000			a
999			_c30729 _d30729
008			220222b xxu||||| |||| 00| 0 eng d
020			_a9783030705749
082			_a515.35 _bGRA
100			_aGray, Jeremy
245			_aChange and variations : a history of differential equations to 1900
260			_bSpringer, _c2021 _aCham :
300			_axxii, 419 p. ; _b44 ill., 13 ill. in color, _c24 cm
365			_b34.99 _cEUR _d88.10
490			_aSpringer undergraduate mathematics series
504			_aIncludes bibliographical references and index.
520			_aThis 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'lembert and Euler; Fourier 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.
650			_aMathematics
650			_aHistory
650			_aMathematical analysis
650			_aDifferential equations
650			_aCurve principal
650			_aCycloid
650			_aHeat equation
650			_a Laplace equation
650			_a Gauss equation.
650			_aPotential theory
650			_aWave equation
650			_a Partial differential equation
650			_aMobins transformations
650			_a Rational mechanics
942			_2ddc _cBK