Synopsis
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.
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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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