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.

chapter |33 pages

The Basic Problem

chapter |24 pages

Piecewise-Smooth Extremals

chapter |27 pages

Modifications of the Basic Problem

chapter |28 pages

A Weak Minimum

chapter |26 pages

A Strong Minimum

chapter |28 pages

The Hamiltonian

chapter |31 pages

Lagrangian Mechanics

chapter |35 pages

Direct Methods

chapter |33 pages

Dynamic Programming

chapter |43 pages

Isoperimetric Constraints

chapter |29 pages

Pointwise Constraints on Extremals

chapter |34 pages

Nonholonomic Constraints

chapter |33 pages

Optimal Control with Linear Dynamics

chapter |46 pages

Optimal Control with General Lagrangians

chapter |41 pages

Several Independent Variables

chapter |41 pages

Linear Theory of Elasticity

chapter |39 pages

Plate Theory

chapter |27 pages

Fluid Mechanics