Complex analysis || L-02 || Translation || Rotation || Magnification || Inversion скачать в хорошем качестве

Complex analysis || L-02 || Translation || Rotation || Magnification || Inversion

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