Change and Variations - A History of Differential Equations to 1900 (Paperback, 1st ed. 2021)

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 Poincare 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.

General

Imprint:	Springer Nature Switzerland AG
Country of origin:	Switzerland
Series:	Springer Undergraduate Mathematics Series
Release date:	June 2021
First published:	2021
Authors:	Jeremy Gray
Dimensions:	235 x 155 x 29mm (L x W x T)
Format:	Paperback
Pages:	419
Edition:	1st ed. 2021
ISBN-13:	978-3-03-070574-9
Categories:	Books > Science & Mathematics > Mathematics > History of mathematics Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Vector & tensor analysis
LSN:	3-03-070574-9
Barcode:	9783030705749

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