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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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