**Colloquium Publications**

Volume: 14;
1932;
172 pp;
Softcover

MSC: Primary 12;

Print ISBN: 978-0-8218-4605-6

Product Code: COLL/14

List Price: $45.00

Individual Member Price: $36.00

**Electronic ISBN: 978-1-4704-3163-1
Product Code: COLL/14.E**

List Price: $45.00

Individual Member Price: $36.00

# Differential Equations from the Algebraic Standpoint

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*Joseph Fels Ritt*

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

# Table of Contents

## Differential Equations from the Algebraic Standpoint

- Cover Cover11
- Title page i2
- Introduction iii4
- Contents ix10
- Chapter I. Decomposition of a system of ordinary algebraic differential equations into irreducible systems 112
- Chapter II. General solutions and resolvents 2132
- Chapter III. First applications of the general theory 4758
- Chapter IV. Systems of algebraic equations 6273
- Chapter V. Constructive methods 92103
- Chapter VI. Constitution of an irreducible manifold 100111
- Chapter VII. Analogue of the Hilbert–Netto theorem. Theoretical decomposition process 108119
- Chapter VIII. Analogue for form quotients of Lüroth’s theorem 124135
- Chapter IX. Riquier’s existence theorem for orthonomic systems 135146
- Chapter X. Systems of algebraic partial differential equations 157168
- Index 172183
- Back Cover Back Cover1184