Theory of Functions of a Complex Variable (Classic Reprint)

Heinrich Burkhardt

ISBN 10: 1440040362 / ISBN 13: 9781440040368

Published by Forgotten Books, 2018

About this Item

Print on Demand. This seminal book from the 19th century introduces beginners to the theory of functions, a foundational concept in modern mathematics. Derived from trigonometry, it profoundly impacted geometry and the study of complex numbers. The author provides a detailed look at rational functions and conformal representations determined by them. He adeptly guides the reader through proofs of fundamental theorems and discusses transformations of the plane into itself. The ideas and techniques laid out in this book helped pave the way for further exploration in the field of complex analysis. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book.

Seller Inventory # 9781440040368_0

Bibliographic Details

• Title: Theory of Functions of a Complex Variable (Classic Reprint)
• Publisher: Forgotten Books
• Publication Date: 2018
• Language: English
• ISBN 10: 1440040362
• ISBN 13: 9781440040368
• Binding: Paperback
• Condition: New
• Book Type: print-on-demand item
• Seller catalogs:
  • Calculus

About this title

Synopsis

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.