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.

Readership

Graduate students and research mathematicians interested in partial differential equations and Pfaffian systems.

Table of Contents

• Introduction
• Generalities on symbols and systems
• Grassmann algebra
• Differential rings
• Commutative monomials and polynomials
• Algebraic systems
• Algebraic differential systems
• Function systems and differential systems
• Pfaffian systems
• Consistency examples
• Illustrative examples
• Bibliography
• Index