Introduction to the Theory of Fourier's Series and Integrals (Classic Reprint), by H. S. Carslaw
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Introduction to the Theory of Fourier's Series and Integrals (Classic Reprint), by H. S. Carslaw
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Excerpt from Introduction to the Theory of Fourier's Series and IntegralsThis book forms the first volume of the new edition of my book on Fourier's Series and Integrals and the Mathematical Theory of the Conduction of Heat, published in 1906; and now for some time out of print. Since 1906 so much advance has been made in the Theory of Fourier's Series and Integrals, as well as in the mathematical discussion of Heat Conduction, that it has seemed advisable to write a completely new work, and to issue the same in two volumes. The first volume, which now appears, is concerned with the Theory of Infinite Series and Integrals, with special reference to Fourier's Series and Integrals. The second volume will be devoted to the Mathematical Theory of the Conduction of Heat.No one can properly understand Fourier's Series and Integrals without a knowledge of what is involved in the convergence of infinite series and integrals. With these questions is bound up the development of the idea of a limit and a function, and both are founded upon the modern theory of real numbers. The first three chapters deal with these matters. In Chapter IV. the Definite Integral is treated from Riemann's point of view, and special attention is given to the question of the convergence of infinite integrals. The theory of series whose terms are functions of a single variable, and the theory of integrals which contain an arbitrary parameter are discussed in Chapters V. and VI. It will be seen that the two theories are closely related, and can be developed on similar lines.The treatment of Fourier's Series in Chapter VII. depends on Dirichlet's Integrals. There, and elsewhere throughout the book, the Second Theorem of Mean Value will be found an essential part of the argument.About the PublisherForgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.comThis book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Introduction to the Theory of Fourier's Series and Integrals (Classic Reprint), by H. S. Carslaw- Published on: 2015-09-27
- Original language: English
- Number of items: 1
- Dimensions: 9.02" h x .71" w x 5.98" l, 1.01 pounds
- Binding: Paperback
- 342 pages
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Most helpful customer reviews
3 of 4 people found the following review helpful. An Abomination By Murty Kanury Very unreadably poor xerographic reproduction on thin cheap bleeding paper. Every page contains many broken type font which especially make this mathematics book not only useless but also mentally annoying and physically irritating. I returned mine for refund; Amazon was quite polite.
1 of 1 people found the following review helpful. One of the best books about series By Ömer Köksal Although very dated, it is one of the best books about series. It is not only about Fourier's series. It covers very deep information about analysing series.
0 of 0 people found the following review helpful. Carslaw introduces Fourier Series and Integrals By Michael R. La Martina My favorite thing about this volume is that it provides an excellent historical introduction. There are many historical footnotes integrated into the presentation.I would not call this a textbook, but it does contain a fair number of exercises, gently called examples. However the level of these examples ranges from moderate to great difficulty. The text is dated 1930 and does not benefit from a modern view, but all results are rigorously presented, and sufficient background is provided for use by anyone with a background of Integral Calculus.The integral used in the development of the material is the Riemann Integral, but the author includes an appendix covering Lebesgue Integration.The Dover edition is of good physical quality, but my original copy is a bit worn from years of reference so I have purchased an additional copy that remains unwrapped.
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