**Colloquium Publications**

Volume: 18;
1934;
368 pp;
Softcover

MSC: Primary 49;

Print ISBN: 978-0-8218-1018-7

Product Code: COLL/18

List Price: $71.00

AMS Member Price: $56.80

MAA Member Price: $63.90

**Electronic ISBN: 978-1-4704-3166-2
Product Code: COLL/18.E**

List Price: $71.00

AMS Member Price: $56.80

MAA Member Price: $63.90

# The Calculus of Variations in the Large

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*M. Morse*

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 & Endorsements

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

# Table of Contents

## The Calculus of Variations in the Large

- Cover Cover11
- Title page iii4
- Foreword v6
- Contents ix10
- Chapter I. The fixed end point problem in non-parametric form 114
- Chapter II. General end conditions 1831
- Chapter III. The index form 3750
- Chapter IV. Self-adjoint systems 8093
- Chapter V. The functional on a Riemannian space 107120
- Chapter VI. The critical sets of functions 142155
- Chapter VII. The boundary problem in the large 192205
- Chapter VIII. Closed extremals 249262
- Chapter IX. Solution of the Poincaré continuation problem 305318
- Bibliography 359372
- Index 367380
- Back Cover Back Cover1383