MATHEMATICS – IV

Credits	Periods			Exam Hrs.	Sessional Marks	Exam Marks	Total Marks
	Theory	Tutorial	Lab
4	3	1	-	3	30	70	100

1.         Functions of a Complex Variables

Continuity concept of f(z), Derivative of f(z), Cauchy - Riemann Equations, Analytic Functions, Harmonic Functions, Orthogonal Systems, Applications to Flow Problems, Integration of Complex Functions, Cauchy’s Theorem, Cauchy’s Integral Formula, Statements of Taylor’s and Laurent’s Series without Proofs, Singular Points, Residues and Residue Theorem, Calculations of Residues, Evaluation of Real Definite Integrals, Geometric Representation of f(z), Conformal Transformation, Some Standard Transformations:- (1) w = z+c, (2) w = 1/z, (3) w = (az+b) (4) w = z², (6) w = e².

2.         Statistical Methods

Review of Probability theory (not be examined), Addition law of probability, Independent events, Multiplication law of probability, Bay’s theorem, Random variable, Discrete probability distribution, Expectation, Moment generation function, repeated trails, Binomial distribution, Poission distribution, Normal distribution, Prabable error, Normal approximation to binomial distribution.

Sampling Theory: Sampling Distribution, Standard Error, Testing of Hypothesis, Level of Significance, Confidence Limits, Simple Sampling of Attributes, Sampling of Variables - Large Samples and Small Samples, Student’s T-distribution, x² - Distribution, F - Distribution, Fisher’s Z - Distribution.

3.         Difference Equations and Z-Transforms

Z-transforms - Definition, Some Standard Z-transforms, Linear Property, Sampling Rule, Some Standard Results, Shifting Rules, Initial and Final Value Theorems, Convolution theorem, Evaluation of inverse transforms, definition, Order and Solution of Difference Equations, Formation of Difference Equations, Linear Difference Equations, Rules for finding C.F., Rule for finding P.L., Difference Equation Reducible to Linear Form, Simultaneous Difference Equations with Constant Coefficients, Application to Deflection of a Loaded String, Applications of Z-transform to Difference Equations.

Text Books :

1.      Higher Engineering Mathematics, Dr. B. S. Grewal, Khanna Publisher - N. Delhi, 34^th Edition, 1998.

Reference Books :

1.      Higher Engineering Mathematics, Dr. M. K. Venkataraman, National Pub. and Co. - Madras.