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Differential Equations from the Algebraic Standpoint
 
Differential Equations from the Algebraic Standpoint
Softcover ISBN:  978-0-8218-4605-6
Product Code:  COLL/14
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $52.00
eBook ISBN:  978-1-4704-3163-1
Product Code:  COLL/14.E
List Price: $60.00
MAA Member Price: $54.00
AMS Member Price: $48.00
Softcover ISBN:  978-0-8218-4605-6
eBook: ISBN:  978-1-4704-3163-1
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
Differential Equations from the Algebraic Standpoint
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Differential Equations from the Algebraic Standpoint
Softcover ISBN:  978-0-8218-4605-6
Product Code:  COLL/14
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $52.00
eBook ISBN:  978-1-4704-3163-1
Product Code:  COLL/14.E
List Price: $60.00
MAA Member Price: $54.00
AMS Member Price: $48.00
Softcover ISBN:  978-0-8218-4605-6
eBook ISBN:  978-1-4704-3163-1
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 Details
     
     
    Colloquium Publications
    Volume: 141932; 172 pp
    MSC: 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).

    Readership

    Graduate 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 141932; 172 pp
MSC: 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).

Readership

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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.