This concise text offers both professionals and students an introduction to the fundamentals and standard methods of the calculus of variations. In addition to surveys of problems with fixed and movable boundaries, it explores highly practical direct methods for the solution of variational problems.
Topics include the method of variation in problems with fixed boundaries; variational problems with movable boundaries and other problems; sufficiency conditions for an extremum; variational problems of constrained extrema; and direct methods of solving variational problems. Each chapter features numerous illustrative problems, and solutions appear at the end.
Reprint of the Pergamon Press, Oxford, 1961 edition.
Author(s): Lev D. Elsgolc
Series: Dover Books on Mathematics
Edition: reprint
Publisher: Dover Publications
Year: 1961,2007
Language: English
Commentary: Dover Catalogue Removed after Index
Pages: C, 178, B
Cover
S Title
Calculus of Variations
ISBN 0486457990
CONTENTS
FROM THE PREFACE TO THE FIRST RUSSIAN EDITION
INTRODUCTION
CHAPTER I THE METHOD OF VARIATION IN PROBLEMS WITH FIXED BOUNDARIES
1. The variation and its properties
2. Euler equation
;. Functionals of the form
4. Functionals involving derivatives of higher order
5. Functionals depending on functions of severalindependent variables
6. Parametric representation of variational problems
?. Some applications
Problems
CHAPTER II VARIATIONAL PROBLEMS WITH MOVABLE BOUNDARIES AND SOME OTHER PROBLEMS
1. Simplest problem with movable boundaries
2. Problems with movable boundaries for functionals of the form
3. Problems with movable boundaries for functionals of the form
4. Extremals with cusps
5. One-sided variations
6. Mixed problems
Problems
CHAPTER III SUFFICIENCY CONDITIONS FOR AN EXTREMUM
1. Fields of extremals
2. The function E(m,y, p, y')
Problems
CHAPTER IV VARIATIONAL PROBLEMS OF CONSTRAINED EXTREMA
1. Constraints of the form
2. Constraints of the form
3. lsoperimetric problems
Problems
CHAPTER V DIRECT METHODS OF SOLVING VARIATIONAL PROBLEMS
1. Direct methods
2. Euler method of finite differences
3. Ritz's method
4. Kantorovic's method
Problems
SOLUTIONS TO THE PROBLEMS
INDEX
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