Theory of Functions of a Complex Variable

Heinrich Burkhardt

Editore: Forgotten Books
Formato: PDF
Testo in en
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Dimensioni: 24,58 MB
  • EAN: 9780243836475
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Descrizione

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.