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Softcover ISBN:  9780821846056 
Product Code:  COLL/14 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $52.00 
eBook ISBN:  9781470431631 
Product Code:  COLL/14.E 
List Price:  $60.00 
MAA Member Price:  $54.00 
AMS Member Price:  $48.00 
Softcover ISBN:  9780821846056 
eBook ISBN:  9781470431631 
Product Code:  COLL/14.B 
List Price:  $125.00 $95.00 
MAA Member Price:  $112.50 $85.50 
AMS Member Price:  $100.00 $76.00 

Book DetailsColloquium PublicationsVolume: 14; 1932; 172 ppMSC: Primary 12
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).
ReadershipGraduate students and research mathematicians interested in differential equations.

Table of Contents

Chapters

Chapter I. Decomposition of a system of ordinary algebraic differential equations into irreducible systems

Chapter II. General solutions and resolvents

Chapter III. First applications of the general theory

Chapter IV. Systems of algebraic equations

Chapter V. Constructive methods

Chapter VI. Constitution of an irreducible manifold

Chapter VII. Analogue of the Hilbert–Netto theorem. Theoretical decomposition process

Chapter VIII. Analogue for form quotients of Lüroth’s theorem

Chapter IX. Riquier’s existence theorem for orthonomic systems

Chapter X. Systems of algebraic partial differential equations


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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).
Graduate students and research mathematicians interested in differential equations.

Chapters

Chapter I. Decomposition of a system of ordinary algebraic differential equations into irreducible systems

Chapter II. General solutions and resolvents

Chapter III. First applications of the general theory

Chapter IV. Systems of algebraic equations

Chapter V. Constructive methods

Chapter VI. Constitution of an irreducible manifold

Chapter VII. Analogue of the Hilbert–Netto theorem. Theoretical decomposition process

Chapter VIII. Analogue for form quotients of Lüroth’s theorem

Chapter IX. Riquier’s existence theorem for orthonomic systems

Chapter X. Systems of algebraic partial differential equations