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Pfaff's Problem and Its Generalizations
J. A. Schouten and W. v. d. Kulk
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AMS Chelsea Publishing
1969; 542 pp; hardcover
ISBN-10: 0-8284-0221-3
ISBN-13: 978-0-8284-0221-7
List Price: US$58
Member Price: US$52.20
Order Code: CHEL/221
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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
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