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A Course of Modern Analysis (Cambridge Mathematical Library), by E. T. Whittaker, G. N. Watson
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This classic text is known to and used by thousands of mathematicians and students of mathematics throughout the world. It gives an introduction to the general theory of infinite processes and of analytic functions together with an account of the principal transcendental functions.
- Sales Rank: #1560968 in eBooks
- Published on: 1996-09-13
- Released on: 1996-09-13
- Format: Kindle eBook
Review
'This classic text is known to and used by thousands of mathematicians and students of mathematics throughout the world.' L'Enseignement Mathématique
'Whittaker and Watson has entered and held the field as the standard book of reference in English on the applications of analysis to the transcendental functions. This end has been successfully achieved by following the sensible course of explaining the methods of modern analysis in the first part of the book and then proceeding to a detailed discussion of the transcendental function, unhampered by the necessity of continually proving new theorems for special applications. In this way the authors have succeeded in being rigorous without imposing on the reader the mass of detail which so often tends to make a rigorous demonstration tedious.' Nature
'A wealth of mathematical ideas with a touch of old times make this book a pleasure to read.' European Mathematical Society
About the Author
Whittaker, Professor of Mathematics in the University of Edinburgh.
Most helpful customer reviews
28 of 28 people found the following review helpful.
The book on analysis and special functions
By A Customer
The older I get, the more I realise the truth of what my expert colleagues told me a long time ago: there is ONE book on analysis, and it's called Whittaker and Watson. Shame on CUP for reprinting it in less than perfectly top quality. I guess they know that people will always buy it. It is a book that starts from the very basics of real and complex analysis, and moves on to the very depths of classical special functions. It's a joy to read and to teach from. No respectable mathematical physicist can afford not to own a copy. And it's about 1/4 the price of a typical, low level, textbook.
23 of 23 people found the following review helpful.
The DEFINITIVE text for classical Analysis
By A Customer
The DEFINITIVE text for classical Analysis
This book is the definitive text in classical Mathematical Analysis. It was first published in 1902 and the fact that it is still in print is testimony to it's wide ranging utility and appeal.
It should be noted that this text is not for those who are new to the rigour of Analysis; its presentation is suitable for a final year undergraduate or for the post-graduate student. More importantly, its wide ranging content of proofs and results would also prove useful to the Physicist.
The first part of the book covers the "essentials" of analysis: continuity, differentiability, summation of series, convergence and uniform convergence, and the theory of the Riemann integral. Subsequent chapters quickly but comprehensively develop the theory of analytic functions, the theorems of Cauchy, Laurent, and Liouville and the calculus of residues. These chapters knit very well into the earlier presentation of the basic processes of analysis! The pleasing thing is that despite the passage of time and the advent of hundreds of books on Complex Variable Theory, Whittaker and Watson's treatment still bears a mark of freshness and rigour.
Also included is a comprehensive treatment of expanding functions in infinite series and asymptotic expansions and summability of series. For completeness, the text also covers the theory of linear differential equations and Fourier series.
The second part of the book is what stands it apart from the rest. The authors provide a comprehensive discussion of the major transcendental functions: Gamma, Zeta, Hypergeometric, Legendre, and Bessel to name the more commonly encountered ones. The treatment is rigorous but the copious number of examples provides opportunity to learn the theory and apply it. Lots of apparently obscure results, many that would be useful in Physics applications, are cited as examples.
The latter chapters presents a treatment of Elliptic, Theta and Mathieu functions.
Overall, Whittaker and Watson will continue to be the guiding light for any serious scholar of classical analysis and an excellent reference point for the solutions to the fundamental equations of Mathematical Physics. Even though I am not a practising Mathematician, I find this a pleasant book to dip into: there's always a little surprise and something new to learn.
This book will live forever!
22 of 22 people found the following review helpful.
A true classic of classics indeed...
By Gaurav Thakur
I decided to purchase this title about three months ago after hearing lots of praise about it on the internet and wanting to learn the subject, and I can now see that this praise was not exaggerated. A hundred years after its first publication, this classic still remains the definitive general reference in the field of special functions and is a very solid textbook in its own right.
The book is split into two main parts: the first consists of short (but detailed) overviews of the various sub-disciplines of analysis from which results are required to develop later results, and the second part is devoted to developing the theories of the various kinds of special functions. The sheer breadth of topics and material that this book covers is utterly incredible. The major topics covered in the first part of the book are convergence theorems, integration-related theories, series expansions of functions and differential/integral equation theories, each of which are split into two or three chapters. The reader is assumed to be familiar with some of the subjects here and these chapters are intended more as a review, but they are still quite self-contained and will also appeal to those who have not encountered the subjects yet. (I am only 16 and know no more than ODEs and a little real analysis, but I learned some material from this)
The second section, which is really the heart of the book, starts off with a detailed treatment of the fundamental gamma and related functions, followed by a chapter on the famous zeta function and its unusual properties. The book then covers the hypergeometric functions - the focus is on the 1F1 and 2F1 types, being ODE solutions - which are perhaps the cornerstone of this field, followed the special cases of Bessel and Legendre functions. There are a number of ways of developing and teaching the ideas regarding these functions; this book mainly uses the differential equation approach, starting by defining these functions as solutions to ODEs and going from there. There is also a chapter on physics applications (using these functions to solve physics equations), which is sure to please the more applied math readers. The next three chapters are devoted to elliptic functions, covering the theta, Jacobi and Weierstrass types. (one chapter on each) The two remaining chapters are on Mathieu functions and ellipsoidal harmonic functions. Along the way, some additional functions are also sometimes mentioned in the problem sets. (barnes G, appell, and a few others) About the only room for improvement here would be some analyses of named integrals (EI, fresnel, etc.) and inverse functions (lambert W log, inverse elliptics, etc.), and perhaps more on multivariable hypergeometrics, but these things are not a big deal considering how much else appears in here, and I have not really seen any book out there that covers these anyway.
Each chapter has several subsections, usually one on each major theorem or property of the function in question, and these consist of the main discussion and proof, a few corollaries, and a couple of exercises that illustrate the usage of the theorem. At the end of the chapter, some more sets of problems are given; these mostly consist of proving identities and formulas involving the functions, so answers are not needed, but it would be nice if there was a showed-work solutions book available for students. The problems themselves are very well designed and some really require the use of novel methods of proof to obtain the result. The language is a bit in the older style with some unconventional spelling and usage, but it does not detract from the subject material at all (actually, I personally liked this form of writing), and the price is about right.
The only real complaint I have with this book has nothing to do with its content; it is the printing quality. The text font is simply too small in a number of places and also sometimes looks "washed out;" while it is still readable, such a classic gem as this definitely deserves a better effort on the publisher's part. (one of CUP's other works on the same subject, Special Functions by Andrews et al, has much better printing, although is not as good as this in other respects)
For those interested in the field of special functions and looking for something to start off with, A Course of Modern Analysis would be, hands down, my first recommendation. You cannot really do much better than this.
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