· Web viewINTEGRAL AND VECTOR CALCULUS UNIT I Multiple Integrals - Definition – Evaluation –...

JMC UG MATHEMATICS - 2008

Sub Code: 08UMA1401 Max Marks: 100Hours/Week: 6 Internal Marks: 25Credit: 5 External Marks: 75

DIFFERENTIAL CALCULUS AND 3DUNIT ISuccessive Differentiation: nth derivatives of standard result - Trigonometrical transformation. Formation of equations involving derivatives– Liebnitz’s theorem for nth derivative of a product of functions – Applicable to some suitable problems

UNIT IIHomogeneous functions – Partial derivatives of a function of two functions – Maxima and minima of function of two variables - Lagrange’s method of undetermined Multipliers.

UNIT IIICurvature: Circle, Radius and Center of Curvature- Cartesian Formula for the Radius of Curvature – Coordinates of the Centre of Curvature – Evolute and Involute - Radius of Curvature when the curve is given in Polar coordinates.

UNIT IVEquation of a sphere – Finding centre and radius – Length of the tangent from the point to the sphere- Plane section of a sphere. Equation of a circle on a sphere – Intersection of two spheres is a circle – Equation of the tangent plane to a sphere at a point - Related examples.

UNIT V Cone – Righr circular cone – Intersection of a straight line and a quadric cone – Condition for the plane to touch the quadric cone – Cylinder – The equation of the cylinder whose generators are parallel to the line and guiding curve – The equation of the right circular cylinder with axix and radius of the guiding circle .Text Books:T.B.1. Calculus Vol.–I: T.K. Manickavasagam Pillai and Others R.Edition – 2004.T.B 2. Analytical geometry of three dimensions, T.K. Manicavachagom Pillai and others. UNIT I Chapter III: Full T.B.1 UNIT II Chapter VIII – Sec 1.6, 1.7 Sec 4, 5 T.B.1 UNIT III Chapter X – Sec 2.1- 2.6 T.B.1 UNIT IV Chapter - IV Sec 2 - 8 T.B 2UNIT V Chapter – V Sec. 2,3,5,8 T.B 2Reference Books:

1. Differential and Integral Calculus by Philip Franklin.2. Calculus by S. Arumugam and Issac.3. Analytical Solid Geometry -Shanti Narayan, S.Chand & Company Ltd, New

Delhi.4. Degree Level Analytical Geometry of Three Dimensions - Dasgupta Prasad,

Bharat Bhawar, publishers and distributors

1



INTEGRAL AND VECTOR CALCULUS

UNIT I Multiple Integrals - Definition – Evaluation – Illustrative Examples – Double Integrals in Cartesian coordinates and polar coordinates – change the order of Integration – Triple Integral - Some more worked examples.

UNIT II Gamma functions – Beta functions – Relation between Beta and Gamma functions – Properties and examples – Integrals using Gamma and Beta functions – Applications of Gamma functions to multiple Integrals.

UNIT III Vector differentiation – vector and scalar field – divergence and curl – application of Laplacian operator.

UNIT IV Vector integration: Line integral – surface integral – volume integral – problems on these.

UNIT V Gauss divergence theorem – Stoke’s theorem, Green’s theorem – simple verification of theorems and problems.

Text Book: T.B 1. Calculus Volume - II by T. K. Manicavachagom and others.S.Viswanathan Publishers, Pvt. Ltd. (2004)T.B 2. Vector Algebra and Analysis, Narayanan.S and ManicavachagomPillai. T.K. S.Viswanathan Pvt.Ltd. 1995

UNIT I: Chapter 5 - Sec.2 – 4 T.B 1 UNIT II: Chapter 7 - Sec.2 – 6 T.B 1 UNIT III: Chapter 4: Sec.6 – 12 T.B 2UNIT IV: Chapter 6:Sec.2 – 5.1 T.B 2UNIT V: Chapter 6:Sec.6 – 10 T.B 2Reference Books:1. Calculus Volume – II, 2nd Edition, Tom.M. Apostol.

2. Vector Analysis, M.L.Khanna, Jai Prakash Nath & Co.

2



SBE1: THEORY OF EQUATIONS AND TRIGONOMETRYUNIT IRelation between the roots and coefficients of equations

UNIT II Symmetric functions of the roots

UNIT IIITransformation of equation – Roots with sign changed, Roots Multiplied by a given number –Diminishing, Increasing the roots of a given equation by a given quantity

UNIT IV Summation of Trigonometrical Series - Methods of difference - Sum of sines of n angles in A.P - Sum of cosines of n angles in A.P

UNIT VSummation of series by using complex quantities - Gregory’s series – Euler’s series

Text Books:T.B 1: Algebra (Volume-I), T.K.Manicavachagam Pillai, T.Natarajan, & K.S Ganapathy, S. Viswanathan (Priters & Pubishers) Pvt. LTD., Chennai , 2004

T.B 2:. Trigonometry , S.Narayanan and T.K.Manicavachagom Pillai , S. Viswanathan (Priters & Pubishers) Pvt. LTD., Chennai, 2006.

UNIT I : Chapter 6: Section 11 T.B. 1UNIT II : Chapter 6: Section 12 T.B. 1UNIT III : Chapter 6: Sections 15.1, 15.2, 17 T.B. 1UNIT IV : Chapter 6: sections 1, 2 T.B. 2UNIT V : Chapter 6: section 3 T.B. 2

Reference Books:1. Theory of Equations - M.L.Kanna, Jai Prakasnath & Co, Meerut.

2. Algebra ( Theory of Equations, Inequalities and Theory of numbers ), Arumugam , Isaac, New Gamma Publishing House, Palayamkottai,2006.

3


SubCode: 08UMA2403 Max Marks: 100Hours/Week: 6 Internal Marks: 25Credit: 4 External Marks: 75

SEQUENCES AND SERIES

UNIT I Sequences: Limit of a Sequence, upper and lower bounds of an aggregate - Bounded Sequence, upper and lower limits of a sequence, Cauchy`s general principle of convergence.

UNIT II Monotone sequence: Infinite series – Definition of convergence, divergence and oscillation – Limit of a monotone sequence - Necessary condition for convergence - Geometric series – Some general theorems concerning infinite series – Series of positive terms.

UNIT III Tests of convergence: Comparison Tests - Tests of convergence of 1/ nk - D’Alembert’s Ratio test – Simple problems.

UNIT IVTests of convergence: Cauchy’s root test - Raabe’s test – Alternate series – Absolutely convergent series – Standard theorems – Series whose terms are alternately positive and negative - Simple problems..

UNIT V Kummer’s test, Logarithmic ratio test – Modified forms for Applications – Cauchy’s condensation test – Gauss test – Cauchy Maclaurin Integral test.

Text Books:T.B 1. Algebra volume I - Manicavasagom Pillai, Natarajan & Ganapathy. T.B 2. Fundamental Real Analysis, S.L. Gupta and Nisha Rani, 2nd Edition, Vikas Publishing House (P) Ltd.

UNIT I: Chapter II Sections 4 – 6 T.B 1 UNIT II: Chapter II Sections 7 - 9, 11, 12. T.B 1 UNIT III: Chapter II Sections 13-16 T.B 1 UNIT IV: Chapter II Sections 17, 19, 21,22, 24 T.B 1 UNIT V: Chapter VI sections 6.4.2., 6.4.3., 6.4.4., 6.5, 6.5.2, 6.6. T.B 2

Reference Book:Elements of Real Analysis, Shanthi Narayan, VI Edition.

4


Sub Code: 08UMA3304:1 Max Marks: 100Hours/Week: 5 Internal Marks: 25Credit: 3 External Marks: 75

MATHEMATICAL STATISTICS-I

UNIT IMeasures of central tendencies- Arithmetic Mean, Properties of Arithmetic Mean, Weighted mean, Median, Mode, Geometric mean and Harmonic mean Graphical Location of the Partition values. Merits and Demerits of Mean, Median and Mode.

UNIT IIMeasures of Dispersion, Skewness and Kurtosis – Dispersion, , characteristics for ideal measure of dispersion, Measures of Dispersion ,Range, Q.D, M.D and S.D, coefficient of dispersion, coefficient of variation, Moments, Pearson’s and Co-efficients, Skewness and Kurtosis - simple problems.

UNIT IIITheory of probability- Classical probability; empirical probability; Axiomatic approach towards probability; Addition and Multiplication theorem; Conditional probability; Baye’s theorem; simple problem.

UNIT IVRandom variable; Distribution function; Properties; Probability mass function; Probability density function; Joint probability mass function; Joint probability density function; Marginal and Conditional distribution – Simple problems.

UNIT VMathematical Expectation; Addition theorem of Expectation; Multiplication theorem of Expectation; Moment Generating Function; Cumulant Generating Function and cumulants, Additive Property of Cumulants – Simple problems.

Text Book:Elements of mathematical statistics - S.C.GUPTA & V.K.KAPOOR, Sultan Chand publication, Third edition, Reprint 2006

UNIT-I: Sec. 2.3 - 2.9.1 & 2.11.1

UNIT-II: Sec. 3.1 – 3.7, 3.7.3, 3.8, 3.8.1, 3.9, 3.10 - 3.12

UNIT-III: Sec. 4.1, 4.3.1, 4.3.2, 4.5, 4.6.2 – 4.9

UNIT-IV: Sec. 5.1 – 5.4.1, 5.5.1 – 5.5.5

UNIT-V: Sec. 6.1- 6.4, 6.10, 6.11 & 6.17

Reference Books:1.Probability and Mathematical Statistics by Marek Fisz – John Wiley & Sons.2.Modern Probability Theory by B.R. Bhat – Wily Eastern Ltd.

5


Sub Code: 08UMA3404 Max Marks: 100Hours/Week: 5 Internal Marks: 25Credit: 4 External Marks: 75 DIFFERENTIAL EQUATIONS AND FOURIER SERIES

UNIT IEquations of the first order but of higher degree: Equations solvable for dy/dx - Equations solvable for y - Equations solvable for x – Clairaut’s form – Equations that do not contain x explicitly - Equations that do not contain y explicitly - Equations homogeneous in x and y – Exact Differential Equations – Practical Rule – Rules for finding Integrating factorsUNIT IIApplications of first order equation: growth, decay and chemical reactions. Flow of water from an orifice – Falling bodies and other rate problems – Free fall under gravity - retarded fall.UNIT IIILinear Equations with constant coefficients: Complementary function of a linear equation with constant coefficients – General methods of finding Particular Integrals – Linear Equations with variable coefficients – Equations reducible to the linear equations UNIT IVPartial differential equations (PDE): Definition - Formation of PDE by eliminating constants – Formation of PDE by eliminating arbitrary functions – Types of solution of PDEs – Solution of first order PDE – Standard forms I, II, III, and IV (Clairaut’s form) – Lagrange’s Linear Equations – Solution of simultaneous Equations – Charpit’s methodUNIT V Fourier series: Definition of Fourier series – Finding Fourier series expansion of a periodic function with period 2л. Odd and Even functions – Development in cosine series and sine series.

Text Books:T.B 1. Differential Equation and its Application, S. Narayanan and T. K. Manicavachagom Pillay, S. Viswanathan (Printers & Publishers) Private Limited, Ninth edition (1996)T.B 2. Dr. M. K. Venkataraman, Engineering Mathematics Volume III B- National Publishing Company, 13th Edition, 1998. T.B 3. Calculus, Volume -III - T.K.Manicavachagam pillai &OthersUNIT I Chapter IV – Sec. 1 – 4 ; Chapter II – Sec. 6.1 – 6.4 . T.B 1.UNIT II Chapter III- Sec. 1 – 3. T.B 1. UNIT III Chapter V – Sec. 1 – 6. T.B 1. UNIT IV Chapter II – Sec. 1 – 4, 6 – 8, 12. T.B 2. UNIT V Chapter VI: 1, 2,3 and 5 T.B 3.Reference Book: 1. A first course in Differential Equations with Applications – A.H.Siddiqi and P. Manchanda. 2. Theory and Problems of Advanced Calculus by Murray. R. Spiegel. SI (Metric) edition.Sub Code: 08UMA3405 Max Marks: 100

6


Hours/Week: 4 Internal Marks: 25Credit: 4 External Marks: 75

STATICS

UNIT IForces Acting at a point - parallelogram of forces – triangle of forces – Lamis Theorem – Extended form of the parallelogram of law of forces – Resultant of any number of coplanar forces acting at a point.

UNIT IIResultant of two like and unlike parallel forces acting on a rigid body – Moments of a force – Vargon’s Theorem of moments – couple – Equilibrium of two couples.

UNIT III Equilibrium of three forces acting on a rigid body – Three coplanar forces – Two trigonometrical theorems – coplanar forces – reduction of any number of coplanar forces – conditions for a system of forces to reduce to a single force or to a couple – equation to the line of action of the resultant.

UNIT IVFriction – Laws of friction – Co-efficient of friction, angle and cone of friction – Equilibrium of a particle on a rough inclined plane under any forces – problems on friction.

UNIT VUniform string under the action of gravity - Equilibrium of strings and chain under gravity – equation of common catenary – tension at any point – geometrical properties of the common catenaries – problems.

Text Book: A text book of Statics, Dr. M.K. Venkataraman , Agasthiar Publication, July 1971

UNIT I: Chapter 2: Sec. 3 to 5, 9,10 and 15 UNIT II: Chapter 3: Sec. 1 to 4, 7, 8, 12; Chapter 4: Sec 1 and 2 UNIT III: Chapter 5: Sec. 1, 2, 5; Chapter 6: Sec 1, 2, 3, 5 and 8UNIT IV: Chapter 8: Sec. 1 to 10 and 13UNIT V: Chapter 11: sec 1 to 6

Reference Books:1. Statics, A.V. Dharmapudam.2. Statics, A.S. Ramsey.

Sub Code: 08UMA3702 Max Marks: 100

7



SBE2: MATHEMATICS FOR COMPETITIVE EXAMINATIONS - I

UNIT I

Numbers: Problems on Addition, Subtraction, Multiplication and Division ( Shortcut Methods) – Various tests for Divisibility – Prime and Composite numbers – Various types of numbers.

UNIT II

HCF and LCM of numbers - Decimal fractions: Addition, Subtraction, Multiplication and Division of Decimal fractions - H.C.F and L.C.M of Decimals – Rule for converting Pure and Mixed Recurring Decimals into a Vulgar Fractions.

UNIT III

Simplification - Square Root: Square Root by means of Factors – General Method – Square Root of Decimal Fractions - Square Root of Vulgar Fractions - Cube Root.

UNIT IVPercentage: Shortcut Method – Problems based on Population, Average, Ratio and Proportion.

UNIT V

Partnership, Chain rule : Direct proportion – Indirect Proportion.

Reference books:1. Arithmetic (Subjective And Objective) For Competitive Examinations, R.S. Aggarwal, S.Chand & Company Ltd, New Delhi, 2004.2. Exhaustive Arithmetic, O.P. Agarwal, Avadh Prakashan, Agra3. Objective Arithmetic, R.S. Aggarwal, S.Chand & Company Ltd, New Delhi, 2004.4. Quantitative Aptitude, R.S. Aggarwal, S.Chand & Company Ltd, New Delhi, 2004.

Note:75 Multiple choice questions only. 15 Questions from each unit.

Sub Code: 08UMA3601 Max Marks: 100

8



NME1: BASIC STATISTICS

UNIT IClassical definition of probability– Axiomatic Approach to probability -Addition theorem – Conditional probability - Multiplication theorem.

UNIT II Measures of Averages - Mean, Median, Mode, Geometric Mean and Harmonic Mean - Merits and Demerits.

UNIT III Measures of Dispersion - Range Quartile Deviation., Mean Deviation., and Standard Deviation – Relative Measures - Merits and Demerits.

UNIT IV Correlation – Rank Correlation – Properties of Correlation coefficient – Regression Analysis – Properties of Regression coefficient ( Numerical problems only )

UNIT V Curve Fitting – Principle of Least squares – Fitting a straight line – Fitting a second degree polynomial – Fitting A curve of the form aebx , abx and axb

Text Book: Mathematical Statistics, P.R. VITTAL, Margham Publications, Chennai, Reprint 2004.

UNIT I Part - I Chapter 1 1.1 to 1.9UNIT II Part - II Chapter 5UNIT III Part - II Chapter 6UNIT IV Part - I Chapter 8 & 9UNIT V Part – I Chapter 10

Reference Book:Elements of mathematical statistics - S.C.GUPTA & V.K.KAPOOR, Sultan Chand publication, Third edition, Reprint 2006

Sub Code: 08UMA4305:1 Max Marks: 100

9



MATHEMATICAL STATISTICS – II

UNIT I Theoretical discrete distribution – Binomial distribution: Moments, Recurrence relation Moment generating Function Characteristic Function and Cumulants. Poisson distribution: Moments, Recurrence relation, Moment generating Function, Characteristic Function and Cumulants - Simple Problems.

UNIT II Theoretical continuous distribution - Rectangular (or) Uniform distribution, Normal distribution, Moment generating Function, Cumulant generating Function, Moments; Area Property, Fitting of Normal Distribution - Simple Problems.

UNIT IIITheoretical continuous distributions – Gamma Distribution, Moment generating Function, Cumulant generating Function, Additive property, Beta Distribution of first kind, Exponential Distribution - Simple Problems.

UNIT IVCurve Fitting and Principles of Least squares – Curve Fitting, Fitting of straight line, Fitting of second degree parabola, Fitting of polynomial of kth degree, Change of origin, Most plausible solution of a system of linear equations - Simple Problems.

UNIT V Bivariate distribution, Correlation, Scatter diagram, Pearson’s Coefficient of Correlation, Properties, Rank correlation, Regression - Lines of Regression, Regression Coefficient and its properties- Simple Problems.

Text Book:Elements of mathematical statistics - S.C.Gupta and V. K. Kapoor, Sultan Chand publication (Third edition, Reprint 2006)

Unit-I: Chapter 7: 7.1 to 7.5Unit-II: Chapter 8: 8.1, 8.2 and 8.6Unit-III: Chapter 13: 13.1 to 13.6; Chapter 14: 14.1 to 14.5.4Unit-IV: Chapter 12Unit-V: Chapter 13, 13.7; Chapter14: 14.5.4 to14.5.10

Reference Books:1. Probability and Mathematical Statistics by Marek Fisz – John Wiley & Sons.2. Statistical Inference by H.C. Saxena and P.U. Surndran S.Chand & Co.

Sub Code: 08UMA4306:1 Max Marks: 100Hours/Week: 5 Internal Marks: 25

10


Credit: 4 External Marks: 75

MATHEMATICAL STATISTICS – III

UNIT-1:Introduction : parameter and statistic, sampling distribution; standard error; principle steps in sample surveys; sampling versus census.

UNIT-2:Simple random sampling; merits and limitation of simple random sampling with specified precision.

UNIT-3:Stratified random sampling; principal advantages of stratification; allocation of sample size systematic sampling; variance of estimated mean; comparison between simple random sampling and stratified random sampling.

UNIT-4:Systematic sampling; Variance of estimated mean: Systematic sampling vs stratified sampling: merits and demerits – Cluster sampling – multistage sampling – quota sampling

UNIT-5:Planning and execution of sample surveys; sampling design; sampling inspection; Methods of data collection; Pilot survey; preparation of reports.

Text Books:

T.B. 1: Fundamentals of Applied Statistics, S.C.Gupta and V. K. Kapoor, Sultan Chand. Publiation.T.B. 2: Sampling Theory, Desraj, TMH Edition.T.B. 3: Sampling Theory, M.N. Murthy.

UNIT I: Chapter 8: 8.1 to 8.8 T.B. 1UNIT II: Chapter 8: 8.9 T.B. 1UNIT III: Chapter 8: 8.10 T.B. 1UNIT IV: Chapter 8: 8.11 to 8.14 T.B. 1UNIT V: Chapter 2: 2.5 T.B. 2 Chapter 14 T.B. 3

Reference Books:1. Probability and Mathematical Statistics by Marek Fisz – John Wiley & Sons.2. Statistical Inference by H.C. Saxena and P.U. Surndran S.Chand & Co.


11


DYNAMICS

UNIT IKinematics-Speed, Displacement - Velocity – Composition of velocities- Triangle of velocities- Relative velocity – Angular velocity -Relative angular velocities – Acceleration s– Motion in a straight line under uniform acceleration – Simple problems.

UNIT IIProjectiles – path of the projectile is a parabola – characteristics of the motion of a projectile – Velocity of the projectile in magnitude and direction at the end of time “ t “– Range on an inclined Plane– Simple problems.

UNIT IIICollision of elastic bodies – Newton’s experimental law – impact of a smooth sphere on a fixed smooth plane – Direct impact of two smooth spheres – Loss of Kinetic Energy -Oblique impact of two smooth spheres and loss of Kinetic Energy– Simple problems .

UNIT IVSimple harmonic motion - Simple harmonic motion in a straight line – General solution of a simple harmonic motion – Composition of two simple harmonic motions of the same period and in the same straight line – Composition of simple harmonic motions of the same period in two perpendicular directions – Simple problems.

UNIT V Motion under the action of central forces – velocity and acceleration in polar coordinates – differential equation of central orbits – pedal equation of the central orbit – Law of the inverse square– Simple problems.

Text Book:A Text Book of Dynamics, Dr. M. K. Venkatraman, Agasthiar Publications, Aug- 1970

UNIT I: Chapter III – 3.1 to 3.4, 3.7, 3.10, 3.11, 3.15, 3.17 and 3.22UNIT II: Chapter IV – 6.2, 6.4, 6.5, 6.9 and 6.12UNIT III: Chapter VIII – 8.3 to 8.8UNIT IV: Chapter X – 10.2, 10.3, 10.6 and 10.7UNIT V: Chapter XI –11.2, 11.4, 11.6, 11.8Reference Books:

1. Dynamics , M.L.Khanna, Jaiprakash Nadhan and Company, Meerut, 10th Edition, 1975.

2. Dynamics , K. Visvanatha Naik and M.S. Kasi, Emerald Publishers, Chennai.


12


NME2: BASIC OPERATIONS RESEARCH

UNIT IOperations Research – Origin and Development of OR – Nature and Features of OR Applications of OR - General Linear Programming Problem – Mathematical Formulation (Simple cases only)

UNIT IIGraphical method to solve an LPP - Solution, Feasible Solution, Optimum Solution, Unbounded solution, Alternative optimum solution and Infeasible solution of an LPP.

UNIT IIITransportation Problem – Balanced and unbalanced TP - Determination of Initial Basic Feasible Solution using 1. North West Corner Rule, 2. Least Cost Method and 3. Vogel’s Approximation Method. (Optimum Solution not expected)

UNIT IVAssignment Problem – Hungarian Algorithm – Unbalanced Assignment Problem – Maximization A.P.

UNIT VIntroduction – Network and Basic Components, Logical sequencing, Rules of Network Construction – Critical Path Analysis.

Text Book:Operations Research – Kanti Swarup,P.K. Gupta and Man Mohan. Sultan Chand & Sons (2005).

UNIT-I: Chapter – 1 :Sec 1.1,1.2 &1.7 Chapter - 2UNIT-II: Chapter – 3 :Sec 3.1,3.2 &3.4UNIT-III: Chapter – 10 :Sec 10.1-10.3, 10.9UNIT-IV: Chapter – 11 :Sec 11.1 – 11.3, 11.4.1UNIT-V: Chapter – 21: Sec 21.1 – 21.5.

Reference Book: Operations Research Theory And Applications, J.K. Sharma, Macmillan India Ltd., 2000.

Sub Code: 08UMA5407 Max Marks: 60Hours/Week: 3 nternal Marks: 15Credit: 3 External Marks: 45

13


C –PROGRAMMINGUNIT IConstants, Variables and Data Types – Character set – C tokens – Keywords and identifiers – Constants – Variables – Data types – Declaration of variables and storage class – Assigning values to variables – Defining symbolic Constants – Operators and Expression – Arithmetic of operators – Relational operators – Logical operators – Assignment operators – Increment and decrement operators – Conditional operator – Bitwise operators – Special operators – Arithmetic expressions – Evaluation of expressions – Precedence of arithmetic operators – Mathematical Functions – Managing Input and Output Operators – Reading character – Writing a character – Formatted input – Formatted output.UNIT IIDecision Making and Branching – Decision making with IF statement – Simple IF statement – The IF ELSE statement – Nesting IF…ELSE statements – The ELSE IF ladder – The switch statement – The ?: operator – The GOTO statement - Decision Making and Looping – The WHILE, DO, FOR statement – Jumps in loops.UNIT IIIHandling of Character String – Declaring and initializing string variables – Reading strings from terminal – Wring strings to screen – Arithmetic operations on characters – Putting strings together – Comparisons of two strings – String – Handling functions – Table of strings – Arrays – One-dimensional, Two-dimensional arrays and Multi-dimensional arrays – Pointers – Understanding pointers – Accessing the address of a variable – Declaring and initializing pointers – Accessing a variable a variable through its pointer – Pointer expressions – Pointer increments and scale factor – Pointers and arrays – Pointers and character strings.UNIT IVUser-Defined Functions – Need for user-defined functions – A multi-function program – The form of C functions – Return values and their types – Calling a function – Category of functions – No arguments and no return values – Arguments with return values – Handling of non-integer functions – Nesting of functions – Recursion.UNIT VFile Management in C – Defining and opening a file – closing file – Input/Output operations on files – Error handling during I/O operations – Random access to files.

Text Book:Programming in ANSI C (Third Edition), E.Balgurusamy, Tata McGraw-Hill Publishing Company Limited, New Delhi.

UNIT I - Chapter 2: 2.2 to 2.11; Chapter 3: 3.2 to 3.16; Chapter 4: 4.2 to 4.5UNIT II - Chapter 5: 5.2 to 5.9; Chapter 6: 6.2 to 6.5UNIT III - Chapter 8: 8.2 to 8.9; Chapter 7: 7.2 to 7.7; Chapter 11: 11.2 to 11.11UNIT IV - Chapter 9: 9.2 to 9.16UNIT V - Chapter 12: 12.2 to 12.6

Reference Book:Let us C by Yashavant Kanetkar – 7th Edition BPB Publications.

Sub Code: 08UMA5407P Max Marks: 40Hours/Week: 3 nternal Marks: 10Credit: 2 External Marks: 30

14


C PROGRAMMING LAB

1. Solving a Quadratic equation.

2. Sum of Series ( Sine, Cosine, ex)

3. Ascending and Descending Order of numbers.

4. Largest and Smallest of given numbers.

5. Sorting names in Alphabetical Order.

6. Finding Factorial, generating Fibonacci numbers using Recursive Functions.

7. Mean, Standard Deviation and Variance

8. Creation and Processing of sequential files for Payroll and Mark List Preparation.


15


MODERN ALGEBRA

UNIT I Groups: sub-groups-cyclic groups-co-sets and Lagrange’s theorem-Normal subgroups and quotient groups-Homomorphism-Isomorphism theorems.

UNIT II Rings: Definition of a ring and some examples-some properties of rings-some special classes of rings-sub rings and subfields-ideals and quotient rings-homomorphism.

UNIT III Euclidean Rings: Definition and some properties of Euclidean Rings- Unique factorization theorem – Gaussian Integers.

UNIT IVVector spaces: Definition and some properties of a vector space-Subspaces and quotient spaces-sums and direct sums-linear independence- basics and dimensions.Vector spaces: Homomorphisms - Dual spaces-inner product spaces.

UNIT VLinear Transformations and Matrices: Algebra of Linear Transformations – Eigen Values and Eigen Vectors – Algebra of Matrices.

Text Book:Modern Algebra by Dr. M.L. Santiago. Arul Publications,Madras (1988).

UNIT I: Chapter 2: Sec 2.4 – 2.9UNIT II: Chapter 3: Sec 3.1 – 3.6UNIT III: Chapter 4: Sec 4.1 – 4.3UNIT IV: Chapter 6: Sec 6.1 – 6.5,6.8UNIT V: Chapter 7: Sec 7.1 – 7.3

Reference book:Modern Algebra by Frank Ayres .JR. McGraw – Hill Book Company.


16


OPERATIONS RESEARCH

UNIT I Definitions of O.R - Application of O.R - Linear Programming Problem-Mathematical formulation - Graphical Solution Method, Alternative optimal solution, Unbounded solution, Infeasible solution, General LPP- Standard LPP-Basic Solution-Basic Feasible and Infeasible solution-Degenerate solution.

UNIT II Simplex Algorithm-Artificial variable Techniques – Big M method and Two-phase method – Alternate optimal solution – Degeneracy – Unbounded and Infeasibility.

UNIT IIIIntroduction – General Primal Dual pair – Formation of a Dual problem - Duality and Simplex method, Dual simplex method.

UNIT IV Introduction – General Transportation Problem -Finding an Initial Basic Feasible Solution using North-West Corner Rule, Least Cost Entry Method and VAM - MODI method –Assignment problem – Hungarian method.

UNIT VNetwork scheduling by CPM and PERT – Network Basic components logical sequencing, Rules of network constructions – Critical Path Analysis – Probability consideration in PERT, Distinction between CPM & PERT.

Note: Theoretical proof not expected.

Text Book: Operation Research: Kanti Swarup, P.K.Gupta and Man Mohan, Sultan Chand and sons, New Delhi, XIIth Edition 2004UNIT I: Chap: 1.1, 1.2, 1.7, 2.1, 2.2, 3.1 to 3.5.UNIT II: Chap: 4.3 and 4.4.UNIT III: Chap: 5.1, 5.2, 5.3, 5.7, 5.9UNIT IV: Chap: 10.1, 10.2,10.9.10.12,10.14,11.2 to11.4.UNIT V: Chap: 21.1-21.7.Reference Books:1. Problems in O.R (methods & solutions) P.K.Gupta and Man mohan Sultan chand and sons.2. Operation Research Theory and Application. J.K.Sharma, Macmillian India Ltd 2000.


17


REAL ANALYSIS

UNIT I Countable and uncountable sets - Limit of a function - Theorems based on limits – Order relation and limits - Infinite limits and limits at infinity

UNIT II Continuous functions - Algebra of continuous functions - Properties of continuous functions - Uniform continuity - Discontinuities of a function.

UNIT IIIDerivative of a function – Algebra of derivatives – Derivative of the composition of two functions - Derivative of the inverse of a function – Darboux’s Theorem - Derivatives of higher order.

UNIT IV Rolle’s theorem-Lagrange’s Mean Value theorem - Cauchy’s Mean Value theorem – Taylor’s theorem with Lagrange’s form of remainder – Taylor’s theorem with Cauchy form of remainder.

UNIT VRiemann Theory of Integration - Upper and Lower Integrals- Riemann Integral - some classes of Integrable Functions - Algebra of Integrable Functions – Inequality relations- Mean value theorems of Integral Calculus - Fundamental theorem of Integral Calculus.

Text Book:Real Analysis by P.K.Gupta and Sharda Gupta, 1st edition, 1993, Sultan Chand & Sons, New Delhi-2.

UNIT I: Chapter-1 Sec 1.7, Chapter-4: Sec 4.1 to 4.4UNIT II: Chapter-4 Sec 4.5 to 4.9UNIT III: Chapter-5 Sec 5.1 to 5.4, 5.6, 5.7UNIT IV: Chapter-6 Sec 6.1,6.2, 6.4 Chapter-8 Sec 8.1,8.2UNIT V: Chapter-9 Sec 9.2 to 9.8, 9.10

Reference Books:1. Real Analysis, M.K.Singhal & Asha Rani Singhal, 14th Edition, 1991, R.Chand &Co, New Delhi.2. Elements of Real analysis for Under Graduates, Dr. K.C. Sharma and Dr.G.N. Purohit, 3 rd

Revised Edition, 1983, Ramesh Book Depot. Jaipur


18


MBE1: NUMERICAL METHODS

UNIT ISolution of Algebraic and Transcendental equation – Bisection Method, Iteration Method, Method of False position, Newton Raphson Method, Generalised Newton`s Method.

UNIT IIFinite differences – Forward differences, Backward differences, Central differences, Symbolic relations, Newton`s formula for interpolation. Interpolation with unevenly spaced points – Lagranges interpolation formula, divided differences and their properties, Newton`s general interpolation formula.

UNIT IIINumerical differentiation and integration - Numerical differentiation (Excluding cubic spline method, maximum and minimum values of a tabulated function), Numerical integration – Trapezoidal Rule and Simpson`s Rule.

UNIT IVSolution of linear Systems - Direct Methods – Gaussian Elimination method, Method of Factorization, Iterative method – Jacobi and Gauss Seidal methods.

UNIT VNumerical Solution of ordinary differential equations – Solution by Taylor Series, Picard’s method of Successive approximations, Euler method, Modified Euler method, Runge-Kutta methods

Text Book:Introductory Methods of Numerical Analysis, S.S. SASTRY, Third Edition, Prentice Hall of India Pvt. Ltd. New Delhi. 2000

UNIT I: Chapter 2: Section 2.1 to 2.5.1 UNIT II: Chapter 3: Section 3.3,3.6, 3.9.1, 3.10, 3.10.1UNIT III: Chapter 5: Section 5.1, 5.2 (Excluding 5.2.1 and 5.2.2), 5.4, 5.4.1, 5.4.2UNIT IV: Chapter 6: Section 6.3, 6.3.2, 6.3.2, 6.3.4, 6.4.UNIT V: Chapter 7: Section 7.2 to 7.4, 7.4.2, 7.5

Reference Book:Introduction to Numerical Analysis by F.B. Hildebrand TMH Edition (II).


19


SBE3: SPSS - PRACTICALS

1. Calculation of Means, Standard deviations, Variances, correlation and regression.

2. Application of t-test for one sample problem.

3. Application of t-test for two sample problems.

4. Application of t-test for testing the significance of Correlation Coefficient.

5. One-tailed and Two-tailed tests.


20


SBE4: MATHEMATICS FOR COMPETITIVE EXAMINATIONS - II

UNIT I

Time and work, Pipes and Cisterns.

UNIT II

Time and Distance, Trains, Boats and Streams

UNIT III

Profit and Loss, Mixture.

UNIT IV

Simple interest and Compound interest, Calendar.

UNIT V

Volume and Area of Solid figures

Reference books:1. Arithmetic (Subjective And Objective) For Competitive Examinations, R.S. Aggarwal, S.Chand & Company Ltd, New Delhi, 2004.2. Exhaustive Arithmetic, O.P. Agarwal, Avadh Prakashan, Agra3. Objective Arithmetic, R.S. Aggarwal, S.Chand & Company Ltd, New Delhi, 2004.4. Quantitative Aptitude, R.S. Aggarwal, S.Chand & Company Ltd, New Delhi, 2004.

Note:75 Multiple choice questions only. 15 Questions from each unit.


21


GRAPH THEORY AND ITS APPLICATIONS

UNIT IIntroduction: Graph – Finite and Infinite graphs – Incidence and Degree – Isolated vertex, pendant vertex and Null graphs. Paths and Circuits: Isomorphism – sub-graphs – walks, paths and circuits – Connected and disconnected graphs – Euler graphs –Hamiltonian paths and circuits.

UNIT IITrees and fundamental circuits: Trees – Properties of Trees – Pendant vertices in a Tree – Distance and centers in a Tree – Spanning Trees – Fundamental circuits – Spanning trees in a weighted graph.

UNIT IIICut sets and cut vertices: Cut sets – Properties of a cut set – all cut sets in a graph – Fundamental circuits and cut sets – Connectivity and Separability.

UNIT IVPlanar and dual graphs: Planar graphs – Kuratowski’s two graphs – Representation of a planar graph – Detection of planarity – Geometric dual.

UNIT VMatrix Representation of graphs: Incidence Matrix – Circuit matrix – Fundamental circuit matrix and Rank of circuit matrix – Cut set matrix – Relationship among Af, Bf

and Cf – Path matrix.

Text Book:Graph theory with application to Engineering and Computer Science, Narsingh Deo – Prentice Hall of India Pvt Ltd, 2005

UNIT I: Chapter 1: sections 1.1, 1.3 – 1.5. Chapter 2: sections 2.1, 2.2, 2.4 – 2.6 and 2.9.UNIT II: Chapter 3: sections 3.1 – 3.4, 3.7,3.8, 3.10UNIT III: Chapter 4: sections 4.1 – 4.5.UNITIV: Chapter 5: sections 5.2 – 5.6.UNIT V: Chapter 7: sections 7.1 – 7.4 & 7.6 – 7.8.

Reference Books:1. Invitation to Graph Theory, Arumugam.S and Dr.Ramachandran.S, New

Gamma Publishing House, Palayamkottai, 2006.2. Graph Theory, Choudum.S.A –Macmillan India Limited, New Delhi.3. Graph Theory, Harary.F –Narosa Publishing House, New Delhi.


22


NUMBER THEORY

UNIT IDivisibility theory in the Integers: The division algorithm-the greatest common divisor-the Euclidean algorithm-the Diophantine equation ax + by = c

UNIT IIPrimes and their distribution: The fundamental theorem of arithmetic- The Sieve of Eratosthenes- The Goldbach Conjecture.

UNIT IIIThe theory of congruences: Karl Friedrich Gauss- Basic properties of congruence- Special divisibility tests- linear congruences.

UNIT IVFermat’s theorem: Pierre de Fermat – Fermat’s factorization method – The Little theorem- Wilson’s theorem

UNIT VNumber – theoretic functions: The functions τ and σ – The MÖbius inversion formula- The greatest integer function.

Text Book: Elementary Number Theory (Second Edition), David M. Burton, Universal Book Stall, New Delhi, 1991

UNIT I: Chapter II UNIT II: Chapter IIIUNIT III: Chapter IVUNIT IV: Chapter V UNIT V: Chapter VI

Reference Book:An introduction to the Theory of Numbers, Third Edition Ivan Niven and Herbert S. Zuckerman, Wiley Eastern Ltd, 1972


23


COMPLEX VARIABLES AND APPLICATIONS

UNIT IAnalytic Functions-Functions of a Complex Variable, Limits, Theorem on Limits, Continuity, Derivatives, Differentiation Formulas, Cauchy-Riemann Equations, Sufficient Condition for Differentiability, Polar Coordinates, Analytical functions, Harmonic Functions.

UNIT IIIntegrals - Derivatives of function w(t), Definite integrals of function w(t), Contours, Contour integrals, Cauchy-Goursat Theorem, Proof of the Theorem, Simply and Multiply Connected Domains, Cauchy Integrals Formula, Derivative of analytic function, Liouville’s theorem and Fundamental theorem of Algebra.

UNIT IIISeries-Taylor’s Series, Laurent series – Linear Fractional Transformations, An implicit form

UNIT IV Residues and Poles - Residues, Cauchy’s Residue Theorem, Using a Single Residue, The three types of Isolated Singular Points, Residue at Poles, Zeros of Analytic Functions, Zeros and Poles.

UNIT VApplications of Residues - Evaluation of Improper Integrals – Improper integrals from Fourier Analysis, Jordan’s Lemma, Indented Paths, Definite Integrals involving Sines and Cosines, Argument Principle, Rouche’s Theorem.

Text Book: Complex Variables and Applications – Seventh Edition, James Ward Brown, Ruel V. Churchill (2003)

UNIT I - Chapter 2 - Sections 11, 14, 15, 17 - 25.UNIT II - Chapter 4 - Sections 36 - 40, 44 - 49UNIT III - Chapter 5 - Sections 53 – 56 and Chapter 8: Sec 86, 87UNIT IV - Chapter 6 - Sections 62 - 69UNIT V - Chapter 7 - Sections 71 – 75, 78 - 80

Reference Book:Complex Analysis, Arumugam and Isaac, New Gamma Publishing House, Palayamkottai, 2006.

Sub Code: 08UMA6502 Max Marks: 100Hours/Week: 5 Internal Marks: 25

24



MBE2: DISCRETE MATHEMATICS

UNIT I Recurrence relation - Permutation functions - Growth of functions

UNIT IIPartially ordered sets - External elements of partially ordered sets - Lattices

UNIT IIIFinite Boolean algebra – Functions of Boolean algebra- Expressing Boolean functions as Boolean polynomials

UNIT IVCoding of Binary information and Error Detection

UNIT VDecoding and Error Correction

Text Book:Discrete Mathematical Structure ( 3th Edition – Twelfth printing ) – Kolman Busby Ross, Prentice-Hall of India, New Delhi, 2001.

UNIT I: Chapter 3 - 3.5, Chapter 5 - 5.3, 5.4UNIT II: Chapter 7 - 7.1 to 7.3UNIT III: Chapter 7 - 7.4 to 7.6UNIT IV: Chapter 11 – 11.1UNIT V: Chapter 11- 11.2

Reference Books:1.Discrete Mathematical structures with Applications to Computer Science – J.P.Tremblay and R.Manohar.2.Introduction to Automata Theory, Languages and Computation – John E.Hopcroft, Jeffery D.Ullman.


25


MBE3: LAPLACE AND FOURIER TRANSFORMS

UNIT ILaplace Transforms – Sufficient conditions for the existence of the Laplace transforms – Properties of Laplace transforms – Laplace transforms of Periodic functions – Some general theorems – Evaluation of integrals. The inverse Laplace transforms.

UNIT IIApplication of Laplace transforms – Solution of ODE with constant coefficients – Solution of ODE with variable coefficients – Solution of simultaneous ODE – Solution of PDE.

UNIT IIIDirichlet’s Conditions – Fourier Transforms – Inversion Theorem for complex Fourier Transforms – Sine and Cosine transforms – Linearity Property of Fourier Transforms – Change of scale property – Shifting property – Modulation Theorem.

UNIT IVFinite Fourier sine and cosine transforms – Inversion formula for sine and cosine transforms – Multiple finite Fourier Transforms – Operational properties of finite Fourier sine and cosine transforms – Combined properties of finite Fourier sine and cosine Transforms – Convolution.

UNIT VApplication of infinite Fourier Transforms – Choice of infinite sine or cosine transforms – Application of finite Fourier Transforms – Finite Fourier Transforms of Partial derivatives – Choice of finite sine and cosine transforms – Examples.

Text Books:T.B.1. Differential Equations and its applications – S. Narayanan & T.K. Manickavachagom Pillay.T.B.2. Integral transforms – A.R. Vasistha & R.K. Gupta.

UNIT-I: Chapter IX – Sec 1 to 7 T.B.1. UNIT-II: Chapter III – Sec 3.1 to 3.4 T.B.2. UNIT-III: Chapter VI – Section 6.1 to 6.13 T.B.2. UNIT-IV: Chapter VII – Section 7.1 to 7.9 T.B.2. UNIT-V: Chapter VIII – Section 8.1 to 8.5 T.B.2.

Reference Book:A First course in Differential equations with applications by A.H. Siddiqi & P.H Manchanda.


26


SBE4: MAT LAB

MATLAB Basics – Input and output – Arithmetic – Algebra – Symbolic Expressions, variable precession, and Exact Arithmetic – Managing variables – Errors in Input-Online Help – Variables and Assignments – Solving Equations – Vectors and Matrices – Vectors – Matrices – Suppressing Output -Functions – Built in function – User – defined functions – Graphics - The MATLAB Interface – M – Files – Loops

TEXT BOOKBrian R . Humt, Ronald L . Lipsman, Jonathan M. Rosenberg , “ A guide to MATLAB beginners and Experienced Users”, Cambridge University Press Edition, 2002.Chapters 2 & 3

MATLAB - PRACTICALS1. Write a MATLAB program involving matrix manipulation such as multiplication,

inverse, determinant 2. Write a MATLAB program to solve a system of linear equations.3. Write a MATLAB program to solve quadratic equation.4. Write a MATLAB program to solve algebraic equation using bisection method,

Newton Raphson method and Gauss elimination method.


27


SBE 6 : WEB DESIGNING UNIT I

Introduction to the Internet: Computers in Business – Networking – Internet – E Mail – Resource Sharing – Gopher – WWW – USENET – TELNET.

UNIT II

Internet Technologies: MODEM – Internet Addressing – Physical Connections – Telephone lines.

UNIT III

Internet Browsers: Internet Explorer – Window – Menus: File, Edit, View, Favorites, Tools – Tool Bar.

UNIT IV

Introduction to HTML – HEAD Section – title – BODY section – Heading Printing – Aligning the heading – Horizontal Rule – Paragraph - IMG tag.

UNIT V

Advanced Concepts: Anchor – Ordered and Unordered Lists – Nested Lists – Tables – Handling Frames.

Text Book:

World Wide Web design with HTML, C.Xavier, TMH 2000.

Reference Books:

The Complete Reference HTML , Second Edition, Thomas A. Powell, TMH 2000

The Complete Reference Web Design, Thomas A. Powell, TMH 2000


28


A4: ALLIED MATHEMATICS- I(For Physics and Chemistry Major)

UNIT IALGEBRA: Binomial Series, Exponential series, Logarithmic series.

UNIT IITHEORY OF EQUATIONS: Relation between the coefficients and the roots of an algebraic equation, Transformation of equations, Reciprocal equations.

UNIT IIIMATRICES: Various types of Matrices – Rank of a matrix, Simultaneous linear equations, Eigen values and Eigen vectors - Verification of Cayley-Hamilton theorem.

UNIT IVFINITE DIFFERENCES: Interpolation – Newton’s (Forward and Backward) Interpolation formula, Lagrange’s Interpolation formula.

UNIT VTRIGONOMETRY: Hyperbolic functions - Inverse hyperbolic functions - separation into real and imaginary parts, Logarithm of complex numbers.

Text Book:Ancillary Mathematics, Vol.1, S. Narayanan, R. Hanumantha Rao and T.K. Manicavachagom Pillay, S.Viswanathan (Printers and Publishers) Pvt Ltd, Revised Edition 2007. UNIT I: Chapter 1 : Sec. 1.2 to 1.4UNIT II: Chapter 2: Sec 2.2 to 2. 4 UNIT III: Chapter 3: Sec 3.1 to 3.4 UNIT IV: Chapter 4: Sec 4.1 and 4.3 UNIT V: Chapter 5: Sec 5.4 and 5.5 Reference Book:Allied Mathematics by A. Abdul Rashid, Vijay Nicole Publishing Company.


29


A5: ALLIED MATHEMATICS – II(For Physics and Chemistry Major)

UNIT IHigher Derivatives – The nth derivatives of standard functions – Trigonometrical transformation, Formation of equations involving derivatives - Leibnitz theorem (Statement only)

UNIT IIJacobian, Curvature, Cartesian formula for radius, circle and centre of curvature, Evolute and involute.

UNIT III Integration of rational algebraic functions, Integration of irrational functions.

UNIT IVProperties of definite Integrals – Integration by parts - Reduction Formulae for xne ax dx, sin n x dx, Cos n x dx, sin m x cos n xdx.

Unit VFourier series – Even and Odd function and Half range series

Text Books :

T.B.1. Ancillary Mathematics, Vol. I, S. Narayanan, R. Hanumantha Rao and T.K. Manicavachagom Pillay, S.Viswanathan (Printers and Publishers) Pvt Ltd, Revised Edition 2007.T.B.2. Ancillary Mathematics, Vol. II, S. Narayanan, R. Hanumantha Rao and T.K. Manicavachagom Pillay, S.Viswanathan (Printers and Publishers) Pvt Ltd, Revised Edition 2007.

UNIT I – Chapter 6: Sec 6.1 T.B.1. UNIT II – Chapter 6: Sec 6.2 and 6.4 T.B.1. UNIT III – Chapter 1: Sec:7 to 10 T.B.2. UNIT IV – Chapter 1: Sec 11, 12, 13.1,13.3, 13.4, 13.5 T.B.2.UNIT V - Chapter 2: Sec 1 to 5 T.B.2.

Reference Book:Allied Mathematics by A.Abdul Rashid, Vijay Nicole Publishing Company.

Sub Code: 08UMA4306:2 Max Marks: 100

30



A6: ALLIED MATHEMATICS –III(For Physics and Chemistry Major)

UNIT IDifferential equations of the first order with higher degree - Equations solvable for p Equations Solvable for y – Equations Solvable for x - Clairaut’s form.

UNIT IIPartial Differential Equations of the first order – Formation of PDE by eliminating arbitrary constants, Standard type of first order equations I, II, III and IV (Clairaut’s form), Lagrange’s equations.

UNIT III Laplace transforms of the function e at, e-at, f’(t), f”(t), cos at, sin at, cosh at, sinh at, tn , e-

at f(t), where n is a positive integer – Inverse transforms relating to the above standard functions, Application to ODE of order two with constant coefficients .

UNIT IVVector differential operator - Gradient – Direction and magnitude of gradient- Divergence and Curl – Laplacian Operator.

UNIT VLine Integral –Volume integral – Surface integral – Application of Gauss and Stoke’s Theorems (Statement Only), Simple Problems.

Text booksAncillary Mathematics, Vol. II, S. Narayanan, R. Hanumantha Rao and T.K. Manicavachagom Pillay, S.Viswanathan (Printers and Publishers) Pvt Ltd, Revised Edition 2007.

UNIT I: Chapter 4: Sec. 1 to 4 (PP. 228 to 236) UNIT II : Chapter 6: Sec. 2.1, 5 and 6 UNIT III: Chapter 7: Sec. 1 to 6 UNIT IV: Chapter 8: Sec. 16 to 20 and 22UNIT V: Chapter 8: Sec. 2 to 6 and 9.

Reference Book:Allied Mathematics by A.Abdul Rashid, Vijay Nicole Publishing Company.


31


A1: ALLIED MATHEMATICS –IFourier Series , Differential Equations and Vector Calculus

(For Computer Science Major)UNIT IFourier series: Definition - Even and Odd function - Half range Fourier series – Development in cosine series and sine series.UNIT IILinear Equations with constant coefficients– Complementary function – General methods of finding particular integrals – Linear Equation with variable coefficients.UNIT IIIPartial Differential Equations of the first order – Different integrals of PDE – Standard type – Solutions of PDE in some simple cases – Standard types of first order equation- Standard forms I,II,III and IV(Clairaut’s form ) – Lagranges methods of Solving Linear equations Pp +qQ = R.UNIT IVLaplace transforms of the function e at, e-at, f’(t), f”(t), cos at, sin at, cosh at, sinh at, tn , e-

at f(t), where n is a positive integer – Inverse transforms relating to the above standard functions - Solution of ODE of order two with constant coefficients using Laplace transforms.UNIT VVector differential operator –Vector and Scalar field - Gradient – Direction and magnitude of gradient- Divergence and Curl – Laplacian Operator.Line Integral –Volume integral – Surface integral – Gauss and Stoke’s Theorems (Statement Only), Verifications. - Simple Problems.

Text Books:1. Ancillary Mathematics (Volume II) Narayanan S., R. Hanumantha Rao and

Manicavachagom Pillai T.K: S.Viswanathan Pvt. Ltd., Chennai, Revised Edition, 2007.

2. Differential Equations and its Applications, Narayanan S. and Manicavachagam Pillai T.K S. Viswanathan Pvt Ltd, 2006

UNIT I: Chapter 2: Sec 1 to 5 T.B 1UNIT II: Chapter V: Sec. 1 to 5 T.B 2UNIT III: Chapter 6: Sec. 1 to 5.4 T.B 1UNIT IV: Chapter 7: Sec. 1 to 6 T.B 1UNIT V: Chapter 8: Sec. 1.15 to 1.20 and1. 22,2 to 6 and 9. T.B 1

Reference Books:1. Vector Analysis, Khanna M.L., Jai Prakash Nath & Co.2. Trigonometry and Fourier Series, Arumugam, Isaac & Somasundaram,

Gamma Publishing Houses


32


A2: ALLIED MATHEMATICS – IIProbability and Statistics

(For Computer Science Major)UNIT ITheory of probability: Classical probability- Axiomatic approach to probability – Probability function – Law of addition of probability - Law of Multiplication – Independent events - Baye’s theorem- Simple problems.

UNIT IIRandom variable-Distribution function – Properties of distribution function - discrete random variable - Probability mass function - Discrete distribution function. - Continuous random variable- Probability density function

UNIT IIIJoint probability law - joint probability mass function - joint probability density function - Marginal and Conditional distribution - Mathematical Expectation - Definition - Moment generating function.

UNIT IVCorrelation and Regression – Bivariate distribution, correlation – scatter diagram – Karl- Pearson’s coefficient of correlation – Calculation of correlation coefficient for a bivariate frequency distribution – Rank correlation – Regression - Properties of correlation and regression coefficients. (Numerical Problems only)

UNIT VTheoretical discrete distribution: Binomial, Poisson distributions, Moment generating function of these distributions and moments - recurrence relation for the moments of these distributions Text Book: Elements of Mathematical Statistics, S.C.GUPTA & V.K.KAPOOR, Sultan Chand & Sons, New Delhi, 3rd Edition (Reprint), 2006.

UNIT I: Chapter 4: Sec 4.3, 4.5, 4.6, 4.7, 4.8 and Chapter 5: Sec 5.1 to 5.3.2.UNIT II: Chapter 5: Sec 5.1 to 5.3.2, 5.4.1; UNIT III: Chapter 5: Sec 5.5.1 to 5.5.5 and Chapter 6: 6.1 to 6.4, 6.9 UNIT IV: Chapter 10: 10.1 to 10.4, 10.6 to 10.7.4 UNIT V: Chapter 7: Sec 7.2.1, 7.2.2, 7.2.6, 7.3.1, 7.3.2, 7.3.4, 7.3.5 and

Reference Books:1. Probability and Mathematical Statistics by MAREK FISZ – John Wiley & Sons.2. Modern Probability Theory, B.R. Bhatt, Wiley Eastern publishers.

Sub Code: 08UMA2303:3 Max Marks: 100Hours/Week: 5 Internal Marks: 25

33



A3: ALLIED MATHEMATICS – IIINumerical methods and Operations Research

(For Computer Science Major)UNIT IAlgebraic Equations – Solving by Newton – Raphson Method, Gauss Elimination method of solving system of Equations – Gauss Sedial Method of Iteration.

UNIT IISolving an ordinary Differential Equation by Euler’s Method, Improved Euler’s method and Modified Euler’s method- Runge – Kutta’s second order and fourth order method of solving ordinary Differential equations.

UNIT IIIOperations Research: Formulation of Linear Programming Problem - Solving a LPP by Graphical method. Solving LPP with (≤) constraints using Simplex Method.

UNIT IVTransportation Problem - Finding Initial Basic Feasible Solution by North West Corner Rule, Least Cost Entry Method and Vogel’s Approximation method for a given Transportation Problem (Balanced and unbalanced ) - Assignment Problem (Balanced and unbalanced) – Hungarian Method.

UNIT VNetwork Scheduling – finding Critical Path – Computation of Total Float – Free Float and Independent Float.

Text Books:T.B.1. Numerical Methods in Science and Engineering – Dr.M.K. Venkatraman, National Publishing (1999), Madras.T.B.2. Operations Research – P.R. Vittal and V. Malini, Margham Publications, Chennai, 2004.

UNIT I: Chapter III – Sec 1, 5; Chapter IV: Sec 1, 2, 6. 2 T.B.1. UNIT II: Chapter XI: Sec 10,11,12,14,15 T.B.1. UNIT III: Chapter II, III, IV T.B.2. UNIT IV: Chapter X, XI T.B.2. UNIT V: Chapter XIV T.B.2. Reference Books:

1. Introductory Methods of Numerical Analysis - S.S. Sastry, Prentice Hall of India Ltd., (1994) New Delhi.

2. Operations Research – S.D. Sharma, Kedarnath and Ramnath Publishers and Co.,

34

· Web viewINTEGRAL AND VECTOR CALCULUS UNIT I Multiple Integrals - Definition – Evaluation –...

Documents

Transcript of · Web viewINTEGRAL AND VECTOR CALCULUS UNIT I Multiple Integrals - Definition – Evaluation –...