An introduction to the theory of infinite series Thomas John I'Anson Bromwich 9781178005462 Books
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An introduction to the theory of infinite series Thomas John I'Anson Bromwich 9781178005462 Books
This book was based on a series lectures in "elementary" analysis given between 1902 and 1907 by Bromwich at Queen's College. Godfrey Hardy, the pure mathematician par excellence from Cambridge, read the manuscript. The material is anything but elementary and says a lot about the standards at the time. The level is essentially pitched at Cambridge's Tripos candidates at that time. The "easy miscellaneous examples" at the end of the book are anything but easy. Many of the problems have names like Dirichlet, Osgood, Pringsheim, Du Bois Reymond, Hardy, Borel etc attached to them. You get the picture. The depth of treatment of convergence of series is much greater than is the case with modern courses on analysis. There is extensive material on various tests: Abel, Weierstrass, Dirichlet, Tannery etc all based on some hard core analysis. If you want to really understand the Gamma function,, say, there is a lot of material (way beyond the stuff given in the standard treatments) that will expand your knowledge. If, for instance, you really want to understand convergence of the Poisson integral or the convergence of the integral of the sinc function ( sin x / x) there is a wealth of material. Students who want to understand more advanced analytical techniques such as Tauberian theorems will find the book useful.This is not a book for lazy students or those who are having trouble with the concept of limit. It is really pitched at top students and will reward them with the depth of the material contained therein. It is a snobbish book at one level but leaving that aside the material is very useful for a student who is seriously interested in analytical techniques.
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An introduction to the theory of infinite series Thomas John I'Anson Bromwich 9781178005462 Books Reviews
PERFECT!!!
This book was based on a series lectures in "elementary" analysis given between 1902 and 1907 by Bromwich at Queen's College. Godfrey Hardy, the pure mathematician par excellence from Cambridge, read the manuscript. The material is anything but elementary and says a lot about the standards at the time. The level is essentially pitched at Cambridge's Tripos candidates at that time. The "easy miscellaneous examples" at the end of the book are anything but easy. Many of the problems have names like Dirichlet, Osgood, Pringsheim, Du Bois Reymond, Hardy, Borel etc attached to them. You get the picture. The depth of treatment of convergence of series is much greater than is the case with modern courses on analysis. There is extensive material on various tests Abel, Weierstrass, Dirichlet, Tannery etc all based on some hard core analysis. If you want to really understand the Gamma function,, say, there is a lot of material (way beyond the stuff given in the standard treatments) that will expand your knowledge. If, for instance, you really want to understand convergence of the Poisson integral or the convergence of the integral of the sinc function ( sin x / x) there is a wealth of material. Students who want to understand more advanced analytical techniques such as Tauberian theorems will find the book useful.
This is not a book for lazy students or those who are having trouble with the concept of limit. It is really pitched at top students and will reward them with the depth of the material contained therein. It is a snobbish book at one level but leaving that aside the material is very useful for a student who is seriously interested in analytical techniques.
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