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Sinopsis
Excerpt from Introduction to the Theory of Fourier's Series and Integrals
The modern theory of integration, associated chiefly with the name of Lebesgue, has introduced into the Theory of Fourier's Series and Integrals functions of a far more complicated nature. Various writers, notably W. H. Young, are engaged in building up a theory of these and allied series much more advanced than any thing treated in this book. These developments are in the meantime chiefly interesting to the Pure Mathematician specialising in the Theory of Functions of a Real Variable. My purpose has been to remove some of the difficulties of the Applied Mathematician.
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This 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.
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Reseña del editor
Excerpt from Introduction to the Theory of Fourier's Series and Integrals
The modern theory of integration, associated chiefly with the name of Lebesgue, has introduced into the Theory of Fourier's Series and Integrals functions of a far more complicated nature. Various writers, notably W. H. Young, are engaged in building up a theory of these and allied series much more advanced than any thing treated in this book. These developments are in the meantime chiefly interesting to the Pure Mathematician specialising in the Theory of Functions of a Real Variable. My purpose has been to remove some of the difficulties of the Applied Mathematician.
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This 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.
Reseña del editor
Excerpt from Introduction to the Theory of Fourier's Series and Integrals
This 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 Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This 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.
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Introduction to the Theory of Fourier's Series and Integrals Classic Reprint
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Introduction to the Theory of Fourier's Series and Integrals (Classic Reprint)
Librería: PBShop.store US, Wood Dale, IL, Estados Unidos de America
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PAP. Condición: New. New Book. Shipped from UK. Established seller since 2000. Nº de ref. del artículo: LW-9781330157077
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Introduction to the Theory of Fourier's Series and Integrals (Classic Reprint)
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Paperback. Condición: New. Print on Demand. This book delves into the fascinating realm of infinite series and integrals, with a particular emphasis on Fourier series and integrals. It embarks on a journey through the foundations of mathematical analysis, exploring the intricacies of rational and irrational numbers, and establishing the concept of the linear continuum. The author meticulously examines the convergence of infinite sequences and series, laying the groundwork for understanding the behaviour of functions and their limits. The definite integral takes centre stage, with Riemann's approach providing a comprehensive framework for analysis. Building upon these concepts, the book delves into the theory of infinite series, exploring uniform convergence and its implications for term-by-term integration and differentiation. Fourier series are introduced and rigorously examined, drawing upon the works of Dirichlet and Poisson. The author explores the nature of convergence of Fourier series, delving into Gibbs Phenomenon and its impact on approximation. The exploration culminates in the study of Fourier integrals, extending the reach of Fourier analysis to a broader class of functions. This comprehensive journey through infinite series and integrals illuminates the profound connections between mathematical theory and its applications, revealing the elegant tools that mathematicians employ to understand and model the world around us. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Nº de ref. del artículo: 9781330157077_0
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Introduction to the Theory of Fourier's Series and Integrals (Classic Reprint)
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Introduction to the Theory of Fourier*s Series and Integrals (Classic Reprint)
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