Authors:
- The first broad-ranging account of the history of ordinary and partial differential equations and the calculus of variations to 1900
- Provides numerous original and translated sources with advice on how to study them
- Emphasises the practical roots of theorems in pure analysis
- Includes important overlooked topics, such as Riemann’s paper on shock waves and Thomson’s contribution to the telegraphists’ equation
- Includes numerous exercises that develop an approach to studying the history of mathematics
Part of the book series: Springer Undergraduate Mathematics Series (SUMS)
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Table of contents (31 chapters)
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Front Matter
About this book
This book presents a history of differential equations, both ordinary and partial, as well as the calculus of variations, from the origins of the subjects to around 1900. Topics treated include the wave equation in the hands of d’Alembert and Euler; Fourier’s solutions to the heat equation and the contribution of Kovalevskaya; the work of Euler, Gauss, Kummer, Riemann, and Poincaré on the hypergeometric equation; Green’s functions, the Dirichlet principle, and Schwarz’s solution of the Dirichlet problem; minimal surfaces; the telegraphists’ equation and Thomson’s successful design of the trans-Atlantic cable; Riemann’s paper on shock waves; the geometrical interpretation of mechanics; and aspects of the study of the calculus of variations from the problems of the catenary and the brachistochrone to attempts at a rigorous theory by Weierstrass, Kneser, and Hilbert. Three final chapters look at how the theory of partial differential equations stood around 1900, as they were treated by Picard and Hadamard. There are also extensive, new translations of original papers by Cauchy, Riemann, Schwarz, Darboux, and Picard.
The first book to cover the history of differential equations and the calculus of variations in such breadth and detail, it will appeal to anyone with an interest in the field. Beyond secondary school mathematics and physics, a course in mathematical analysis is the only prerequisite to fully appreciate its contents. Based on a course for third-year university students, the book contains numerous historical and mathematical exercises, offers extensive advice to the student on how to write essays, and can easily be used in whole or in part as a course in the history of mathematics. Several appendices help make the book self-contained and suitable for self-study.
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Authors and Affiliations
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School of Mathematics and Statistics, Open University, Milton Keynes, UK
Jeremy Gray
About the author
Bibliographic Information
Book Title: Change and Variations
Book Subtitle: A History of Differential Equations to 1900
Authors: Jeremy Gray
Series Title: Springer Undergraduate Mathematics Series
DOI: https://doi.org/10.1007/978-3-030-70575-6
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
Softcover ISBN: 978-3-030-70574-9Published: 04 June 2021
eBook ISBN: 978-3-030-70575-6Published: 03 June 2021
Series ISSN: 1615-2085
Series E-ISSN: 2197-4144
Edition Number: 1
Number of Pages: XXII, 419
Number of Illustrations: 31 b/w illustrations, 13 illustrations in colour
Topics: History of Mathematical Sciences, Analysis