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| Softcover ISBN: | 978-0-8218-4619-3 |
| eBook: ISBN: | 978-1-4704-3169-3 |
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| Softcover ISBN: | 978-0-8218-4619-3 |
| Product Code: | COLL/21 |
| List Price: | $65.00 |
| MAA Member Price: | $58.50 |
| AMS Member Price: | $52.00 |
| eBook ISBN: | 978-1-4704-3169-3 |
| Product Code: | COLL/21.E |
| List Price: | $60.00 |
| MAA Member Price: | $54.00 |
| AMS Member Price: | $48.00 |
| Softcover ISBN: | 978-0-8218-4619-3 |
| eBook ISBN: | 978-1-4704-3169-3 |
| Product Code: | COLL/21.B |
| List Price: | $125.00 $95.00 |
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Book DetailsColloquium PublicationsVolume: 21; 1937; 118 ppMSC: Primary 57; Secondary 35; 58
The main goal of this book is to present the theory of systems of partial differential equations and the theory of Pfaffian systems so as to exhibit clearly the relations between them.
In presenting the theory of Pfaffian systems, the author develops, in detail, the theories of Grassmann algebras and rings with differentiation. In particular, following Grassmann and É. Cartan, he introduces and freely uses what is now known as a ring of differential forms with functional coefficients. In presenting the theory of systems of partial differential equations, the author concentrates on the existence of solutions and methods of approximating them, rather than on their properties. The relations and similarities of two theories are displayed through the systematic use of various versions of the elimination method.
ReadershipGraduate students and research mathematicians interested in partial differential equations and Pfaffian systems.
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Table of Contents
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Chapters
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Chapter I. Introduction
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Chapter II. Generalities on symbols and systems
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Chapter III. Grassmann algebra
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Chapter IV. Differential rings
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Chapter V. Commutative monomials and polynomials
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Chapter VI. Algebraic systems
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Chapter VII. Algebraic differential systems
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Chapter VIII. Function systems and differential systems
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Chapter IX. Pfaffian systems
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Chapter X. Consistency examples
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Chapter XI. Illustrative examples
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The main goal of this book is to present the theory of systems of partial differential equations and the theory of Pfaffian systems so as to exhibit clearly the relations between them.
In presenting the theory of Pfaffian systems, the author develops, in detail, the theories of Grassmann algebras and rings with differentiation. In particular, following Grassmann and É. Cartan, he introduces and freely uses what is now known as a ring of differential forms with functional coefficients. In presenting the theory of systems of partial differential equations, the author concentrates on the existence of solutions and methods of approximating them, rather than on their properties. The relations and similarities of two theories are displayed through the systematic use of various versions of the elimination method.
Graduate students and research mathematicians interested in partial differential equations and Pfaffian systems.
-
Chapters
-
Chapter I. Introduction
-
Chapter II. Generalities on symbols and systems
-
Chapter III. Grassmann algebra
-
Chapter IV. Differential rings
-
Chapter V. Commutative monomials and polynomials
-
Chapter VI. Algebraic systems
-
Chapter VII. Algebraic differential systems
-
Chapter VIII. Function systems and differential systems
-
Chapter IX. Pfaffian systems
-
Chapter X. Consistency examples
-
Chapter XI. Illustrative examples
