Partial Differential Equations

Abstract

Since the chronology of Kovalevskaya’s work with Weierstrass cannot be definitely established, the three papers she wrote during this period will be discussed in the order of their publication. Very likely the topic of the present chapter was the last of the three to be completed, since the result was so significant that it would constitute a dissertation all by itself. To appreciate the significance of this result it is necessary to understand aspects of the development of differential equations in the nineteenth century. The latter subject is vast, and the present account can sketch only part of its growth along one of its many lines of development. Nevertheless the developments which will be discussed were of central importance, being direct consequences of one major idea-regarding the solution of a differential equation as an analytic function of a complex variable.