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# engineering mathematics iV

VTU
Subject code
21MAT41
Semester
4th Sem

## COMPLEX ANALYSIS, PROBABILITY AND STATISTICAL METHODS

### Module-1

Calculus of complex functions: Review of the function of a complex variable, limits, continuity, and differentiability. Analytic functions: Cauchy-Riemann equations in Cartesian and polar forms and consequences. Construction of analytic functions: Milne-Thomson method-Problems.

### Module-2

Conformal transformations: Introduction. Discussion of transformations : w=z², w=e² , w=z+1/2, (z≠0) . Bilinear transformations – Problems.
Complex integration: Line integral of a complex function-Cauchy’s theorem and Cauchy’s integral formula and problems.

### Module-3

Probability Distributions: Review of basic probability theory. Random variables (discrete and continuous), probability mass/density functions. Binomial, Poisson, exponential and normal distributions- problems (No derivation for mean and standard deviation)-Illustrative examples.

### Module-4

Curve Fitting: Curve fitting by the method of least squares- fitting the curves of the form – y=ax + b, y= axª &  y= ax² + bx + c.
Statistical Methods: Correlation and regression-Karl Pearson’s coefficient of correlation and rank correlation-problems. Regression analysis- lines of regression –problems.

### Module-5

Joint probability distribution: Joint Probability distribution for two discrete random variables, expectation and covariance.
Sampling Theory: Introduction to sampling distributions, standard error, Type-I and Type-II errors. Test of hypothesis for means, student’s t-distribution, Chi-square distribution as a test of goodness of fit.