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copson e introduction theory functions complex variable 1936

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Textbook in PDF format This book is based on courses of lectures given to undergraduates in the Universities of Edinburgh and St. Andrews, and is intended to provide an easy introduction to the methods of the theory of functions of a complex variable. The reader is assumed to have a knowledge of the elements of the theory of functions of a real variable, such as is contained, for example, in Hardy's Course of Pure Mathematics; an acquaintance with the easier parts of Bromwich's Infinite Series would prove advantageous, but is not essential. The first six chapters contain an exposition, based on Cauchy's Theorem, of the properties of one-valued differentiable functions of a complex variable. In the rest of the book the problem of conformal representation, the elements of the theory of integral functions and the behaviour of some of the special functions of analysis are discussed by the methods developed in the earlier part. The book concludes with the classical proof of Picard's Theorem. No attempt has been made to give the book an encyclopaedic character. My object has been to interest the reader and to encourage him to study further some of the more advanced parts of the subject; suggestions for further reading have been made at the end of each chapter Complex Numbers The Convergence of Infinite Series Functions of a Complex Variable Cauchy's Theorem Uniform Convergence The Calculus of Residues Integral Functions Conformal Representation The Gamma Function The Hypergeometric Functions Legendre Functions Bessel Functions The Elliptic Functions of Weierstrass Jacobi's Elliptic Functions Elliptic Modular Functions and Picard's Theorem

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Copson E. Introduction to the Theory of the Functions of a Complex Variable 1936.pdf 17.2 MB

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copson e introduction theory functions complex variable 1936