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e-Book The Theory of Functions epub download

e-Book The Theory of Functions epub download

Author: E.C. Titchmarsh
ISBN: 0198533195
Pages: 464 pages
Publisher: Oxford University Press; 2nd edition (1939)
Language: English
Category: Mathematics
Size ePUB: 1141 kb
Size Fb2: 1272 kb
Size DJVU: 1794 kb
Rating: 4.2
Votes: 719
Format: lrf doc docx mbr
Subcategory: Science

e-Book The Theory of Functions epub download

by E.C. Titchmarsh



The Theory of Functions has been added to your Cart. Titchmarsh gives an excellent presentation of Dirichlet series in this book, and beyond his presentation being excellent, there few other textbooks that give expositions of Dirichlet series.

The Theory of Functions has been added to your Cart. There are indeed many other books that talk about the Riemann zeta function and L-functions (usually either they gave a standard issue presentation of the Riemann zeta function, or they are at a higher level), but not many that talk about the analysis of general Dirichlet series

This is a book on complex analysis, followed by some measure theory. It is the complex analysis part which is superb.

This is a book on complex analysis, followed by some measure theory. 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.

Categories: Mathematics. Other readers will always be interested in your opinion of the books you've read. Whether you've loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them. 1. Topics in differential topology. R. L. E Schwarzenberger.

The zeros of an analytic function.

ISBN 978-0-198-53349-8. The zeros of an analytic function.

The Titchmarsh convolution theorem is named after Edward Charles Titchmarsh, a British mathematician. The theorem describes the properties of the support of the convolution of two functions.

should be on everyone's bookshelf I love the old writing style. should be on everyone's bookshelf

Titchmarsh was known for work in analytic number theory, Fourier analysis and other parts of mathematical analysis

Titchmarsh was known for work in analytic number theory, Fourier analysis and other parts of mathematical analysis. Titchmarsh was Savilian Professor of Geometry at the University of Oxford from 1932 to 1963.

VERY GOOD hardcover, free tracking number, clean text, 2nd edition, 1958 printing, solid binding, NO remainders NOT ex-library, smoke free; slight gentle shelfwear / storage-wear; previous owner's name on endpaper; jacket lacking WE SHIP FAST. Carefully packed and quickly sent. 201609646da 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 amount of material, and to cover it very well. Please choose Priority / Expedited shipping for faster delivery. (No shipping to Mexico, Brazil or Italy.)
Ceck
Titchmarsh gives an excellent presentation of Dirichlet series in this book, and beyond his presentation being excellent, there few other textbooks that give expositions of Dirichlet series. There are indeed many other books that talk about the Riemann zeta function and L-functions (usually either they gave a standard issue presentation of the Riemann zeta function, or they are at a higher level), but not many that talk about the analysis of general Dirichlet series.

The chapter on Dirichlet series and the chapters on power series (chapters VII to IX) are what make me like Titchmarsh's book so much. Power series are a fascinating topic by themselves, not just as something that comes up in a complex analysis course. Some material in this book that is not in common textbooks: In the first chapter Titchmarsh presents Abel's theorem, Tauber's theorem, infinite products, and finds the asymptotic behavior of the gamma function. In the fourth chapter he writes about functions with natural boundaries and about Lambert series. In the seventh chapter he proves results on singularities on the circle of convergence of a power series (e.g., if a power series has radius of convergence 1 and nonnegative terms then z=1 is a singular point of it), introduces over-convergence of power series (convergence outside the circle of convergence of a subsequence of the sequence of partial sums), treats the asymptotic behavior near the circle of convergence, and gives a proof of Littlewood's Tauberian theorem.

The book is also valuable for the large number of examples Titchmarsh gives at the end of the sections.

However, the material on Lebesgue integration is done much better in other recent books and I wouldn't bother reading Titchmarsh's exposition of it.
Dianantrius
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.
Tygrarad
I bought a used one. It is so expensive. :P
Kirizan
Very good and useful book. Has chapters on the Lebesgue measure and integration which is difficult to find in other textbooks
Fecage
In past years I used this text as supplementary reading to E.T.Copson's text on complex variables and found this to be more rigorous and complete than the course text.. It assumes familiarity with Hardy's "A Course Of Pure Mathematics' and freely references this book for basic theorems like Heine-Borel, Dedekind Construction, etc. More important is Hardy's use of L and R classes to partition the rationals for Dedekind sections in the construction of a real number. Rudin used just the L classes (a Dedekind cut) as discovered by Russell to be sufficient for real number construction (given in an appendix to ch.1 in Rudin's Principles 3rd). L and R classes are also used in the Whittaker and Watson classic text. Idea is that these sections lead to a fixed point or define an epsilon neighborhood of the point. The fixed point or real number being either the supremum of the L class or the infimum of the R class. These concepts contain the key ideas and were actually extrapolated from Dedekind's construction. Anyway though Titchmarsh belonged to the distinguished class of Pre-War British mathematicians, he did not rely heavily on the power series approach to complex analysis and you'll find that a great deal of the text has the geometric or elementary topology flavor.Some people viewed him as arrogant and in hindsight it may have been because he was so at ease with the power of this method where to most mathematicians it was quite alien at the time. Classic theorems like Rouche's are given elementary proofs (winding number in Rouche). I would recommend you read this text prior to tackling his monograph on the Riemann Zeta function to get used to his style as well as to have it available as a reference as it is cited frequently in this monograph.
Titchmarsh also provides an elementary proof of Picard's Big Theorem on essential singulaitries of a complex function-a rarity indeed.
Thiama
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.