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.
