COMPLEX ANALYSIS, PROBABILITY AND STATISTICAL METHODS | 18MAT41
Module-1 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. Module-2 Conformal transformations : Introduction. Discussion of transformations:𝑤 = 𝑍 2 , 𝑤 = 𝑒 𝑧 , 𝑤 = 𝑧 + 1 𝑧 , 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 Statistical Methods: Correlation and regression-Karl Pearson‟s coefficient of correlation and rank correlation -problem
