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Preface to the Fourth Printing | |
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Preface to the Second Edition | |
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Preface to the First Edition | |
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Calculus of Variations | |
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Introduction | |
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Example Solved | |
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Simplest Problem-Euler Equation | |
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Examples and Interpretations | |
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Solving the Euler Equation in Special Cases | |
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Second Order Conditions | |
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Isoperimetric Problem | |
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Free End Value | |
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Free Horizon-Transversality Conditions | |
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Equality Constrained Endpoint | |
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Salvage Value | |
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Inequality Constraint Endpoints and Sensitivity Analysis | |
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Corners | |
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Inequality Constraints in (t, x) | |
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Infinite Horizon Autonomous Problems | |
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Most Rapid Approach Paths | |
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Diagrammatic Analysis | |
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Several Functions and Double Integrals | |
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Optimal Control | |
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Introduction | |
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Simplest Problem-Necessary Conditions | |
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Sufficiency | |
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Interpretations | |
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Several Variables | |
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Fixed Endpoint Problems | |
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Various Endpoint Conditions | |
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Discounting, Current Values, Comparative Dynamics | |
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Equilibria in Infinite Horizon Autonomous Problems | |
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Bounded Controls | |
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Further Control Constraint | |
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Discontinuous and Bang-Bang Control | |
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Singular Solutions and Most Rapid Approach Paths | |
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The Pontryagin Maximum Principle, Existence | |
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Further Sufficiency Theorems | |
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Alternative Formulations | |
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State Variable Inequality Constraints | |
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Jumps in the State Variable, Switches in State Equations | |
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Delayed Response | |
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Optimal Control with Integral State Equations | |
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Dynamic Programming | |
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Stochastic Optimal Control | |
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Differential Games | |
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Calculus and Nonlinear Programming | |
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Calculus Techniques | |
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Mean-Value Theorems | |
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Concave and Convex Functions | |
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Maxima and Minima | |
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Equality Constrained Optimization | |
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Inequality Constrained Optimization | |
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Line Integrals and Green's Theorem | |
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Differential Equations | |
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Introduction | |
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Linear First Order Differential Equations | |
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Linear Second Order Differential Equations | |
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Linear nth Order Differential Equations | |
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A Pair of Linear Equations | |
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Existence and Uniqueness of Solutions | |
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References | |
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Author Index | |
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Subject Index | |