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Complex Analysis

Unit 1- Algebra of complex numbers, geometric representation of complex numbers. Functions of complex variable, Mapping , Limits,Continuity, Derivative , C.R Equations, Analytical Functions. Harmonic functions, ReflectionprinciplesView Link
Unit 2- Basic properties of Complex Integration, Complex Valued Functions, Contour integral, Cauchy’s theorem, Gourat theorem, Morera’s theorem, Fundamental theorem of algebra Laurent’s series, The Maximum modulus principle, Schewarz lemma, Liouville’s theorem.View Link
Unit 3- Convergence of sequences, Convergence of series, Power Series and Analytical Functions, Taylor series, Laurent Series, Absolute and uniform convergence of Power series,
Uniqueness of series representation, Zeroes of an Analytical Function
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Unit 4- Residue at a finite point, Residue at the point at infinity, Cauchy Residue Theorem,
Residue at pole Number of zeros and poles, evaluation of Improper Integrals, evaluation of
Definite Integrals, Argument principle, Rouche’s theorem, , Application of residues,
Jordan‟s lemma, Riemann Mapping theorem, Weierstrass theorem
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Unit 5- chapter 5View Link

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