VTU Notes

The Complete 18MAT41 | COMPLEX ANALYSIS, PROBABILITY AND STATISTICAL METHODS Notes

• To provide an insight into applications of complex variables, conformal mapping and special

functions arising in potential theory, quantum mechanics, heat conduction and field theory.

• To develop probability distribution of discrete, continuous random variables and joint

probability distribution occurring in digital signal processing, design engineering and

microwave engineering.

Calculus of complex functions: Review of 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.

Conformal transformations: Introduction. Discussion of transformations: Bilinear transformations- Problems.

Complex integration: Line integral of a complex function-Cauchy’s theorem and Cauchy’s integral formula

and problems.

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.

Statistical Methods: Correlation and regression-Karl Pearson’s coefficient of correlation and rank correlation

-problems. Regression analysis- lines of regression –problems.

Curve Fitting: Curve fitting by the method of least squares- fitting the curves of the form-

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.

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