Differential Equations from the Algebraic Standpoint

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Mathematics - Differential Equations
Differential Equations from the...

Differential Equations from the Algebraic Standpoint

Name: Differential Equations from the Algebraic Standpoint
ISBN: 9780821846056

Joseph Fels Ritt

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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).

Категории:

Mathematics - Differential Equations

Тип съдържание:

Книги

Година:

1932

Издателство:

American Mathematical Society

Език:

english

Страници:

183