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Chapman and Hall Mathematics Series

A First Course on Complex Functions

Authors: Jameson, G.

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  • ISBN 978-94-009-5680-3
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About this book

This book contains a rigorous coverage of those topics (and only those topics) that, in the author's judgement, are suitable for inclusion in a first course on Complex Functions. Roughly speaking, these can be summarized as being the things that can be done with Cauchy's integral formula and the residue theorem. On the theoretical side, this includes the basic core of the theory of differentiable complex functions, a theory which is unsurpassed in Mathematics for its cohesion, elegance and wealth of surprises. On the practical side, it includes the computational applications of the residue theorem. Some prominence is given to the latter, because for the more sceptical student they provide the justification for inventing the complex numbers. Analytic continuation and Riemann surfaces form an essentially different chapter of Complex Analysis. A proper treatment is far too sophisticated for a first course, and they are therefore excluded. The aim has been to produce the simplest possible rigorous treatment of the topics discussed. For the programme outlined above, it is quite sufficient to prove Cauchy'S integral theorem for paths in star-shaped open sets, so this is done. No form of the Jordan curve theorem is used anywhere in the book.

Table of contents (4 chapters)

Table of contents (4 chapters)

Buy this book

eBook $84.99
price for USA in USD
  • ISBN 978-94-009-5680-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $109.99
price for USA in USD
  • ISBN 978-0-412-09710-2
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
A First Course on Complex Functions
Authors
Series Title
Chapman and Hall Mathematics Series
Copyright
1970
Publisher
Springer Netherlands
Copyright Holder
G. J. O.Jameson
eBook ISBN
978-94-009-5680-3
DOI
10.1007/978-94-009-5680-3
Softcover ISBN
978-0-412-09710-2
Edition Number
1
Number of Pages
XII, 148
Topics