Università Roma Tre

Part I: Functions of several variables – Constrained optimization (10 hours)
Vectorial functions and the Jacobian matrix. Chain rule. Implicit function theorem. Properties of the gradient (w.p.). Constrained optimization: equality constraints and inequality constraints. Lagrange multiplier theorem (w.p. geometrical). Second order conditions for constrained local problem (bordered Hessian matrix). Optimization for convex functions. Economic applications.
Part II: Ordinary differential equations and systems: (14 hours)
Definitions and examples. Exact differential. Equations in separable variables. Exact equations. Homogeneous equations. Malthusian growth model. Logistic growth model. Second order linear differential equations. General theorem of existence and uniqueness of the solution. Field of directions. Economic applications. Two-dimensional differential equation systems. Systems of linear differential equations: resolving method using eigenvalues, stationary states and their stability. Economic applications.
(w.p. = with proof)

Simon & Blume: “Matematica per le scienze economiche” ed. Egea.
Other materials will be available in the course Moodle class

Other Textbooks:
Mastroeni L. and Mazzoccoli A.: “Matematica per le applicazioni economiche” ed. Pearson.