A Course of Modern Analysis (Cambridge Mathematical Library) (Paperback)

by E. T. Whittaker (Author), G. N. Watson (Author) "The idea of a set of numbers is derived in the first instance from the consideration of the set of positive integral numbers, or positive..." (more)
Key Phrases: shew that the series, limited total fluctuation, shew that the equation, London Math, Journal de Math, Edinburgh Math (more...)

Editorial Reviews

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

Product Description
This classic text has entered and held the field as the standard book on the applications of analysis to the transcendental functions. The authors explain the methods of modern analysis in the first part of the book and then proceed 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 that so often tends to make a rigorous demonstration tedious. Researchers and students will find this book as valuable as ever.

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Product Details

• Paperback: 616 pages
• Publisher: Cambridge University Press; 4 edition (September 13, 1996)
• Language: English
• ISBN-10: 0521588073
• ISBN-13: 978-0521588072
• Product Dimensions: 8.8 x 6 x 1.3 inches
• Shipping Weight: 1.8 pounds (View shipping rates and policies)
• Average Customer Review: 4.6 out of 5 stars See all reviews (18 customer reviews)
• Amazon.com Sales Rank: #128,438 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

39 of 39 people found the following review helpful:

5.0 out of 5 stars This book seems to be eternal!, July 24, 1998

By A Customer

This book isn't Modern anymore. Thank God! It is certainly the most useful book of mathematics I ever put my hands on. If you read its page of contents, you'll call it prophetic! Every kind of function he studied became important in theoretical physics some time. String theory was started with an amplitude containing only Gamma functions. Renormalization, reborn from the ashes, discovered the Zeta-function (in Whittaker-Watson, for sure), Legendre's less familiar functions were prominent in Regge pole theory (again, the source was Whittaker), and even the Theta functions became important for some field theory skirmishes. You could travel light: Whittaker, Watson, tooth brush, etc. It's not only what there is in it. It's also the fact that it's done better! Consider this: I had once an ugly series to sum up. These were the days before Maple! I couldn't find it anywhere, having looked into immense mathematical tables. I came back to old Whittaker and there it was: in an e! xercise, asking you to prove that the sum of MY series was some function he wrote in all detail! This is Whittaker-Watson. God bless them.

29 of 30 people found the following review helpful:

5.0 out of 5 stars The Bible of math methods in physics, May 10, 2002

By	Professor Joseph L. McCauley "Joseph L. McCauley" (Austria+Texas) - See all my reviews

Although I was aware that he'd read other books, and knew much more than is taught here, this was (in my years as his grad student) the only book that I saw Lars Onsager pull off his shelf, well-worn and dog-eared, it was! It's one of the many 'Onsager tales' that circulate among his former students and postdocs that he'd worked through all the problems in this text (just for mental exercise) as undergrad at NTH. One can believe it if one takes the trouble to read his Ph.D. dissertation on weak electrolytes, where a pde is solved exactly by using an 'extremely inventive' method based on complex analysis (the dissertation lies in Yale's Beineke library). I later used the book, along with Stakgold (on boundary-value problems) to teach a first semester grad 'math methods' course to physics and engineering students. I must say that in that time the grad students had no difficulty working the problems, although I certainly did not assign the hardest ones (Tripos...). I usually went as far in series expansions and complex variables as the Mittag-Leffler expansion, spending about a half a semester on W&W before switching to delta functions, boundaty value problems, and Stakgold. Fuch's theorem was covered in the second semester via Bender & Orszag.

23 of 24 people found the following review helpful:

5.0 out of 5 stars All Business Hall of Famer, December 23, 2000

By	Nimbus (Clownifornia) - See all my reviews

I own the 1940 HB edition (which was itself a reprint). It was terribly hard to track down and I had to pay a fortune for it. Be glad it's now in reprint. This book is probably in more bibliographies than any other in the 20th century mathematics. For that reason alone it's worth every penny. The book is all business with little extraneous comments, applications, or excursions that often make higher mathematics such a joy. That being said, the 608 pages cover a lot of ground which is probably why it is on so many reference lists.

Despite it's fanfare in the mathematic communitiy, the subjects dealt arise from physics and engineering rather than pure mathematics. I don't think there is a chapter without practical application. Unlike many more recent texts on the subject, the authors cover Theta Functions and Elliptic Functions (Jacobian and Weistrass).

This is definitely a Hall of Famer in the Math Universe.