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The Theory of Functions: Edward C. Titchmarsh
Oxford University Press, USA | ISBN: 0198533497 | 1976-05-13 | djvu (ocr) | 464 pages | 5.98 Mb

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 teneleven 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, intuitiveotherwise, 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

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