Complex analysis ||L-03 || Translation || translation magnification rotation inversion

Complex analysis msc mathematics
Translation

Complex analysis for bsc and msc mathematics.

#mathematics #complexanalysis #mscmath #bsc

Function of a complex variable, Continuity, Differentiability, Analytic functions and their properties, Cauchy-Riemann equations in cartesian and polar coordinates, Power series, Radius of convergence, Differentiability of sum function of a power series, Branches of many valued functions with special reference to argz, logz and za.

Section - II
Path in a region, Contour, Complex integration, Cauchy theorem, Cauchy integral formula, Extension of Cauchy integral formula for multiple connected domain, Poisson integral formula, Higher order derivatives, Complex integral as a function of its upper limit, Morera theorem, Cauchy inequality, Liouville theorem, Taylor theorem.

Section - III
Zeros of an analytic function, Laurent series, Isolated singularities, Cassorati-Weierstrass theorem, Limit point of zeros and poles. Maximum modulus principle, Schwarz lemma, Meromorphic functions, Argument principle, Rouche theorem, Fundamental theorem of algebra, Inverse function theorem.

Section - IV
Calculus of residues, Cauchy residue theorem, Evaluation of integrals of the
types Space of analytic functions and their completeness, Hurwitz theorem, Montel theorem, Rieman