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The most important topics in the theory and application of complex variables receive a thorough, coherent treatment in this introductory text. Intended for undergraduates or graduate students in science, mathematics, and engineering, this volume features hundreds of solved examples, exercises, and applications designed to foster a complete understanding of complex variables as well as an appreciation of their mathematical beauty and elegance.
Prerequisites are minimal; a three-semester course in calculus will suffice to prepare students for discussions of these topics: the complex plane, basic properties of analytic functions (including a r
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Book ID Asin: 0486406792
Book Title: Complex Variables: Second Edition (Dover Books on Mathematics)
Book Author: Stephen D. Fisher
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Book Category: Books, Science & Math, Mathematics and unknown
Book Rating: 48 ratings
Complex Variables: Second Edition (Dover Books on Mathematics) by Stephen D. Fisher Book Review
Name: Palle E T Jorgensen
Rating: 5.0 out of 5 stars
Title: an excellent beginning
Date: Reviewed in the United States 🇺🇸 on August 11, 2006
Review: Fisher’s book is ideal for a first course in complex variables: the complex plane, geometry of the plane, analytic functions (zeros, singularities, residue computations), Cauchy-and residue theorems, harmonic functions, conformal mappings, boundary value problems, applications, and a lovely last chapter on transform theory, Fourier, Laplace etc, and using contour integration.
Pedagogical features: The figures and illustrations are lovely! The exercises are many and well designed. Inclusion of solutions to odd-numbered exercises represents a good compromise. The book will work well for a mixed audience, students in math, in science, and in engineering alike. The presentation starts with a review of complex numbers functions and sequences, moves quickly to central aspects of complex function theory, elementary geometry, Mobius transformations, and conformal maps.
The book was published first in 1990, but reprinted since by Dover, starting in 1999. It is suitable as a text or as a supplement in a beginning course in complex function theory, at the undergraduate level. And it is suitable for self-study. While it contains the standard elements in such a course, we note that a systematic treatment of physical problems comes relatively late, in Section 4.2, beginning on page 254 (a little past halfway into the book.) Some readers might want to begin with that.
There are other Dover titles on the same subject, also elementary and suitable for a first course. They are slanted differently, and in particular, they point to different applications. Fisher’s inclusion of transform theory gives this book an edge. See however also Churchill-Brown.
Other Dover books: We recommend the books by Fisher, Volkovyskii et al, Silverman, Schwerdtfeger, and Flanigan; all inexpensive! These books cover the fundamentals in functions of a single complex variable: analytic, harmonic, conformal mappings, and related applications. Further, there are non-Dover books such as: (a) R. V. Churchill — J. W. Brown, and (b) J. E. Marsden — M. J. Hoffman; both a lot more expensive. Review by Palle Jorgensen, August, 2006.
Name: payne
Rating: 2.0 out of 5 stars
Title: There Are Better Books Out There
Date: Reviewed in the United States 🇺🇸 on August 16, 2021
Review: I bought this book because it was required for a class. If you’re looking for a book to self-study complex analysis look elsewhere.
If you’re younger than a baby boomer you’ll probably find that the language and grammar doesn’t flow well. I imagine this is because the book was originally written in 1990 by someone born in the 40's.
Most examples given throughout each section are useless. A lot of them are just statements without any explanation given which kills building intuition and just feels lazy.
This book also commits the annoying sin of “the proof is left as an exercise” for very important theorems and special cases. Again, this kills intuition building and is just frustrating.
There a some typos, misplaced notation, and some of the symbols and variables used are very confusing.
The only pro I can think of for this book is that it contains all the relevant information. Just be prepared to do a lot of rereading, googling, asking your professor/TA, or just staring at an equation long enough to realize the reason you’re confused is because the author used the worst possible choice for notation/symbols.
Name: C
Rating: 3.0 out of 5 stars
Title: The book is terrible, but at this price I can’t complain
Date: Reviewed in the United States 🇺🇸 on February 22, 2013
Review: Let me start by saying the only reason I purchased this book was for my course in Intro to Complex Analysis. Although the price of the book is excellent and there is a lot of valuable information discussed in the book, it is completely useless for understanding the underlying concepts and proofs. Most proofs are, as they say, “left to the reader” and the ones that are included have large jumps in logical steps, expecting the reader to follow from his own intuition i suppose. The proofs make use of lemmas and corollaries that have not themselves been proven by the author which leaves the reader with huge holes in their comprehension of the subject. If you’re looking for a book that provides a example with which to model each of the exercise questions from, an exercise in triviality, then this is your book. If you want to understand the underlying concepts in detail, look somewhere else.
However, if you’re buying this book for a class, the price is unbeatable.
Name: Frank
Rating: 2.0 out of 5 stars
Title: Book Little More than Reference — No Motivation
Date: Reviewed in the United States 🇺🇸 on April 27, 2012
Review: This is a very strange book — more like a reference book than a textbook that you can use to learn complex analysis for the first time.
The problem with the book is that it offers very little in the way of explanation or motivation for any of the concepts it introduces. It mostly follows the format of: 1) definition, 2) motivation-less symbol pushing proof, 3) several computational examples. Not enlightening. If you’re interested in the applications, this book will motivate none of the concepts, so you’ll wonder why complex analysis matters at all. For example, there is a section about the Fourier transform — an extremely useful concept; however what the Fourier transform can be used for is relegated to a scanty paragraph at the very beginning of the chapter, and it even fails to mention how it can be used to decompose signals into its component frequencies!! If you’re interested in the mathematics behind it, you’ll probably be frustrated for the same reason — no motivation anywhere in the book.
Its worth mentioning that almost everyone in my class did not like this book, even the instructor thought it was a terrible book! I think the positive reviews here may be from professors how already know the meaning behind the material, so the fact that this is just a reference book that does not really explain the significance of anything is lost on them.
