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.


Major Textbook

Other Textbooks in Spanish

Calculus Catalanus