Synopsis
Discover the origins and growth of the calculus of variations through the 19th century, traced chapter by chapter by a careful historian. This volume offers a clear, accessible account of how leading mathematicians—Poisson, Ostrogradsky, Sarrus, Delaunay, Cauchy, Jacobi, Legendre, and others—shaped the subject. Readers glimpse the evolution from early ideas to more advanced criteria for maxima and minima, and see how these ideas influenced subsequent work in geometry and analysis.
Structured as a historical survey, the book compiles key memoirs and treatises, explaining what they achieved and how they influenced later developments. It emphasizes the progress of the Calculus of Variations across major figures and includes discussion of the methods and problems that guided the field in the nineteenth century. The author also reflects on the accessibility and reception of these works, providing context for students and researchers approaching the subject today.
- Who contributed essential ideas about variable limits and the variation of double and multiple integrals.
- How Jacobi’s and Legendre’s methods influenced later work, including proofs and applications.
- How the subject intersected with geometry, differential equations, and mechanics.
- What the history reveals about the development of criteria distinguishing maxima from minima.
Ideal for readers of the history of mathematics, and for students seeking a clear map of the Calculus of Variations’ nineteenth‑century trajectory.
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Présentation de l'éditeur
HlSTORY OF THE PROGRESS OF THE CALCULUS OF VARIATIONS DURING THE NINETEENTH CENTURY LIBRARY OF CONGRESS CATALOG CARD NUMBER 61-18586 PRINTED IN THE UNITED STATES OF AMERICA .
(Typographical errors above are due to OCR software and don't occur in the book.)
About the Publisher
Forgotten Books is a publisher of historical writings, such as: Philosophy, Classics, Science, Religion, History, Folklore and Mythology.
Forgotten Books' Classic Reprint Series utilizes the latest technology to regenerate facsimiles of historically important writings. Careful attention has been made to accurately preserve the original format of each page whilst digitally enhancing the aged text. Read books online for free at www.forgottenbooks.org
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A History of the Progress of the Calculus of Variations During the Nineteenth
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Paperback. Etat : New. Print on Demand. This book provides a comprehensive and detailed history of the Calculus of Variations during the 19th century. It delves into the subject's development, showcasing how prominent mathematicians of the era expanded its boundaries. The author meticulously analyzes key treatises and memoirs, comparing and contrasting different approaches to solving problems involving the variation of integrals, both single and multiple. The book also examines the criteria for distinguishing maximum from minimum values in integral expressions, tracing the evolution of these criteria through the works of Legendre, Brunacci, and Jacobi. Beyond merely outlining the chronological progress of the subject, the author delves into the conceptual and methodological shifts that occurred within the Calculus of Variations during this period. He highlights the emergence of new approaches, such as those involving variable limits of integration, and carefully analyzes the impact of key insights from various mathematicians. The author's thorough examination of past work allows him to identify and clarify errors, offering a valuable resource for those interested in understanding the evolution of this important mathematical field. 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 9781440045752_0
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