A First Course on Complex Functions is popular PDF and ePub book, written by G. Jameson in 2013-03-09, it is a fantastic choice for those who relish reading online the Science genre. Let's immerse ourselves in this engaging Science book by exploring the summary and details provided below. Remember, A First Course on Complex Functions can be Read Online from any device for your convenience.
A First Course on Complex Functions Book PDF Summary
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.
Detail Book of A First Course on Complex Functions PDF
- Author : G. Jameson
- Release : 09 March 2013
- Publisher : Springer Science & Business Media
- ISBN : 9789400956803
- Genre : Science
- Total Page : 159 pages
- Language : English
- PDF File Size : 20,9 Mb
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