Problems and Exercises in the Calculus of Variations torrent

In this post we will see Problems and Exercises in the Calculus of
Variations by M. L. Krasnov, G. I. Makarenko, A. I. Kiselev .

The calculus of variations is one of the most important divisions of
classical mathematical analysis as regards applications.The authors'
aim was to supply the reader with a certain minimum of problems
covering the basic divisions of the classical calculus of variations,
and they deliberately avoided questions pertaining to the theory of
optimal control.



This book was translated from the Russian by George Yankovsky. The book
was published by first Mir Publishers in 1975.

All credits to the original uploader.

DJVU | 3.1 MB | Pages: 221 | Bookmarked | OCR


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Table of Contents
CONTENTS
Introduction 6
Preliminary Remarks 7

CHAPTER I.
THE EXTREMUM OF A FUNCTION OF MANY VARIABLES

1. Absolute Extremum 9
2. Conditional Extremum 19

CHAPTER II.
EXTREMA OF FUNCTIONALS

3. The Functional. The Variation of a Functional and Its Properties 27
4. An Elementary Problem in the Calculus of Variations. Euler's Equation 54
5. Generalizations of the Elementary Problem of the Calculus of Variations 75
6. Invariance of Euler's Equation 85
7. Field of Extremals 88
8. Sufficient Conditions for the Extremum of a Functional 102
9. Conditional Extremum 118
10. Moving Boundary Problems 137
11. Discontinuous Problems. One-Sided Variations 151
12. The Hamilton-Jacobi Theory. The Variational Principles of Mechanics

CHAPTER III.
DIRECT METHODS IN THE CALCULUS OF VARIATIONS

13. Euler's Finite-Difference Method 177
14. Ritz Method. Kantorovich Method 179
15. Variational Methods for Finding Eigenvalues and Eigenfunctions 188

ANSWERS AND HINTS 202

BIBLIOGRAPHY 215

INDEX 217