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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 rewritten and reorganized discussion of Cauchy's Theorem), analytic functions as mappings, analytic and harmonic functions in applications, and transform methods. Useful appendixes include tables of conformal mappings and Laplace transforms, as well as solutions to odd-numbered exercises.
Students and teachers alike will find this volume, with its well-organized text and clear, concise proofs, an outstanding introduction to the intricacies of complex variables.
- Sales Rank: #214489 in Books
- Published on: 1999-02-16
- Released on: 1999-02-16
- Original language: English
- Number of items: 1
- Dimensions: 9.20" h x 1.00" w x 6.50" l, 1.30 pounds
- Binding: Paperback
- 448 pages
From the Back Cover
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 rewritten and reorganized discussion of Cauchy's Theorem), analytic functions as mappings, analytic and harmonic functions in applications, and transform methods. Useful appendixes include tables of conformal mappings and Laplace transforms, as well as solutions to odd-numbered exercises.
Students and teachers alike will find this volume, with its well-organized text and clear, concise proofs, an outstanding introduction to the intricacies of complex variables.
Unabridged Dover (1999) republication of the work published by Wadsworth & Brooks, Pacific Grove, California, 1990.
Most helpful customer reviews
29 of 32 people found the following review helpful.
Great text
By A Customer
It is wonderful to see this great book on undergraduate complex analysis back in print at even a more affordable price. I've used it in in one of my junior level courses and been totally satisfied with it. I will use a part of it again in a continuation course.
What is nice about this book is that it is a textbook, and not a cookbook nor a book that tries to include everything and fails at all of them. This book never lists too many results; instead it aims at the understanding of the subject matter. Its treatment of Cauchy's theorem clearly exposes the fact that different points of view (derivatives, series, integrals) in the complex plane lead to the same object, analytic functions. The sections on geometric and applied topics, such as linear fractional transformations and fluid mechanics, are a delight to read.
The book assumes nothing other than calculus (Green's theorem) as background. Topological concepts are kept at a reasonable level and some are introduced later when necessary so as not to hinder the development of its main topic. Some short side issues are discussed in tiny sections within the exercises. There are also plenty of regular exercises ranging from elementary calculations to rigorous proofs. This book also contains an appendix that I love on the zeros of polynomials, including the cubic and the quartic.
What attracted me most in this book is that one can read it straight through. There are no secondary undeveloped paths, sections to omit, unnecessary details, or long list of formulas. I recomend it for any course or self-study at the introductory level complex analysis.
4 of 4 people found the following review helpful.
Complex Variables by Francis Flanigan is much better
By A Customer
This book does a very poor job of explaining both proofs and examples. Many steps are skipped or neglected leaving the reader confused until, after much thought, the step is understood (and it is many times a non-obvious step in logic). I would not recommend this book.
5 of 6 people found the following review helpful.
Book Little More than Reference - No Motivation
By Frank
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.
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