Differential Equations from the Algebraic Standpoint
Joseph Fels Ritt · Colloquium Publications - American Mathematical Society/Colloquium Publications · 1932
This book can be viewed as a first attempt to systematically develop an algebraic theory of nonlinear differential equations, both ordinary and partial. The main goal of the author was to construct a theory of elimination, which "will reduce the existence problem for a finite or infinite system of algebraic differential equations to the application of the implicit function theorem taken with Cauchy's theorem in the ordinary case and Riquier's in the partial." In his 1934 review of the book, J. M. Thomas called it "concise, readable, original, precise, and stimulating", and his words still rema