DIFFERENTIAL ALGEBRA

The theory of differential algebra delas with the application of methods of abstract algebra to differential equations with algebraic coefficients. This book is a modern (1950) account of developments in the subject, a field that the author first covered in his 1932 book. Differential Equations from the Algebraic Standpoint. What makes it so valuable s its incorporation of the work of many contributors and its clear rendition of the material.

The concrete problems which the book treats deal with situations of the classical theory of differential equations. It is divided into chapters on differential polynomials and their ideals; algebraic differential manifolds’ structure of differential polynomials (manifold of a differential polynomial, exponents of ideals); systems of  algebraic equations; constructive methods; analytical considerations; intersections of algebraic differential manifolds; Riquier’s existence theorem for orthonomic systems; and partial differential algebra.