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| Softcover ISBN: | 978-0-8218-1018-7 |
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| Softcover ISBN: | 978-0-8218-1018-7 |
| Product Code: | COLL/18 |
| List Price: | $99.00 |
| MAA Member Price: | $89.10 |
| AMS Member Price: | $79.20 |
| eBook ISBN: | 978-1-4704-3166-2 |
| Product Code: | COLL/18.E |
| List Price: | $89.00 |
| MAA Member Price: | $80.10 |
| AMS Member Price: | $71.20 |
| Softcover ISBN: | 978-0-8218-1018-7 |
| eBook ISBN: | 978-1-4704-3166-2 |
| Product Code: | COLL/18.B |
| List Price: | $188.00 $143.50 |
| MAA Member Price: | $169.20 $129.15 |
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Book DetailsColloquium PublicationsVolume: 18; 1934; 368 ppMSC: Primary 49
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.
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Table of Contents
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Chapters
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Chapter I. The fixed end point problem in non-parametric form
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Chapter II. General end conditions
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Chapter III. The index form
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Chapter IV. Self-adjoint systems
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Chapter V. The functional on a Riemannian space
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Chapter VI. The critical sets of functions
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Chapter VII. The boundary problem in the large
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Chapter VIII. Closed extremals
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Chapter IX. Solution of the Poincaré continuation problem
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Reviews
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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
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RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
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- Requests
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.
-
Chapters
-
Chapter I. The fixed end point problem in non-parametric form
-
Chapter II. General end conditions
-
Chapter III. The index form
-
Chapter IV. Self-adjoint systems
-
Chapter V. The functional on a Riemannian space
-
Chapter VI. The critical sets of functions
-
Chapter VII. The boundary problem in the large
-
Chapter VIII. Closed extremals
-
Chapter IX. Solution of the Poincaré continuation problem
-
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
