Complex Analysis (Springer Undergraduate Mathematics Series)

by John M. Howie

Complex analysis is one of the most attractive of all the core topics in an undergraduate mathematics course. Its importance to applications means that it can be studied both from a very pure perspective and a very applied perspective. This book takes account of these varying needs and backgrounds and provides a self-study text for students in mathematics, science and engineering. Beginning with a summary of what the student needs to know at the outset, it covers all the topics likely to feature in a first course in the subject, complex numbers, differentiation, integration, Cauchy's theorem, and its consequences, Laurent series and the residue theorem, applications of contour integration, conformal mappings, and harmonic functions. A brief final chapter explains the Riemann hypothesis, the most celebrated of all the unsolved problems in mathematics, and ends with a short descriptive account of iteration, Julia sets and the Mandelbrot set. Clear and careful explanations are backed up with worked examples and more than 100 exercises, for which full solutions are provided.

Genres: Mathematics, Science

271 pages, Paperback

First published March 1, 2007

Reviews

[Robert · Rating 4 out of 5]

I never studied complex analysis in university so I bought this to learn a little bit about it.

Well, more than 10 years later I STILL haven't learned complex analysis, but if I was ever going to I would start with this book.

I really John Howie's style (I also have his "Real Analysis") and in fact the entire "Springer Undergraduate Mathematics Series".

It's about as gentle as you could find with all the things you could typically want, plenty of examples, explanations and exercises with a clear emphasis on key concepts and lots of motivation.

Now this came out a while ago so perhaps there is something newer and better, but on the other hand the basics of complex analysis haven't changed, so it should still be good!

[Erickson · Rating 5 out of 5]

Finished with first reading of complex analysis up to applications of contour integration. Further topics such as conformal mapping will be read for second reading. The book is very clear and is one of the rare texts with worked solutions.

['Asem Ismaiel · Rating 4 out of 5]

Very nice and easy introduction to Complex Analysis.