Nir Dagan / Teaching

Mathematics III

Academic year 1997/98

The Course's main website. (In Catalan) is Maintained by Prof. Udina.

1. Differential calculus of several variables: Graphical presentation. Level curves. Partial derivatives. Quadratic forms. The chain rule. Implicit derivation. Homogeneous functions. Linear approximation.
2. Unconstrained optimization with one or more variables: Optimization and decision problems. Topological notions. Existence of optimum and Weierstrass' theorem. Local optima and first and second order conditions.
3. Concavity and convexity: Convex sets. Convex and concave functions. Conditions for concavity and convexity.
4. Optimization with equality constraints: Lagrange method. Global optimum: Application of Weierstrass' theorem and convexity criteria. Regular points. Generalized Lagrangian.
5. Optimization with inequality constraints: The Kuhn-Tucker conditions. Binding constraints in a point. Regular points. Interior and corner critical points.
6. Dynamic optimization: State and control variables. Problems with discrete time. Euler's equation. Dynamic programming. Problems with continuous time. Theory of optimal control.

Knut Sydsaeter and Peter J. Hammond, Mathematics for Economic Analysis, Prentice Hall, 1995.
Knut Sydsaeter and Peter J. Hammond (1996) Matemáticas para el análisis económico Prentice Hall.

J. Borrel (1992) Métodos matemáticos para la economía. Programación matemática Madrid: Pirámide.
A. Heras et al. (1990) Programación matemática y modelos económicos: un enfoque teórico-práctico Madrid: AC.
P. Madden (1987) Concavidad y optimización en microeconomía Madrid: Alianza Editorial.