I Term September - December

• Mathematics for economics and finance (Prof. Achille Basile)

Homogeneous functions and Euler’s formula. Continuous functions and compact sets. Concave and quasi concave functions. The implicit function theorem. Convex sets and separating hyperplanes: separating hyperplanes theorem, supporting hyperplanes theorem. Difference equations. Unconstrained maximization: local and global maximizer (minimizer), maximization theorems. Constrained maximization: the Lagrangian function and constraints qualification, Lagrange multipliers. Inequality constraints: Kuhn Tucker conditions. Comparative statics. Differential equations and systems of differential equations. Dynamic maximization: the calculus of variations and its applications to economic models, Euler equation of maximization problems . Control theory and applications to economic models. 

  Bibliography:

• Alpha C. Chiang and Kevin Wainwright, "Fundamental Methods of Mathematical Economics", New York, Mc-Graw Hill - Irwin.
• Peter Hammond, Knut Sydsaeter, Atle Seierstad and Arne Strom, "Further Mathematics dor Economic Analysis", 2nd Edition, Pearson Education 2008.