Complex Variables: Introduction and Applications (Cambridge Texts in Applied Mathematics) [Hardcover]

Mark J. Ablowitz (Author), Athanssios S. Fokas (Author)

Book Description

Publication Date: February 13, 1997 | ISBN-10: 0521480582 | ISBN-13: 978-0521480581

In addition to being mathematically elegant, complex variables provide a powerful tool for solving problems that are either very difficult or virtually impossible to solve in any other way. Part I of this text provides an introduction to the subject, including analytic functions, integration, series, and residue calculus and also includes transform methods, ODEs in the complex plane, numerical methods and more. Part II contains conformal mappings, asymptotic expansions, and the study of Riemann-Hilbert problems. The authors also provide an extensive array of applications, illustrative examples and homework exercises. This book is ideal for use in introductory undergraduate and graduate level courses in complex variables.

Editorial Reviews

Review

'... the quality of the print is really first rate and the narration is measured, well reasoned, rigorous and nicely layed out ... the book in total constitutes a very good resource for teachers of, and researchers in, this particular area of mathematics.' Peter Larcombe, Mathematics Today

Book Description

This text provides both an introduction to complex variables and an extensive array of applications, illustrative examples and homework exercises. It is ideal for use in introductory undergraduate and graduate level courses in complex variables.

Product Details

• Hardcover: 664 pages
• Publisher: Cambridge University Press (February 13, 1997)
• Language: English
• ISBN-10: 0521480582
• ISBN-13: 978-0521480581
• Product Dimensions: 9.4 x 6.4 x 1.7 inches
• Shipping Weight: 2.3 pounds
• Average Customer Review: 4.5 out of 5 stars  See all reviews (6 customer reviews)
• Amazon Best Sellers Rank: #5,181,587 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

45 of 49 people found the following review helpful:

5.0 out of 5 stars A complete reference book for complex variables, December 11, 2000

By 

Duwayne Anderson (Saint Helens, Oregon) - See all my reviews
(REAL NAME)   

This review is from: Complex Variables: Introduction and Applications (Cambridge Texts in Applied Mathematics) (Paperback)

Whether you are a student, or just in need of a good reference text, Mark J. Ablowitz' and Athanassios Fokas' book belongs in your library. Complex Variables, Introduction and Applications is refreshingly well written. In clear and logical flow, the authors present the subject of complex variables in an easy-to-understand, yet complete format suitable for both students and practicing professionals.

This text offers a broad coverage of the subject, from fundamental properties of complex numbers, analytic functions, and singularities to more advanced topics such as conformal mapping and Riemann-Hilbert problems. Although individuals interested in pure mathematics may find some of the proofs insufficiently rigorous, those using the book as a reference for engineering or scientific problems may find the text too rigid. Overall, however, the authors have done an excellent job balancing the subject matter and successfully achieving their goal of, when necessary, "sacrificing a rigorous axiomatic development with a logical development based upon suitable assumptions."

Although the mathematical development of the text is clear, concise, and easy to follow, many of the applied examples, such as those for uniform flow in section 2.1, would benefit from further physical insight. Individuals already familiar with physics will have no difficulty following many of the examples, and extending them to other situations. Those less grounded in the physical sciences, however, may find the starting equations for some of the examples to be less than intuitive. Though additional explanations would increase the book's already substantial heft, the change would benefit many readers.

It is a joy to read a well-written technical book with almost no typographical or technical errors. Except for minor (and easily recognizable) typographical errors such as that in equation 2.2.12b, the book is nearly flawless. This leaves the student free to concentrate on learning the material unencumbered by worries about the text's accuracy.

The index is nicely composed, complete, and accurate. This makes the book particularly useful as a reference. Typically, the reader will have little trouble using the index to go directly to the pages of most interest and applicability regarding the subject of inquiry. It would be nice to see a more complete bibliography, as well as a summary of common symbols. Especially useful would be a summary of some of the more important equations (such as Green's theorem, Cauchy's theorem, the Fourier transform, the Helmholtz equation, etc.) derived or demonstrated in the book. A list of important equations, particularly, would improve the book's utilization as a desk reference.

For the student, the text presents answers to odd-numbered questions in the back of the book. For the most part, the text presents only the answers, but occasionally the authors provide additional insight into the problem's solution, as in section 5.2. This will be useful for those engaged in independent study.

Overall, this is an excellent text, and one of the most complete and well-written books on complex variables I have seen. I highly recommend it to anyone interested in the subject, and have placed it prominently upon my reference bookshelf.

22 of 22 people found the following review helpful:

5.0 out of 5 stars The numerous pictures are enough to recommend this text, June 7, 2001

By 

UNPINGCO (Los Angeles, CA) - See all my reviews

This review is from: Complex Variables: Introduction and Applications (Cambridge Texts in Applied Mathematics) (Paperback)

This text is distinguished by the numerous diagrams that appear on practically every other page. If you're graphically oriented, like I am, then this itself is enough to recommend this book. Concepts such as branch points and multivalued complex functions are much easier to understand when there is a picture to accompany the concept. The second half of the book is concerned with applications and includes several useful asymptotic methods such as Laplace's integral method. These asymptotic techniques are good for evaluating particularly nasty integrals in which the integrand is really concentrated somewhere in the interval. On the downside, this is not a very formally rigorous book. On the other hand, such formalism is easier to digest once you've seen numerous pictures and examples, in my own opinion.

18 of 19 people found the following review helpful:

5.0 out of 5 stars Excellent book -- Unique selection of topics, March 7, 2003

By A Customer

This review is from: Complex Variables: Introduction and Applications (Cambridge Texts in Applied Mathematics) (Hardcover)

This is the only textbook that I know that introduces and explains the Hilbert-Riemann problem in a pedagogical way. If anyone knows of any other such book, please tell us. It also deals in a very introductory way with all sort of really nice topics that one cannot find discussed (at a really introductory level) in any similar book: the Painleve property, the classification of singularities, asymptotic expansions, etc, etc. All very powerful applied mathematics.