Incluye bibliografía.

Pte.1. Preliminaries: 1. Review of basic concepts -- 2. Metric and normed spaces -- 3. Vector spaces and linear transformations -- 4. Differential calculus -- Pte.2. Statics: 5. Static models and comparative statics -- 6. Convex sets and concave functions -- 7. Static optimization -- 8. Some applications to microeconomics -- Pte.3. Dynamics: 9. Dynamical systems, basic concepts and scalar systems -- 10. Dynamical systems, higher dimensions -- 11. Dynamical systems, some applications -- 12. An introduction to dynamic optimization -- 13. Some applications of dynamic optimization -- Appendix: solutions to the problems.

This book is intended as a textbook for a first-year PhD course in mathematics for economists and as a reference for graduate students in economics. It provides a self-contained, rigorous treatment of most of the concepts and techniques required to follow the standard first-year theory sequence in micro and macroeconomics. The topics covered include an introduction to analysis in metric spaces, differential calculus, comparative statics, convexity, static optimization, dynamical systems and dynamic optimization. The book includes a large number of applications to standard economic models and over two hundred fully worked-out problems.