Theory of Functions of a Complex Variable (Classic Reprint) - Softcover

Burkhardt, Heinrich

9781440040368: Theory of Functions of a Complex Variable (Classic Reprint)

Softcover

ISBN 10: 1440040362 ISBN 13: 9781440040368

Verlag: Forgotten Books, 2018

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Excerpt from Theory of Functions of a Complex Variable

In the first chapter, I have introduced the algebra of complex num bers as an algebra of number-pairs without giving a general theory of number systems of two (or more) units; I have rather assumed with out discussion the hypotheses characteristic of the theory of ordinary complex numbers.

The second chapter contains a detailed geometrical theory of the elementary rational functions of a complex variable and the conformal representations determined by them. The transition from the plane to the sphere by stereographic projection is also considered; it is used at various places in the following chapters. The chapter closes with a discussion of the symmetric invariants of four points as a function of their double ratio; this takes the place of an example (in itself unimportant) of a rational function of a more general character.

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Theory ofF unctions of aC omplex Variable written in English and adapted in other ways to the use of students beginning their graduate work. Professor Burkhardt sbook Einfnhrung in dieT heorie der analytischen Funktionen einer komplexen Ver dnderlicheti has seemed admirably suited to this purpose both in the matter of material and arrangement. The translation of this text into English was undertaken at the suggestion and encouragement of prominent American mathematicians, sinct there is no book in theE nglish language treating the subject from the point of view adopted here. The translation preserves the same arrangement of material as the original book, even to the numbering of sections and theorems. Footnotes not in the original text are always signed. All of the exercises, which include a number of additional fig ures and which follow various sections and each of the chap ters, are added by the translator. It is hoped that they will prove of assistance not only in illustrating and fixing the ideas contained in the text but as well in stimulating the reader to independent attack and further study in larger treatises.
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