Department of Mathematics-2

8/3/2019 Department of Mathematics-2

1/11

Courses offered :Level 1

Semester Title Course

code

GPA

credits

No. of Hours

1 Eng. Mathematics I MA 1013 3 Lecture 35

Tutorial/Assessments

30

practical -

2 Eng. Mathematics II MA 2023 3 Lecture 35

Tutorial/

Assessments

30

practical -


2/11

Courses offered :Level 2Semester Title Course

code

GPA

credits

No. of Hours

3 Advanced Eng. Mathematics I MA 3033

3

Lecture 35

Tutorial/

Assessments

30

practical -

4 Advanced Eng .Mathematics II MA 4042

2

Lecture 15

Tutorial/

Assessments

45

practical -

Applied Statistics MA 4051

1

Lecture 10

Tutorial/

Assessments

15

practical -


3/11

Eng. Mathematics I

Algebra / Matrix Algebra:

Roots of the algebraic equations, Remainder theorem, Factor theorem, Matrix

notation, Matrix algebra: Additions, Multiplication, Inversion, Determinants, Linear

dependence, set of the linear equations, Gauss elimination with pivoting methods.

Complex Numbers:

Complex numbers, Algebra of complex numbers, De Moivres theorem, Roots of

complex numbers, Solving Complex equations, Modules, Argument, Polar form,

Argand diagram.

Vectors:Scalars; vectors; Addition and subtraction of vectors; Position vector of a point; Ratio

formula; Vector equation of the straight line; Scalar product; vector product;

properties of scalar and vector product; Scalar triple product; Vector triple product;

Geometrical interpretation; Gradient; divergence and Curl.


4/11

Cont Eng. Mathematics I

Probability & Statistics:

Theory of probability:

Sample space, Event, Probability axioms, addition and multiplication rules, Conditional

Probability, Bayes Theorem

Introduction of Statistics:

Classification of data, Frequency tables, Bar charts, Histograms, Frequency polygons,

Mode, Median, Means, Variance, and Standard deviation

Discrete and continuous variables, Expectation, Mean and Variance, Binomial, Poisson,

Geometric, Uniform, Exponential, Gamma and Normal distribution, Normal

approximation to Binomial and Poisson distributions


5/11

Eng. Mathematics II

CALCILUS:

Functions, limit of function, continuity, inverse functions, natural logarithms and

exponential function, hyperbolic functions, the derivative and higher derivatives, Tangent,

Normal, Curvature, Curve sketching, LHopitals rule, definite integral of functions,

Indefinite integral of functions, infinite series, Taylors theorem, Introduction to Fourier

series.ORDINARY DIFFERENTIAL EQUATIONS:

Formulation of differential equations, First order first degree differential equations,

Second order differential equations with constant coefficients, solution by D-operator,

Series solutions of differential equations.

OPERATIONAL RESEARCH:

Linear programming, Maximization, Minimization, Big-M method, Two phase method,

Duality, Transportation, Network Analysis, Game theory.


6/11

Advanced Eng. Mathematics I

MULTIVARIATE CALCULUS :

Functions of Several Variables, Limits,Conninuity, Partial Derivatives, Increments &

Differentials, The chain Rules ,Differential derivatives, Tangent planes, Normal lines to

surface, Extreme Values of functions of several variables, Lagranges multipliers , Double

integrals , Evaluation of double integrals, Area and Volume moments and centre of mass ,

Double integrals in Polar Coordinates , Change of variables in multiple integrals, Tripleintegrals , in Cylindrical and Spherical Coordinates, Surface Area.

DIFFRENTIAL EQUATIONS:

Solutions of Linear Differential Equations with constant coefficients by Laplace

Transforms, Variation of Parameters and other miscellaneous methods, Power Series

Solutions of Differential Equations, Bassels equation ,Bassels Function , Classification of

second order Partial Differential Equations, Solution by Separation of Variables,

Introduction to Fourier with application to boundary value problems, Fourier Transform,

Legendres Equation, Spherical Harmonics.

Introduction to MATLAB soft ware :


7/11

Advanced Eng .Mathematics II

FUNCTIONS OF COMPLEX VARIABLE :

Line integrals in Complex plane, Cauchys Theorem, Cauchys integral formula, Taylors

series, Laurent series, Zeros and singularities , Poles, Residues , Residue Theorem,

Evaluation of Real integrals, Conformal mapping.

VECTOR ANALISIS:Scalar and vector fields, Line integrals, Conservative fields, Surface integrals, Greens

theorem in the plane, Divergence Theorem, Stokes theorem.

LINEAR ALGEABRA:

Vector spaces, subspaces, linear combination, spanning sets, linear independence, bases

and dimension. Linear transformation, the matrix of a linear transformation the Kernel andimage of a linear transformation. Eigen values and Eigen vectors, the minimal polynomial of

a matrix and the Caley-Hamilton theorem. Diagonalization of a matrix and Quadratic forms.


8/11

Advance Eng .Mathematics II

NUMERICAL METHODS :

Numerical Solutions of System of Linear Equations: LU Factorization, Gauss Seidel and

Jacobi Methods. Solutions of Non-linear Equations: Bisection, Simple Iterative, Newton-

Raphson and False Method. Polynomial Approximation of Functions: Lagrange

Polynomials, Newtons Divided Differences, Least Square Polynomials and Functions, Finite

Differences, Interpolation and Extrapolation, Numerical Differentiation, Numerical

Integration: Trapezoidal, Simpsons Rules, Numerical Solution of Ordinary Differential

Equations: Eulers Method, Taylor Series Method.


9/11

Applied Statistics

Estimation, Sampling distributions, central limit theorem, confidence

intervals for mean and variance. Hypothesis tests for mean.

Difference between means, proportions and variance. Goodness-of-

fit tests and contingency table. Regression, correlation, least square

estimation and hypothesis tests in simple linear regression.Introduction to Quality Control, O.C Curve. Control charts, attribute

type sampling schemes. Variable type sampling schemes.


10/11

ASSESSMENT CRITERIA

Semester-end Examination:70%

Tutorial/ Assignments: 20%

Class Quizzes: 10%


11/11

The End

Department of Mathematics-2

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