0 Review of Optimization in ?d. - Problems. - One Basic Theory. - 1 Standard Optimization Problems. - 2 Linear Spaces and Gâteaux Variations. - 3 Minimization of Convex Functions. - 4 The Lemmas of Lagrange and Du Bois-Reymond. - 5 Local Extrema in Normed Linear Spaces. - 6 The Euler-Lagrange Equations. - Two Advanced Topics. - 7 Piecewise C1 Extremal Functions. - 8 Variational Principles in Mechanics. - 9 Sufficient Conditions for a Minimum. - Three Optimal Control. - 10 Control Problems and Sufficiency Considerations. - 11 Necessary Conditions for Optimality. - A. 1. The Intermediate and Mean Value Theorems. - A. 2. The Fundamental Theorem of Calculus. - A. 3. Partial Integrals: Leibniz' Formula. - A. 4. An Open Mapping Theorem. - A. 5. Families of Solutions to a System of Differential Equations. - A. 6. The Rayleigh Ratio. - Historical References. - Answers to Selected Problems. Language: English