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The Calculus of Variations in the Large
M. Morse
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Colloquium Publications
1934; 368 pp; softcover
Volume: 18
Reprint/Revision History:
tenth printing 2001
ISBN-10: 0-8218-1018-9
ISBN-13: 978-0-8218-1018-7
List Price: US$67
Member Price: US$53.60
Order Code: COLL/18
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Morse theory is a study of deep connections between analysis and topology. In its classical form, it provides a relationship between the critical points of certain smooth functions on a manifold and the topology of the manifold. It has been used by geometers, topologists, physicists, and others as a remarkably effective tool to study manifolds. In the 1980s and 1990s, Morse theory was extended to infinite dimensions with great success. This book is Morse's own exposition of his ideas. It has been called one of the most important and influential mathematical works of the twentieth century. Calculus of Variations in the Large is certainly one of the essential references on Morse theory.

Reviews

"This monumental book is one of the most important and influential works written in mathematics in this century. It had and is having a very profound impact in the development of the study of mathematical and physical sciences."

-- Mathematical Reviews

"... a fascinating and stimulating book ... represents a signal contribution to mathematics.

"The background for the theory elaborated in this volume lies in two rather distinct fields of mathematics. We have on the one hand the theory of critical points of functions of \(n\) real variables, largely created and developed by the author and his students; on the other hand, the classical calculus of variations and its modern treatment as a part of the functional calculus, to which Hadamard and Tonelli have made the fundamental contributions."

-- Bulletin of the AMS

Table of Contents

  • The fixed end point problem in non-parametric form
  • General end conditions
  • The index form
  • Self-adjoint systems
  • The functional on a Riemannian space
  • The critical sets of functions
  • The boundary problem in the large
  • Closed extremals
  • Solution of the Poincaré continuation problem
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