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Differential Equations from the Algebraic Standpoint

by Joseph Fels Ritt

Part of the Colloquium Publications Series

Differential Equations from the Algebraic Standpoint Synopsis

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).

Book Information

ISBN: 9780821846056
Publication date: 15th July 1932
Author: Joseph Fels Ritt
Publisher: American Mathematical Society
Format: Paperback / softback
Pagination: 172 pages
Categories: Mathematics,

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