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Complex Variables: Introduction and Applications (Cambridge Texts in Applied Mathematics), by Mark J. Ablowitz, Athanassios S. Fokas
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Complex variables offer very efficient methods for attacking many difficult problems, and it is the aim of this book to offer a thorough review of these methods and their applications. Part I is an introduction to the subject, including residue calculus and transform methods. Part II advances to conformal mappings, and the study of Riemann-Hilbert problems. An extensive array of examples and exercises are included. This new edition has been improved throughout and is ideal for use in introductory undergraduate and graduate level courses in complex variables. First Edition Hb (1997): 0-521-48058-2 First Edition Pb (1997): 0-521-48523-1
- Sales Rank: #185895 in Books
- Brand: Brand: Cambridge University Press
- Published on: 2003-04-28
- Original language: English
- Number of items: 1
- Dimensions: 8.98" h x 1.46" w x 5.98" l, 1.96 pounds
- Binding: Paperback
- 660 pages
- Used Book in Good Condition
Review
'... an excellent text, and one of the most complete and well-written books on complex variables I have seen ... The index is nicely composed, complete, and accurate ... useful as a reference ... I highly recommend it to anyone interested in the subject and have placed it prominently upon my reference bookshelf.' Duwayne Anderson, Optics and Photonics News
'... 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...'. Optics and Photonics News
'Overall the book feels 'road-tested' both in the lecture theatre and in the crucible of research and the clear well-written text is complemented by a superb collection of worked examples and exercises ranging in scope from routine applications of techniques to more substantial illustrations of the theory.' The Mathematical Gazette
'... the book is valuable for students in engineering and physical sciences.' ZAMM
About the Author
Mark J. Ablowitz is Professor of Applied Mathematics at the University of Colorado, Boulder.
Previous books by this editor: Acta Numerica 1992 - 2003 (Vols 1 - 12); as author: First Course in the Numerical Analysis of Differential Equations (0521 553768), Approximation Theory and Optimization (0521 581907).
Most helpful customer reviews
0 of 0 people found the following review helpful.
Good book
By Michael Steiner
Good book on complex variables.
10 of 12 people found the following review helpful.
many typos and sloppy explanations
By Alan
I taught an undergraduate course on complex analysis using this book several years ago. My choice of the book was partly based on the authors' outstanding reputations as good researchers. The authors make good choices of topics and they are experts in the subject. A casual perusing of this book might leave you impressed, but if you carefully work through the details of this book you will find numerous typographical errors and many explanations are sloppy. The proof of the Cauchy-Goursat Theorem is simply wrong. One of the proofs of a major theorem about Taylor series contained circular reasoning. I found it necessary to provide the students with my own typed lecture notes to replace various section of the book with explanations that weren't so sloppy. If you are looking for a good textbook at the undergraduate level, I recommend finding another book that was more carefully written.
16 of 17 people found the following review helpful.
A very good text!
By A Customer
A very good text!
The best description of this book is that it provides a comprehensive, classical treatment of the subject with a modern touch and serves ideally the needs of anyone studying Complex Analysis.
Starting from the foundations of defining a complex number, through to applications in the evaluation of integrals, the WKB method, Fourier transforms and Riemann-Hilbert problems, the book covers a lot of ground in an easy to follow style. The chapters are long, but logically broken down into digestible sections and interspersed with well illustrated diagrams, numerous worked examples and exercises. The end of chapter exercises provide further opportunity for reinforcing the methods and there's a useful section at the end giving brief hints and answers to selected problems.
Complex Variable analysis is treated from the definition of an analytic function and its relation to the Cauchy-Riemann equations, and in turn their application to an ideal fluid flow. The ideas of multi-valued functions, complex integration, and Cauchy's theorem are excellently treated, as are the consequences: the generalised Cauchy integral formula, the Max-Mod principle, and Liouiville and Morera's theorems.
The rest of the first part of this book, which is essentially pure mathematics, deals with Laurent series, singularities, analytic continuation, the Mittag-Leffler theorem, the ALL IMPORTANT Cauchy Residue Theorem, dealing with branch points, Rouche's theorem, and their application to Fourier transforms.
The second half starts off with perhaps the best I have seen on Conformal Mappings and their application to physical problems in Fluid Mechanics and Electromagnetism. Asymptotic evaluation of integrals covers methods like Watson's lemma, the method of steepest descent, and the WKB method.
A good combination of pure and applied mathematics, though the book avoids either the rigour of classical works such as Whittaker and Watson or the marvellously visual presentation of Tristan Needham.
Highly recommended!
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