Complex Analysis

by Ian Stewart, David Tall

This new edition of a classic textbook develops complex analysis from the established theory of real analysis by emphasising the differences that arise as a result of the richer geometry of the complex plane. Key features of the authors' approach are to use simple topological ideas to translate visual intuition to rigorous proof, and, in this edition, to address the conceptual conflicts between pure and applied approaches head-on. Beyond the material of the clarified and corrected original edition, there are three new chapters: Chapter 15, on infinitesimals in real and complex analysis; Chapter 16, on homology versions of Cauchy's theorem and Cauchy's residue theorem, linking back to geometric intuition; and Chapter 17, outlines some more advanced directions in which complex analysis has developed, and continues to evolve into the future. With numerous worked examples and exercises, clear and direct proofs, and a view to the future of the subject, this is an invaluable companion for any modern complex analysis course.

Genres: Mathematics

402 pages, Paperback

First published March 10, 1983

About the author

Ian Nicholas Stewart is an Emeritus Professor and Digital Media Fellow in the Mathematics Department at Warwick University, with special responsibility for public awareness of mathematics and science. He is best known for his popular science writing on mathematical themes.
--from the author's website

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Reviews

[A · Rating 4 out of 5]

Today was my last pure mathematics exam... This was an interesting read and highlighted important concepts and examples. Would recommend for further reading!

[Mira · Rating 5 out of 5]

This is my first time removing a math textbook from my collection! I am specifically referring to the first edition of this book, I do not recommend it. I ended up reading the second edition instead, which was able to fix the mathetical errors and formatting issues in the first edition which had made it almost unreadable (I still am in shock it was published). It is so rare (in my experience) for textbooks to have such a drastic change in quality in between editions. Usually, it is just a money grab... However, I do have the utmost praise for the re-release, and it will go into my shrine of math textbooks that I will treat like family heirlooms. I am still in shock, I spoke badly about Ian Stewart. Ian, I am so sorry, I still love you, and I will still eat up everything you write like a starved stray ❤️