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Synopsis
The book then explains the notions of limit, continuity and differentiability by developing a thorough grounding on analytic functions and their relations with harmonic functions. It also introduces the exponential function of a complex variable and, with the help of this function, the trigonometric and hyperbolic functions are defined and their properties are analyzed. While discussing different mathematical concepts, the book analyzes a number of theorems such as Cauchy s integral theorem for the integration of a complex variable, Taylor s theorem for the analysis of complex power series, the residue theorem for evaluation of residues, and the argument principle and Rouche s theorem for the determination of the number of zeros of complex polynomials. Finally, it gives a thorough exposition of conformal mappings and develops the theory of bilinear transformation.
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