The Theory of Functions of a Real Variable and the Theory of Fourier's Series, Vol. 1 (Classic Reprint) - Couverture souple
Synopsis
Explore the foundations of real-variable theory and how Fourier’s series fit in. This edition presents Hobson’s approach to rigor, definitions, and the conditions that justify the limiting processes used in mathematical analysis.
The text introduces the arithmetic continuum, the nature of limits, and the precise formulation of when limiting techniques are valid. It surveys the theory of sets of points, aggregates, and the representation of functions by series or sequences, with a focus on functions of one variable and, to a lesser extent, two.
- Clear definitions of continuity, discontinuity, and related function classes.
- Discussion of point-wise discontinuous functions and the structure of their discontinuities.
- Explanations of monotone functions, saltus (jumps), oscillation, and the behavior of limits.
- Connections between the theory of sets, aggregates, and the representation of functions by trigonometrical series.
Ideal for readers of real analysis and the history of the subject, this edition helps students grasp the core ideas behind modern function theory and its applications to mathematical physics.
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The Theory of Functions of a Real Variable and the Theory of Fourier's Series
impression à la demandeVendeur : Forgotten Books, London, Royaume-Uni
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Paperback. Etat : New. Print on Demand. This book delves into the intricate world of mathematical analysis, specifically focusing on the theory of functions of a real variable. It provides a comprehensive exploration of this theory's evolution, tracing its roots back to the challenges posed by Fourier series and the need for a rigorous understanding of concepts like continuity and limits. The author meticulously examines the foundations of real numbers, delving into the theories of Cantor and Dedekind, and constructs a framework for understanding sets of points and their properties. The book delves into the complexities of functions, their classifications, and their representation through series. A significant portion is dedicated to the exploration of Fourier series, reflecting their historical importance in shaping the field. Integration, a cornerstone of calculus, is thoroughly examined, encompassing both the Riemann and Lebesgue approaches. The author's dedication to clarity and accessibility makes this book a valuable resource for both students and mathematicians seeking a deeper understanding of the theory of functions. By unraveling the intricacies of mathematical analysis, this book offers invaluable insights into the fundamental principles that underpin our understanding of the continuous and the infinite. 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. N° de réf. du vendeur 9781330135020_0
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The Theory of Functions of a Real Variable and the Theory of Fourier's Series, Vol. 1 (Classic Reprint)
Vendeur : PBShop.store US, Wood Dale, IL, Etats-Unis
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PAP. Etat : New. New Book. Shipped from UK. Established seller since 2000. N° de réf. du vendeur LW-9781330135020
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The Theory of Functions of a Real Variable and the Theory of Fourier's Series, Vol. 1 (Classic Reprint)
Vendeur : PBShop.store UK, Fairford, GLOS, Royaume-Uni
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PAP. Etat : New. New Book. Shipped from UK. Established seller since 2000. N° de réf. du vendeur LW-9781330135020
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EUR 33,95
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Expédition depuis Royaume-Uni vers Etats-Unis
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