Introduction To The Calculus of Variations And Its Applications

This book introduces the technique of dynamic programming and shows how it can be used to solve problems in the calculus of variations. It discusses the basic elements of elasticity theory and some variational formulations of the relevant boundary-value problems.

Autorentext

Wan, Frederic

Zusammenfassung
This comprehensive text provides all information necessary for an introductory course on the calculus of variations and optimal control theory. Following a thorough discussion of the basic problem, including sufficient conditions for optimality, the theory and techniques are extended to problems with a free end point, a free boundary, auxiliary and inequality constraints, leading to a study of optimal control theory.

Inhalt

1. The Basic Problem 2. Piecewise-Smooth Extremals 3. Modifications of the Basic Problem 4. A Weak Minimum 5. A Strong Minimum 6. The Hamiltonian 7. Lagrangian Mechanics 8. Direct Methods 9. Dynamic Programming 10. Isoperimetric Constraints 11. Pointwise Constraints on Extremals 12. Nonholonomic Constraints 13. Optimal Control with Linear Dynamics 14. Optimal Control with General Lagrangians 15. Several Independent Variables 16. Linear Theory of Elasticity 17. Plate Theory 18. Fluid Mechanics