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Problems and Exercises in the Calculus of Variations

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Author(s): M.L. Krasnov, G. Yankovsky
Publisher: Central Books Ltd
Year: 1975

Language: English
Pages: 221

Contents......Page 3
Introduction......Page 4
Preliminary Remarks......Page 5
1. Absolute Extremum......Page 7
2. Conditional Extremum......Page 17
3. The Functional. The Variation of a Functional and Its Properties......Page 25
4. An Elementary Problem in the Calculus of Variations. Euler's Equation......Page 52
5. Generalizations of the Elementary Problem of the Calculus of Variations......Page 73
6. Invariance of Euler's Equation......Page 83
7. Field of Extremals......Page 86
8. Sufficient Conditions for the Extremum of a Functional......Page 100
9. Conditional Extremum......Page 116
10. Moving Boundary Problems......Page 135
11. Discontinuous Problems. One-Sided Variations......Page 149
12. The Hamilton-Jacobi Theory. The Variational Principles of Mechanics......Page 159
13. Euler's Finite-Difference Method......Page 175
14. Ritz Method. Kantorovich Method......Page 177
15. Variational Methods for Finding Eigenvalues and Eigenfunctions......Page 186
Answers and Hints......Page 200
Bibliography......Page 213
Index......Page 215