Colloquium Publications 1937; 118 pp; softcover Volume: 21 ISBN10: 0821846191 ISBN13: 9780821846193 List Price: US$31 Member Price: US$24.80 Order Code: COLL/21
 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
