Numerical Integration - Part I (Methodology of Numerical Integration and Rectangular rule )Lecture 32 - Numerical Integration - Part II (Quadrature formula and Trapezoidal rule with associated errors)merical Integration Part-I (Methodology of Numerical Integration and Rectangular rule )Lecture 33 - Numerical Integration - Part III (Simpsons 1/3rd rule with associated errors)Lecture 34 - Numerical Integration - Part IV (Composite Simpsons 1/3rd rule and Simpsons 3/8th rule with examples)Lecture 35 - Numerical Integration - Part V (Gauss Legendre 2-point and 3-point formula with examples)Lecture 36 - Introduction to Ordinary Differential equationsLecture 37 - Numerical methods for ODE-1Lecture 38 - Numerical Methods - IILecture 39 - R-K Methods for solving ODEsLecture 40 - Multi-step Method for solving ODEs

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NPTEL Video Course - Mathematics - NOC:Numerical Linear Algebra

Subject Co-ordinator - Prof.D. N Pandey, Prof. P.N. Agrawal

Co-ordinating Institute - IIT - Roorkee

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Matrix Operations and Types of MatricesLecture 2 - Determinant of a MatrixLecture 3 - Rank of a MatrixLecture 4 - Vector Space - ILecture 5 - Vector Space - IILecture 6 - Linear dependence and independenceLecture 7 - Bases and Dimension - ILecture 8 - Bases and Dimension - IILecture 9 - Linear Transformation - ILecture 10 - Linear Transformation - IILecture 11 - Orthogonal SubspacesLecture 12 - Row Space, Column Space and Null SpaceLecture 13 - Eigen Values and Eigen Vectors - ILecture 14 - Eigen Values and Eigen Vectors - IILecture 15 - Diagonalizable MatricesLecture 16 - Orthogonal SetsLecture 17 - Gram Schmidt ortthogonalization and orthogonal basesLecture 18 - Introduction to MatlabLecture 19 - Sign Integer RepresentationLecture 20 - Computer Representation of NumbersLecture 21 - Floating Point RepresentationLecture 22 - Round-off ErrorLecture 23 - Error Propagation in Computer ArithmeticLecture 24 - Addition and Multiplication of Floating Point NumbersLecture 25 - Conditioning and Condition Numbers - ILecture 26 - Conditioning and Condition Numbers - IILecture 27 - Stability of Numerical Algorithms - ILecture 28 - Stability of Numerical Algorithms - IILecture 29 - Vector Norms - I

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Lecture 30 - Vector Norms - IILecture 31 - Matrix Norms - ILecture 32 - Matrix Norms - IILecture 33 - Convergent Matrices - ILecture 34 - Convergent Matrices - IILecture 35 - Stability of non linear systemLecture 36 - Condition number of a matrixLecture 37 - Sensitivity Analysis - ILecture 38 - Sensitivity Analysis - IILecture 39 - Residual TheoremLecture 40 - Nearness to SingularityLecture 41 - Estimation of the Condition NumberLecture 42 - Singular value decomposition of a matrix - ILecture 43 - Singular value decomposition of a matrix - IILecture 44 - Orthonormal ProjectionsLecture 45 - Algebraic and geometric properties of SVDLecture 46 - SVD and their applicationsLecture 47 - Perturbation theorem for singular valuesLecture 48 - Outer product expansion of a matrixLecture 49 - Least square solutions - ILecture 50 - Least square solutions - IILecture 51 - Householder matricesLecture 52 - Householder matrices and their applicationsLecture 53 - Householder QR factorization - ILecture 54 - Householder QR factorization - IILecture 55 - Basic theorems on eigenvalues and QR methodLecture 56 - Power MethodLecture 57 - Rate of Convergence of Power MethodLecture 58 - Applications of Power Method with ShiftLecture 59 - Jacobi Method - ILecture 60 - Jacobi Method - II

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NPTEL Video Course - Mathematics - NOC:Numerical Methods - Finite Difference Approach

Subject Co-ordinator - Prof. Ameeya Kumar Nayak

Co-ordinating Institute - IIT - Roorkee

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Introduction to Numerical solutionsLecture 2 - Numerical Solution of ODELecture 3 - Numerical solution of PDELecture 4 - Finite difference approximationLecture 5 - Polynomial fitting and one-sided approximationLecture 6 - Solution of parabolic equationLecture 7 - Implicit and C-N scheme for solving 1D parabolic equationLecture 8 - Stability analysis of Explicit scheme for solving parabolic equationLecture 9 - Stability of Crank-Nicoloson's schemeLecture 10 - Approximation of derivative boundary conditionsLecture 11 - Solution of two-dimensional parabolic equationLecture 12 - Solution of 2D parabolic equation using ADI schemeLecture 13 - Solution of Elliptic EquationLecture 14 - Solution of Elliptic equation using SOR methodLecture 15 - Solution of Elliptic equation using ADI schemeLecture 16 - Solution of Hyperbolic equationLecture 17 - Stability analysis for Hyperbolic equationsLecture 18 - Characteristics of PDELecture 19 - Lax-Wendroff's methodLecture 20 - Wendroff's method

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NPTEL Video Course - Mathematics - NOC:Multivariable Calculus

Subject Co-ordinator - Dr. Sanjeev Kumar, S. K. Gupta

Co-ordinating Institute - IIT - Roorkee

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Functions of several variablesLecture 2 - Limits for multivariable functions - ILecture 3 - Limits for multivariable functions - IILecture 4 - Continuity of multivariable functionsLecture 5 - Partial Derivatives - ILecture 6 - Partial Derivatives - IILecture 7 - Differentiability - ILecture 8 - Differentiability - IILecture 9 - Chain rule - ILecture 10 - Chain rule - IILecture 11 - Change of variablesLecture 12 - Euler�s theorem for homogeneous functionsLecture 13 - Tangent planes and Normal linesLecture 14 - Extreme values - ILecture 15 - Extreme values - IILecture 16 - Lagrange multipliersLecture 17 - Taylor�s theoremLecture 18 - Error approximationLecture 19 - Polar-curvesLecture 20 - Multiple IntegralsLecture 21 - Change Of Order Of IntegrationLecture 22 - Change of Variables in Multiple IntegralLecture 23 - Introduction to Gamma FunctionLecture 24 - Introduction to Beta FunctionLecture 25 - Properties of Beta and Gamma Functions - ILecture 26 - Properties of Beta and Gamma Functions - IILecture 27 - Dirichlet's IntegralLecture 28 - Applications of Multiple IntegralsLecture 29 - Vector Differentiation

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Lecture 30 - Gradient of a Scalar Field and Directional DerivativeLecture 31 - Normal Vector and Potential fieldLecture 32 - Gradient (Identities), Divergence and Curl (Identities)Lecture 33 - Some Identities on Divergence and CurlLecture 34 - Line Integral (I)Lecture 35 - Applications of Line IntegralsLecture 36 - Green's TheoremLecture 37 - Surface AreaLecture 38 - Surface IntegralLecture 39 - Divergence Theorem of GaussLecture 40 - Stoke's Theorem

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NPTEL Video Course - Mathematics - NOC:Ordinary and Partial Differential Equations and Applications

Subject Co-ordinator - Prof.D. N Pandey, Prof. P.N. Agrawal

Co-ordinating Institute - IIT - Roorkee

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Introduction to differential equations - ILecture 2 - Introduction to differential equations - IILecture 3 - Existence and uniqueness of solutions of differential equations - ILecture 4 - Existence and uniqueness of solutions of differential equations - IILecture 5 - Existence and uniqueness of solutions of differential equations - IIILecture 6 - Existence and uniqueness of solutions of a system of differential equationsLecture 7 - Linear SystemLecture 8 - Properties of Homogeneous SystemsLecture 9 - Solution of Homogeneous Linear System with Constant Coefficients - ILecture 10 - Solution of Homogeneous Linear System with Constant Coefficients - IILecture 11 - Solution of Homogeneous Linear System with Constant Coefficients - IIILecture 12 - Solution of Non-Homogeneous Linear System with Constant CoefficientsLecture 13 - Power SeriesLecture 14 - Uniform Convergence of Power SeriesLecture 15 - Power Series Solution of Second Order Homogeneous EquationsLecture 16 - Regular singular points - ILecture 17 - Regular singular points - IILecture 18 - Regular singular points - IIILecture 19 - Regular singular points - IVLecture 20 - Regular singular points - VLecture 21 - Critical pointsLecture 22 - Stability of Linear Systems - ILecture 23 - Stability of Linear Systems - IILecture 24 - Stability of Linear Systems - IIILecture 25 - Critical Points and Paths of Non-linear SystemsLecture 26 - Boundary value problems for second order differential equationsLecture 27 - Self - adjoint FormsLecture 28 - Sturm - Liouville problem and its propertiesLecture 29 - Sturm - Liouville problem and its applications

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Lecture 30 - Green�s function and its applications - ILecture 31 - Green�s function and its applications - IILecture 32 - Origins and Classification of First Order PDELecture 33 - Initial Value Problem for Quasi-linear First Order EquationsLecture 34 - Existence and Uniqueness of SolutionsLecture 35 - Surfaces orthogonal to a given system of surfacesLecture 36 - Nonlinear PDE of first orderLecture 37 - Cauchy method of characteristics - ILecture 38 - Cauchy method of characteristics - IILecture 39 - Compatible systems of first order equationsLecture 40 - Charpit�s method - ILecture 41 - Charpit�s method - IILecture 42 - Second Order PDE with Variable CoefficientsLecture 43 - Classification and Canonical Form of Second Order PDE - ILecture 44 - Classification and Canonical Form of Second Order PDE - IILecture 45 - Classification and Characteristic Curves of Second Order PDEsLecture 46 - Review of Integral Transforms - ILecture 47 - Review of Integral Transforms - IILecture 48 - Review of Integral Transforms - IILecture 49 - Review of Integral Transforms - IIILecture 50 - Laplace Equation - ILecture 51 - Laplace Equation - IILecture 52 - Laplace and Poisson EquationsLecture 53 - One dimensional wave equation and its solution - ILecture 54 - One dimensional wave equation and its solution - IILecture 55 - One dimensional wave equation and its solution - IIILecture 56 - Two dimensional wave equation and its solution - ILecture 57 - Solution of non-homogeneous wave equationLecture 58 - Solution of homogeneous diffusion equation - ILecture 59 - Solution of homogeneous diffusion equation - IILecture 60 - Duhamel�s principle

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NPTEL Video Course - Mathematics - NOC:Matrix Analysis with Applications

Subject Co-ordinator - Dr. Sanjeev Kumar, S. K. Gupta

Co-ordinating Institute - IIT - Roorkee

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Elementary row operationsLecture 2 - Echelon form of a matrixLecture 3 - Rank of a matrixLecture 4 - System of Linear Equations - ILecture 5 - System of Linear Equations - IILecture 6 - Introduction to Vector SpacesLecture 7 - SubspacesLecture 8 - Basis and DimensionLecture 9 - Linear TransformationsLecture 10 - Rank and NullityLecture 11 - Inverse of a Linear TransformationLecture 12 - Matrix Associated with a LTLecture 13 - Eigenvalues and EigenvectorsLecture 14 - Cayley-Hamilton Theorem and Minimal PolynomialLecture 15 - DiagonalizationLecture 16 - Special MatricesLecture 17 - More on Special Matrices and Gerschgorin TheoremLecture 18 - Inner Product SpacesLecture 19 - Vector and Matrix NormsLecture 20 - Gram Schmidt ProcessLecture 21 - Normal MatricesLecture 22 - Positive Definite MatricesLecture 23 - Positive Definite and Quadratic FormsLecture 24 - Gram Matrix and Minimization of Quadratic FormsLecture 25 - Generalized Eigenvectors and Jordan Canonical FormLecture 26 - Evaluation of Matrix FunctionsLecture 27 - Least Square ApproximationLecture 28 - Singular Value DecompositionLecture 29 - Pseudo-Inverse and SVD

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Lecture 30 - Introduction to Ill-Conditioned SystemsLecture 31 - Regularization of Ill-Conditioned SystemsLecture 32 - Linear SystemsLecture 33 - Linear SystemsLecture 34 - Non-Stationary Iterative MethodsLecture 35 - Non-Stationary Iterative MethodsLecture 36 - Krylov Subspace Iterative Methods (Conjugate Gradient Method)Lecture 37 - Krylov Subspace Iterative Methods (CG and Pre-Conditioning)Lecture 38 - Introduction to Positive MatricesLecture 39 - Positive Matrices, Positive Eigenpair, Perron Root and vector, ExampleLecture 40 - Polar Decomposition

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NPTEL Video Course - Mathematics - NOC:Mathematical Modelling: Analysis and Applications

Subject Co-ordinator - Prof. Ameeya Kumar Nayak

Co-ordinating Institute - IIT - Roorkee

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Introduction to Mathematical ModelingLecture 2 - Discrete Time Linear Models in Population Dynamics - ILecture 3 - Discrete Time Linear Models in Population Dynamics - IILecture 4 - Discrete Time Linear Age Structured ModelsLecture 5 - Numerical Methods to Compute Eigen ValuesLecture 6 - Discrete Time Non-Linear Models in Population Dynamics - IILecture 7 - Analysis on Logistic Difference EquationLecture 8 - Classifications of BifurcationLecture 9 - Discrete Time Non - Linear Models in Population Dynamics - IILecture 10 - Discrete Time Prey - Predator ModelLecture 11 - Introduction to Continuous Time ModelsLecture 12 - Solution of First Order First Degree Differential EquationsLecture 13 - Continuous Time Models in Population Dynamics - ILecture 14 - Continuous Time Models in Population Dynamics - IILecture 15 - Stability and Linearization of System of Ordinary Differential EquationsLecture 16 - Continuous Time Single Species ModelsLecture 17 - Qualitative Solution of Differential Equations - Phase Diagrams - ILecture 18 - Qualitative Solution of Differential Equations - Phase Diagrams - IILecture 19 - Continuous Time Lotka - Volterra Competition ModelLecture 20 - Continuous Time Prey - Predator Model

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NPTEL Video Course - Mathematics - NOC:Dynamical System and Control

Subject Co-ordinator - Prof.D. N Pandey, Dr. N. Sukavanam

Co-ordinating Institute - IIT - Roorkee

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Formulation of Dynamical Systems - ILecture 2 - Formulation of Dynamical Systems - IILecture 3 - Existence and Uniqueness Theorem - ILecture 4 - Existence and Uniqueness Theorem - IILecture 5 - Linear Systems - ILecture 6 - Linear Systems - IILecture 7 - Solutions of Linear Systems - ILecture 8 - Solutions of Linear Systems - IILecture 9 - Solutions of Linear Systems - IIILecture 10 - Fundamental Matrix - ILecture 11 - Fundamental Matrix - IILecture 12 - Fundamental Matrix for Non-Autonomous systemsLecture 13 - Solutions of Non-Homogeneous SystemsLecture 14 - Stability of SystemsLecture 15 - Stability of Linear Autonomous Systems - ILecture 16 - Stability of Linear Autonomous Systems - IILecture 17 - Stability of Linear Autonomous Systems - IIILecture 18 - Stability of Weakly Non-Linear Systems - ILecture 19 - Stability of Weakly Non-Linear Systems - IILecture 20 - Stability of Non-Linear Systems using LinearizationLecture 21 - Properties of Phase PortraitLecture 22 - Properties of OrbitsLecture 23 - Phase PortraitLecture 24 - Phase Portrait of Linear Differential Equations - ILecture 25 - Phase Portrait of Linear Differential Equations - IILecture 26 - Phase Portrait of Linear Differential Equations - IIILecture 27 - Poincare Bendixson TheoremLecture 28 - Limit CycleLecture 29 - Lyapunov Stability - I

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Lecture 30 - Lyapunov Stability - IILecture 31 - Introduction to Control Systems - ILecture 32 - Introduction to Control Systems - IILecture 33 - Controllability of Autonomous SystemsLecture 34 - Controllability of Non-autonomous SystemsLecture 35 - Observability - ILecture 36 - Observability - IILecture 37 - Results on Controllability and ObservabilityLecture 38 - Companion FormLecture 39 - Feedback Control - ILecture 40 - Feedback Control - IILecture 41 - Feedback Control - IIILecture 42 - Feedback Control - IVLecture 43 - State ObserverLecture 44 - StabilizabilityLecture 45 - Introduction to Discrete Systems - ILecture 46 - Introduction to Discrete Systems - IILecture 47 - Lyapunov Stability Theory - ILecture 48 - Lyapunov Stability Theory - IILecture 49 - Lyapunov Stability Theory - IIILecture 50 - Optimal Control - ILecture 51 - Optimal Control - IILecture 52 - Optimal Control - IIILecture 53 - Optimal Control - IVLecture 54 - Optimal Control for Discrete Systems - ILecture 55 - Optimal Control for Discrete Systems - IILecture 56 - Controllability of Discrete SystemsLecture 57 - Observability of Discrete SystemsLecture 58 - Stability for Discrete SystemsLecture 59 - Relation between Continuous and Discrete Systems - ILecture 60 - Relation between Continuous and Discrete Systems - II

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NPTEL Video Course - Mathematics - NOC:Advanced Engineering Mathematics

Subject Co-ordinator - Prof. P.N. Agarwal

Co-ordinating Institute - IIT - Roorkee

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Analytic FunctionLecture 2 - Cauchy-Riemann EquationsLecture 3 - Harmonic Functions, Harmonic Conjugates and Milne's MethodLecture 4 - Applications to the Problems of Potential Flow - ILecture 5 - Applications to the Problems of Potential Flow - IILecture 6 - Complex IntegrationLecture 7 - Cauchy's Theorem - ILecture 8 - Cauchy's Theorem - IILecture 9 - Cauchy's Integral Formula for the Derivatives of Analytic FunctionLecture 10 - Morera's Theorem, Liouville's Theorem and Fundamental Theorem of AlgebraLecture 11 - Winding Number and Maximum Modulus PrincipleLecture 12 - Sequences and SeriesLecture 13 - Uniform Convergence of SeriesLecture 14 - Power SeriesLecture 15 - Taylor SeriesLecture 16 - Laurent SeriesLecture 17 - Zeros and Singularities of an Analytic FunctionLecture 18 - Residue at a SingularityLecture 19 - Residue TheoremLecture 20 - Meromorphic FunctionsLecture 21 - Evaluation of real integrals using residues - ILecture 22 - Evaluation of real integrals using residues - IILecture 23 - Evaluation of real integrals using residues - IIILecture 24 - Evaluation of real integrals using residues - IVLecture 25 - Evaluation of real integrals using residues - VLecture 26 - Bilinear TransformationsLecture 27 - Cross RatioLecture 28 - Conformal Mapping - ILecture 29 - Conformal Mapping - II

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Lecture 30 - Conformal mapping from half plane to disk and half plane to half plane - ILecture 31 - Conformal mapping from disk to disk and angular region to diskLecture 32 - Application of Conformal Mapping to Potential TheoryLecture 33 - Review of Z-transforms - ILecture 34 - Review of Z-transforms - IILecture 35 - Review of Z-transforms - IIILecture 36 - Review of Bilateral Z-transformsLecture 37 - Finite Fourier TransformsLecture 38 - Fourier Integral and Fourier TransformsLecture 39 - Fourier SeriesLecture 40 - Discrete Fourier Transforms - ILecture 41 - Discrete Fourier Transforms - IILecture 42 - Basic Concepts of ProbabilityLecture 43 - Conditional ProbabilityLecture 44 - Bayes Theorem and Probability NetworksLecture 45 - Discrete Probability DistributionLecture 46 - Binomial DistributionLecture 47 - Negative Binomial Distribution and Poisson DistributionLecture 48 - Continuous Probability DistributionLecture 49 - Poisson ProcessLecture 50 - Exponential DistributionLecture 51 - Normal DistributionLecture 52 - Joint Probability Distribution - ILecture 53 - Joint Probability Distribution - IILecture 54 - Joint Probability Distribution - IIILecture 55 - Correlation and Regression - ILecture 56 - Correlation and Regression - IILecture 57 - Testing of Hypotheses - ILecture 58 - Testing of Hypotheses - IILecture 59 - Testing of Hypotheses - IIILecture 60 - Application to Queuing Theory and Reliability Theory

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NPTEL Video Course - Mathematics - NOC:Higher Engineering Mathematics

Subject Co-ordinator - Prof. P.N. Agarwal

Co-ordinating Institute - IIT - Roorkee

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Symbolic Representation of Statements - ILecture 2 - Symbolic Representation of Statements - IILecture 3 - Tautologies and ContradictionsLecture 4 - Predicates and Quantifires - ILecture 5 - Predicates and Quantifiers - IILecture 6 - Validity of ArgumentsLecture 7 - Language and Grammers - ILecture 8 - Language and Grammers - IILecture 9 - Language and Grammers - IIILecture 10 - Finite- State MachinesLecture 11 - Partially Ordered Sets - ILecture 12 - Partially Ordered Sets - IILecture 13 - Partially Ordered Sets - IIILecture 14 - Lattices - ILecture 15 - Lattices - IILecture 16 - Lattices - IIILecture 17 - Lattices - IVLecture 18 - Lattices - VLecture 19 - Boolean Algebra - ILecture 20 - Boolean Algebra - IILecture 21 - Boolean Algebra - IIILecture 22 - Boolean Algebra - IVLecture 23 - Logic GatesLecture 24 - Karnaugh Map - ILecture 25 - Karnaugh Map - IILecture 26 - Various type of Graphs - ILecture 27 - Various types of Graphs - IILecture 28 - Paths and ConnectivityLecture 29 - Subgraphs and Traversable Multigraphs

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Lecture 30 - Undirected and Directed GraphsLecture 31 - Eulerian and Hamiltonian GraphsLecture 32 - Planar GraphsLecture 33 - Representation of GraphsLecture 34 - Isomorphic and Homeomorphic GraphsLecture 35 - Kuratowski's TheoremLecture 36 - Dual of a GraphLecture 37 - Coloring of Graphs - ILecture 38 - Coloring of Graphs - IILecture 39 - Tree - ILecture 40 - Tree - IILecture 41 - Graphical Method - ILecture 42 - Graphical Method - IILecture 43 - General Linear Programming ProblemLecture 44 - Simplex Method - ILecture 45 - Simplex Method - IILecture 46 - Big - M Method - ILecture 47 - Big - M Method - II (Special Cases)Lecture 48 - Two Phase Method - ILecture 49 - Two Phase method - IILecture 50 - Duality - ILecture 51 - Duality - IILecture 52 - Dual Simplex MethodLecture 53 - Transportation Problem - ILecture 54 - Transportation Problem - IILecture 55 - Assignment Problem - ILecture 56 - Assignment Problem - II

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NPTEL Video Course - Mathematics - NOC:Operations Research

Subject Co-ordinator - Prof. Kusumdeep

Co-ordinating Institute - IIT - Roorkee

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Introduction to OR ModelsLecture 2 - More OR ModelsLecture 3 - Graphical Method for LPPLecture 4 - Convex setsLecture 5 - Simplex MethodLecture 6 - Big M MethodLecture 7 - Two PhaseLecture 8 - Multiple solutions of LPPLecture 9 - Unbounded solution of LPPLecture 10 - Infeasible solution of LPPLecture 11 - Revised Simplex MethodLecture 12 - Case studies and Exercises - ILecture 13 - Case studies and Exercises - IILecture 14 - Case studies and Exercises - IIILecture 15 - Primal Dual ConstructionLecture 16 - Weak Duality TheoremLecture 17 - More Duality TheoremsLecture 18 - Primal-Dual relationship of solutionsLecture 19 - Dual Simplex MethodLecture 20 - Sensitivity Analysis - ILecture 21 - Sensitivity Analysis - IILecture 22 - Case studies and Exercises - ILecture 23 - Case studies and Exercises - IILecture 24 - Integer ProgrammingLecture 25 - Goal ProgrammingLecture 26 - Multi-Objective ProgrammingLecture 27 - Dynamic ProgrammingLecture 28 - Transportation ProblemLecture 29 - Assignment Problem

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Lecture 30 - Case studies and ExercisesLecture 31 - Processing n Jobs on Two MachinesLecture 32 - Processing n Jobs through Three MachinesLecture 33 - Processing two jobs through m machinesLecture 34 - Processing n jobs through m machinesLecture 35 - Case studies and ExercisesLecture 36 - Two Person Zero-Sum GameLecture 37 - Theorems of Game TheoryLecture 38 - Solution of Mixed Strategy GamesLecture 39 - Linear Programming method for solving gamesLecture 40 - Case studies and Exercises

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NPTEL Video Course - Mathematics - Advanced Matrix Theory and Linear Algebra for Engineers

Subject Co-ordinator - Prof. Vittal Rao

Co-ordinating Institute - IISc - Bangalore

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Prologue - Part 1Lecture 2 - Prologue - Part 2Lecture 3 - Prologue - Part 3Lecture 4 - Linear Systems - Part 1Lecture 5 - Linear Systems - Part 2Lecture 6 - Linear Systems - Part 3Lecture 7 - Linear Systems - Part 4Lecture 8 - Vector Spaces - Part 1Lecture 9 - Vector Spaces - Part 2Lecture 10 - Linear Independence and Subspaces - Part 1Lecture 11 - Linear Independence and Subspaces - Part 2Lecture 12 - Linear Independence and Subspaces - Part 3Lecture 13 - Linear Independence and Subspaces - Part 4Lecture 14 - Basis - Part 1Lecture 15 - Basis - Part 2Lecture 16 - Basis - Part 3Lecture 17 - Linear Transformations - Part 1Lecture 18 - Linear Transformations - Part 2Lecture 19 - Linear Transformations - Part 3Lecture 20 - Linear Transformations - Part 4Lecture 21 - Linear Transformations - Part 5Lecture 22 - Inner Product and Orthogonality - Part 1Lecture 23 - Inner Product and Orthogonality - Part 2Lecture 24 - Inner Product and Orthogonality - Part 3Lecture 25 - Inner Product and Orthogonality - Part 4Lecture 26 - Inner Product and Orthogonality - Part 5Lecture 27 - Inner Product and Orthogonality - Part 6Lecture 28 - Diagonalization - Part 1Lecture 29 - Diagonalization - Part 2

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Lecture 30 - Diagonalization - Part 3Lecture 31 - Diagonalization - Part 4Lecture 32 - Hermitian and Symmetric matrices - Part 1Lecture 33 - Hermitian and Symmetric matrices - Part 2Lecture 34 - Hermitian and Symmetric matrices - Part 3Lecture 35 - Hermitian and Symmetric matrices - Part 4Lecture 36 - Singular Value Decomposition (SVD) - Part 1Lecture 37 - Singular Value Decomposition (SVD) - Part 2Lecture 38 - Back To Linear Systems - Part 1Lecture 39 - Back To Linear Systems - Part 2Lecture 40 - Epilogue

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NPTEL Video Course - Mathematics - Ordinary Differential Equations and Applications

Subject Co-ordinator - Prof. A.K. Nandakumaran, Prof. Raju K. George, Prof. P.S. Datti

Co-ordinating Institute - IISc - Bangalore | IIST - Trivandrum | TIFR-CAM - Bangalore

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - General IntroductionLecture 2 - ExamplesLecture 3 - Examples (Continued - I)Lecture 4 - Examples (Continued - II)Lecture 5 - Linear AlgebraLecture 6 - Linear Algebra (Continued - I)Lecture 7 - Linear Algebra (Continued - II)Lecture 8 - AnalysisLecture 9 - Analysis (Continued...)Lecture 10 - First Order Linear EquationsLecture 11 - Exact EquationsLecture 12 - Second Order Linear EquationsLecture 13 - Second Order Linear Equations (Continued - I)Lecture 14 - Second Order Linear Equations (Continued - II)Lecture 15 - Well-posedness and Examples of IVPLecture 16 - Gronwall's LemmaLecture 17 - Basic Lemma and Uniqueness TheoremLecture 18 - Picard's Existence and Uniqueness TheoremLecture 19 - Picard's Existence and Uniqueness (Continued...)Lecture 20 - Cauchy Peano Existence TheoremLecture 21 - Existence using Fixed Point TheoremLecture 22 - Continuation of SolutionsLecture 23 - Series SolutionLecture 24 - General System and DiagonalizabilityLecture 25 - 2 by 2 systems and Phase Plane AnalysisLecture 26 - 2 by 2 systems and Phase Plane Analysis (Continued...)Lecture 27 - General SystemsLecture 28 - General Systems (Continued...) and Non-homogeneous SystemsLecture 29 - Basic Definitions and Examples

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Lecture 30 - Stability Equilibrium PointsLecture 31 - Stability Equilibrium Points (Continued - I)Lecture 32 - Stability Equilibrium Points (Continued - II)Lecture 33 - Second Order Linear Equations (Continued - III)Lecture 34 - Lyapunov FunctionLecture 35 - Lyapunov Function (Continued...)Lecture 36 - Periodic Orbits and Poincare Bendixon TheoryLecture 37 - Periodic Orbits and Poincare Bendixon Theory (Continued...)Lecture 38 - Linear Second Order EquationsLecture 39 - General Second Order EquationsLecture 40 - General Second Order Equations (Continued...)

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NPTEL Video Course - Mathematics - NOC:Linear Algebra

Subject Co-ordinator - Prof. Dilip P. Patil

Co-ordinating Institute - IISc - Bangalore

Sub-Titles - Available / Unavailable | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Introduction to Algebraic Structures - Rings and FieldsLecture 2 - Definition of Vector SpacesLecture 3 - Examples of Vector SpacesLecture 4 - Definition of subspacesLecture 5 - Examples of subspacesLecture 6 - Examples of subspaces (Continued...)Lecture 7 - Sum of subspacesLecture 8 - System of linear equationsLecture 9 - Gauss eliminationLecture 10 - Generating system, linear independence and basesLecture 11 - Examples of a basis of a vector spaceLecture 12 - Review of univariate polynomialsLecture 13 - Examples of univariate polynomials and rational functionsLecture 14 - More examples of a basis of vector spacesLecture 15 - Vector spaces with finite generating systemLecture 16 - Steinitzs exchange theorem and examplesLecture 17 - Examples of finite dimensional vector spacesLecture 18 - Dimension formula and its examplesLecture 19 - Existence of a basisLecture 20 - Existence of a basis (Continued...)Lecture 21 - Existence of a basis (Continued...)Lecture 22 - Introduction to Linear MapsLecture 23 - Examples of Linear MapsLecture 24 - Linear Maps and BasesLecture 25 - Pigeonhole principle in Linear AlgebraLecture 26 - Interpolation and the rank theoremLecture 27 - ExamplesLecture 28 - Direct sums of vector spacesLecture 29 - Projections

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Lecture 30 - Direct sum decomposition of a vector spaceLecture 31 - Dimension equality and examplesLecture 32 - Dual spacesLecture 33 - Dual spaces (Continued...)Lecture 34 - Quotient spacesLecture 35 - Homomorphism theorem of vector spacesLecture 36 - Isomorphism theorem of vector spacesLecture 37 - Matrix of a linear mapLecture 38 - Matrix of a linear map (Continued...)Lecture 39 - Matrix of a linear map (Continued...)Lecture 40 - Change of basesLecture 41 - Computational rules for matricesLecture 42 - Rank of a matrixLecture 43 - Computation of the rank of a matrixLecture 44 - Elementary matricesLecture 45 - Elementary operations on matricesLecture 46 - LR decompositionLecture 47 - Elementary Divisor TheoremLecture 48 - Permutation groupsLecture 49 - Canonical cycle decomposition of permutationsLecture 50 - Signature of a permutationLecture 51 - Introduction to multilinear mapsLecture 52 - Multilinear maps (Continued...)Lecture 53 - Introduction to determinantsLecture 54 - Determinants (Continued...)Lecture 55 - Computational rules for determinantsLecture 56 - Properties of determinants and adjoint of a matrixLecture 57 - Adjoint-determinant theoremLecture 58 - The determinant of a linear operatorLecture 59 - Determinants and VolumesLecture 60 - Determinants and Volumes (Continued...)

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