Change and Variations: A History of Differential Equations to 1900 (Springer Undergraduate Mathematics Series) free ebook download.

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Change and Variations: A History of Differential Equations to 1900 (Springer Undergraduate Mathematics Series) free ebook download

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Mathematics

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Author(s):	Jeremy Gray

Date:	2021	Format:	pdf	Language:	English	ISBN/ASIN:	3030705749
Pages:	444	OCR:		Quality:		ISBN13:
Uploader:	alex21s	Upload Date:	6/10/2021 11:27:29 PM

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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 dAlembert and Euler  Fouriers solutions to the heat equation and the contribution of Kovalevskaya  the work of Euler, Gauss, Kummer, Riemann, and Poincar on the hypergeometric equation  Greens functions, the Dirichlet principle, and Schwarzs solution of the Dirichlet problem  minimal surfaces  the telegraphists equation and Thomsons successful design of the trans-Atlantic cable  Riemanns 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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Tags: Change Differential Equations History Mathematics Springer Undergraduate Variations

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