Customer Reviews

The Theory of Functions

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This is a book on complex analysis, followed by some measure theory. It is the complex analysis part which is superb. Titchmarsh is one of those rare authors that manage to motivate the results, get them with rigour and clarity and, especially, select theorems so well that you always find what you need for applications. It's like the famous short table of integrals in the famous, multi-edition, "Handbook of Physics and Chemistry". It was so wisely made that it was said that when you could not find in it the integral you needed, you probably went wrong somewhere. So is the venerable Theory of Functions. It is particularly good in asymptotic theorems like Phragmen-Lindelof's, or in the treatment of analytic continuation. But the whole book is a joy! When the Regge Pole theory appeared in particle physics, I published several papers that were not much more than transpositions of results from Titchmarsh to the language of particle physics. So I earned my living f! rom it, for some years.

Many people would rather buy a Dover Book than this one, just because it is so high-priced. Most of the time, that is a good idea, but it isn't when it comes to THIS book. This book serves as an excellent complement to A Course of Modern Analysis by Whittaker and Watson (yes, together the two books are 135 dollars, but buy them BOTH). While Modern Analysis essentially covers the basics of the theory of functions before moving on to the greatest treatment of special functions ever written, this book by Titchmarsh expands tremendously upon the material in the first ten or eleven chapters of Whittaker and Watson's book. While Titchmarsh does not cover special functions in much detail (except for Dirichlet Series, which are not in Modern Analysis) he provides an EXCELLENT coverage of the general theory of functions, ranging from conformal representation to Fourier's theorem to Lebesgue Integration. Titchmarsh's treatment of the latter topic in particular is one of the best introductions to measure-theory I have EVER seen. Titchmarsh has not written a traditional "proof-theorem" book--rather, like Whittaker and Watson, he provides at least some motivation, intuitive or otherwise, for most of the concepts in this book. He manages to cover a huge ammount of material, and to cover it very well. Buy this book-it's worth even more than it's 75 dollar price.

This is a very very enjoyable book. I am sad to see that this style of writing Mathematics is no longer in vogue. I am studying this book along with the Whitaker & Watson's book, which is another excellent book. However, I sometimes find that the exposition is clearer in Titchmarsh's book. This book refers to Hardy's book, which is yet another classic.

Be warned that this book references Hardy's "Pure Mathematics" regularly. This book is principally a collection of results in complex analysis. The upside is that there are many problems developed in detail and the author sincerely tries to motivate every topic. The downside is that the language is so dated that often topics are excessively difficult to digest. I would not recommend this as a first book in complex functions theory. It's more useful as a supplement to other more modern courses.

This is an excellent book and a very good resourc