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Index
Cover Page Title Page Copyright Page Table of Contents Preface to the Fourth Printing Preface to the Second Edition Preface to the First Edition PART I. CALCULUS OF VARIATIONS
Section 1. Introduction Section 2. Example Solved Section 3. Simplest Problem—Euler Equation Section 4. Examples and Interpretations Section 5. Solving the Euler Equation in Special Cases Section 6. Second Order Conditions Section 7. Isoperimetric Problem Section 8. Free End Value Section 9. Free Horizon—Transversality Conditions Section 10. Equality Constrained Endpoint Section 11. Salvage Value Section 12. Inequality Constraint Endpoints and Sensitivity Analysis Section 13. Corners Section 14. Inequality Constraints in (t, x) Section 15. Infinite Horizon Autonomous Problems Section 16. Most Rapid Approach Paths Section 17. Diagrammatic Analysis Section 18. Several Functions and Double Integrals
PART II: OPTIMAL CONTROL
Section 1. Introduction Section 2. Simplest Problem—Necessary Conditions Section 3. Sufficiency Section 4. Interpretations Section 5. Several Variables Section 6. Fixed Endpoint Problems Section 7. Various Endpoint Conditions Section 8. Discounting, Current Values, Comparative Dynamics Section 9. Equilibria in Infinite Horizon Autonomous Problems Section 10. Bounded Controls Section 11. Further Control Constraint Section 12. Discontinuous and Bang-Bang Control Section 13. Singular Solutions and Most Rapid Approach Paths Section 14. The Pontryagin Maximum Principle, Existence Section 15. Further Sufficiency Theorems Section 16. Alternative Formulations Section 17. State Variable Inequality Constraints Section 18. Jumps in the State Variable, Switches in State Equations Section 19. Delayed Response Section 20. Optimal Control with Integral State Equations Section 21. Dynamic Programming Section 22. Stochastic Optimal Control Section 23. Differential Games
APPENDIX A. CALCULUS AND NONLINEAR PROGRAMMING
Section 1. Calculus Techniques Section 2. Mean-Value Theorems Section 3. Concave and Convex Functions Section 4. Maxima and Minima Section 5. Equality Constrained Optimization Section 6. Inequality Constrained Optimization Section 7. Line Integrals and Green’s Theorem
APPENDIX B. DIFFERENTIAL EQUATIONS
Section 1. Introduction Section 2. Linear First Order Differential Equations Section 3. Linear Second Order Differential Equations Section 4. Linear nth Order Differential Equations Section 5. A Pair of Linear Equations Section 6. Existence and Uniqueness of Solutions
References Author Index Subject Index Back Cover
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