Colloquium Publications 1932; 172 pp; softcover Volume: 14 ISBN10: 0821846051 ISBN13: 9780821846056 List Price: US$42 Member Price: US$33.60 Order Code: COLL/14
 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 remain true. A more fundamental and complete account of further developments of the algebraic approach to differential equations is given in Ritt's treatise Differential Algebra, written almost 20 years after the present work (Colloquium Publications, Vol. 33, American Mathematical Society, 1950). Readership Graduate students and research mathematicians interested in differential equations. Table of Contents  Decomposition of a system of ordinary algebraic differential equations into irreducible systems
 General solutions and resolvents
 First applications of the general theory
 Systems of algebraic equations
 Constructive methods
 Constitution of an irreducible manifold
 Analogue of the HilbertNetto theorem. Theoretical decomposition process
 Analogue for form quotients of Lüroth's theorem
 Riquier's existence theorem for orthonomic systems
 Systems of algebraic partial differential equations
 Index
