AMS Chelsea Publishing 1969; 542 pp; hardcover ISBN10: 0828402213 ISBN13: 9780828402217 List Price: US$58 Member Price: US$52.20 Order Code: CHEL/221
 In its simplest form, the Pfaff problem (formulated by Pfaff in 1819) consists of determining the maximal integrable manifold of a Pfaffian system, i.e. of a system of vector fields in \(R^n\). This book gives a solution of this problem and discusses various generalizations, giving an essentially complete treatment of the theory as it was known in 1949. Readership Graduate students and research mathematicians. Table of Contents  Algebraic preliminaries
 Analytical preliminaries
 The outer problem
 Classification of covariant vector fields and pfaffians
 The simplest arithmetic invariants of covariant \(q\)vector fields
 Contact transformations
 Theory of vector manifolds and element manifolds
 The inner problem
 Theory of \(\mathfrak{S}^m_d\)fields
 Solution of systems of differential equations
 Table of operations
 Suggestions for the solution of exercises
 Bibliography
 Index
