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Synopsis
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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Introduction to the Theory of Fourier's Series and Integrals (Classic Reprint)
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Paperback. Condition: 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. Seller Inventory # 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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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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