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Pfaff's Problem and Its Generalizations
J. A. Schouten and W. v. d. Kulk

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.


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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