The Theory of Differential Equations

Abstract

SINCE Newton and Leibniz began to study differential equations in the seventeenth century, mathematics has made great strides. Though the creative mathematicians have mainly been inspired by the art of their subject rather than by the prospect of its useful applications, yet the demands made by the rapid progress of science have been responsible for a considerable amount of research. Much of this has been devoted to differential equations, for herein lies primarily the mathematical basis of applied science, notably physics and engineering. Unfortunately, however, most practical equations cannot be solved in finite terms, so that resort has to be made to approximations. Even Newton himself realized this difficulty and tentatively applied power-series, but before such a method could be reliably applied, it was necessary to show, not only that the power-series was valid within specified boundary conditions, but also that a solution to the given equation actually existed. It was not, therefore, until Cauchy discriminated between analytic and non-analytic systems and gave rigorous existence theorems for each type that any material progress was made.

Introduction to the Theory of Linear Differential Equations

By E. G. C. Poole. Pp. viii + 202. (Oxford: Clarendon Press; London: Oxford University Press, 1936.) 17s. 6d. net.