Complex Variables

by Francis J. Flanigan

Book Overview

A caution to mathematics professors: Complex Variables does not follow conventional outlines of course material. One reviewer noting its originality wrote: "A standard text is often preferred to a superior text like this] because the professor knows the order of topics and the problems, and doesn't really have to pay attention to the text. He can go to class without preparation." Not so here -- Dr. Flanigan treats this most important field...

• Format: Paperback
• Language: English
• ISBN: 0486613887
• ISBN13: 9780486613888
• Release Date: September 1983
• Publisher: Dover Publications
• Length: 384 Pages
• Weight: 0.95 lbs.
• Dimensions: 0.7" x 5.4" x 8.4"

Customer Reviews

An extraordinary book!

This book has just arrived last week at my home and I'm almost finishing the last chapter. I never saw a book about complex variables like this. It's funny, easy to read but, at the same time, very rigorous and complete. It's truth - as some others reviews have said - that some theorems are just stated and not entirely proved, like for example the Riemann Mapping Theorem. But, by the other side, there is a fantastic discussion about harmonic functions, the Cauchy Integral Theorem, the Argument Principle and Conformal Mappings. This book makes every topic fantastically clear. It is important to notice that the approach to complex variables adopted by Flanigan is entirely different from the standard textbooks. The main difference is that he starts by calculus on the real plane, and only after he develops the complex calculus. His intention is to present first the harmonic functions, which he uses after to define analytic complex functions. This is an extraordinary book with a really new approach to the subject. My opinion is that this is the best book on complex variables I ever saw. T. Hartz Once there is no "search inside" for this book, these are the chapters: 1. Calculus in the plane 2. Harmonic Functions in the Plane 3. Complex Numbers and Complex Functions 4. Integrals and Analytic Functions 5. Analytic Functions and Power Series 6. Singular Points and Laurent Series 7. The Residue Theorem and the Argument Principle 8. Analytic Functions as Conformal Mappings

Perfect...

...for engineers and scientists. As some of the reviewers have mentioned, the graduate student in mathematics or theoretical physics may want something a bit more formal, and a bit more comprehensive. However for a researcher such as myself (working in physical chemistry), the treatment of the topics presented is spot on. Having said that, the aforementioned graduate students may benefit fom the crystal clear exposition and emphasis on an intuitive understanding of complex analysis too. For the price Dover are asking, this book is a must have.

Excellent undergrad text

Comparing this to other books, I think this is the best complex variable book I have seen at the undergrad level. I say that because the overall style is very informal and very easy to read, almost "babyish" in a small sense. Also the text generally developes the basics of advanced calculus needed for the book (stuff like uniform convergence, the M-test, proof of the increment theorem of two variables, etc etc.) in the same informal style which makes this book almost worthwhile alone as a supplement to an advanced calculus course. It does cover all the material that is needed for a complex variable course, but I would be weary to use it for a beginning graduate course since it is a little on the easy side, and I think one would expect a graduate student to be at a higher "maturity" level then that of this book. But for an undergradute course, all of the above (espically a book that has can provide an easy review of advanced calculus) is just what is needed in my opinion. And besides, the price is quite nice too :)

Unconventional style, but excellent

This book is unusual in that it starts out with harmonic functions and only later develops the complex analysis. I think this approach develops intuition about complex analysis. The book contains numerous examples and very illustrative diagrams. There are also interesting historical references, which make the book easier to read. This is a good book for you if the popular book by in Ruel & Churchill does not suit you.

Greatest book I've ever read on this topic!

Great book! The order of the exposition is great. The topics flow naturally. The intuition is nourished by this book. It's not the dogmatic Def -> Theorem -> Proof format that purists will want, but it's a good engineering book.