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Precize COMPLEX ANALYSIS-I

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The entire subject matter in the present book has been arranged in a simple, systematic, graded, lucid and exhaustive manner. Each chapter begins with definitions followed by theorems with complete proofs and solved problems. A large number of notes and remarks have been added for better understanding of the subject. For UGC-CSIR NET examination, some MCQ’s from the previous years papers and other similar questions have been added at the end of the book.

Description

Complex plane, Geometric representation of complex numbers, Joint equation of circle and straight line, Stereographic projection and the spherical representation of the extended complex plane. Topology on the
complex plane, Connected and simply connected sets. Complex valued functions and their continuity. Curves, Connectivity through polygonal lines. Analytic functions, Cauchy-Riemann equations, Harmonic functions and Harmonic conjugates. Power series, Exponential and Trigonometric functions, arg z, log z, az and their Continuous branches.

Complex Integration, Line integral, Cauchy’s theorem for a rectangle, Cauchy’s theorem in a disc, Index of a point with respect to a closed curve, Cauchy’s integral formula, Higher derivatives, Morrera’s theorem,
Liouville’s theorem, Fundamental theorem of Algebra. The general form of Cauchy’s theorem.

Additional information

ISBN

9789382295761

Language

English

Binding

Paperback

Year of Publication

2019

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