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Complex Analysis: Demystified and Simplified
Author(s): Vivek V. Rane

ISBN:    978-81-8487-738-0 
Publication Year:   2024
Pages:   142
Binding:   Paper Back
Dimension:   160mm x 240mm
Weight:   250

About the book

COMPLEX ANALYSIS: Demystified and Simplified gives a new approach to local complex analysis, which is based on generalization of method of solution of Dirichletís problem for the Unit Disc. We explicitly construct an analytic function locally, giving its characteristic properties such as Cauchyís theorem/integral formula; power series development; Poissonís integral formula; maximum modulus principle, in one stroke. In the process, we present and develop the theory of exponential Fourier series as a generalization of trigonometric Fourier series and show that locally, analytic and elementary methods are the same.

Table of Contents

Preface, Intent and Introduction / Complex Numbers and Functions / Riemann-Stieltjes Integration, Functions of Bounded Variation, Curves and Line Integrals / Differentiability, Analytic Functions and Moebius Transformations / Power Series, Exponential Function and Logarithm / Generalised Eulerís Summation formula, the Basic Fourier Series and Exponential Fourier Series / From Fourier Series to Laurent Series and Isolated Singularities / Dirichletís Problem for a Disc, Local Complex Analysis and Generalisations / Cauchyís Theorem and its Consequences / Notations and Definitions.


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