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The calculus of variations. Transl. from the Russian by Michael E. Alferieff. (English) Zbl 0718.49001
Chur etc.: Harwood Academic Publishers. 280 p. $ 134.00 (1988).
This translation from the Russian original (1981; Zbl 0507.49001) gives a good introduction to the calculus of variations. The following chapters are contained:
Chap. 1. Introduction; Chap. 2. The simplest problem; Chap. 3. Lagrangian derivatives; Chap. 4. Canonical variables; Chap. 5. Field theory; Chap. 6. Jacobi’s condition; Chap. 7. The simplest problem in parametric form; Chap. 8. Problems on a conditional extremum; Chap. 9. The direct method for nonparametric problems; Chap. 10. The Sturm-Liouville problem; Chap. 11. The direct method for a problem in parametric form; Chap. 12. Two- dimensional problems; App. 1. The generalized Dirichlet problem for a linear equation of elliptic type; App. 2. S. N. Bernshtein’s principle; App. 3. Geodesic lines on a triaxial ellipsoid; App. 4. PoincarĂ©’s theorem on periodic extremals; App. 5. E. Noether’s theorem on invariant functionals.

MSC:
49-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to calculus of variations and optimal control
49Kxx Optimality conditions
49Jxx Existence theories in calculus of variations and optimal control
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