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517.53 --- Functions of a complex variable --- Functions of complex variables. --- 517.53 Functions of a complex variable

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This textbook is an introduction to the classical theory of functions of a complex variable. The author's aim is to explain the basic theory in an easy-to-understand and careful way. He emphasizes geometrical considerations and, to avoid topological difficulties associated with complex analysis, begins by deriving Cauchy's integral formula in a topologically simple case and then deduces the basic properties of continuous and differentiable functions. The general versions of Cauchy's Theorem and integral formula are proved in Chapter 2. The remainder of the book deals with conformal mappings, analytic continuation, and Riemann's Mapping Theorem. The presentation here is very full and detailed. The book is profusely illustrated and includes many examples. Problems are collected together at the end of the book. It should be an ideal text for first courses in complex analysis.

Holomorphic functions --- 517.53 --- Functions of a complex variable --- Holomorphic functions. --- 517.53 Functions of a complex variable --- Functions, Holomorphic --- Functions of several complex variables --- Fonctions d'une variable complexe

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Calculus of residues --- 517.53 --- 517.58 --- Analytic functions --- Residues, Calculus of --- Congruences and residues --- Functions of complex variables --- Integrals --- Functions, Analytic --- Functions, Monogenic --- Functions, Regular --- Regular functions --- Series, Taylor's --- Functions of a complex variable --- Special functions. Hyperbolic functions. Euler integrals. Gamma functions. Elliptic functions and integrals. Bessel functions. Other cylindrical functions. Spherical functions. Legendre polynomials. Orthogonal polynomials. Chebyshev polynomials. --- Analytic functions. --- Calculus of residues. --- 517.58 Special functions. Hyperbolic functions. Euler integrals. Gamma functions. Elliptic functions and integrals. Bessel functions. Other cylindrical functions. Spherical functions. Legendre polynomials. Orthogonal polynomials. Chebyshev polynomials. --- 517.53 Functions of a complex variable