Change and Variations

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 Poincar¿n 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 trea