Università Roma Tre

Parte I: Integral calculus
Primitive functions. Indefinite integral. Characterization of the set of primitives. Properties of the indefinite integral. Integral of elementary functions. Integration by parts. Integration by substitution. Definite integral. Properties of the definite integral. Integral function. Integral mean theorem. Fundamental theorem of integral calculus. Corollary to Torricelli-Barrow's theorem: relationship between the definite integral and the indefinite integral.
Part II: Optimization:
Local and global maximum or minimum. First order conditions and second order conditions for free optimization. Equality constraints. Inequality constraints. Substitution method. Lagrange multiplier theorem. Second order conditions with constraints. Optimization for convex functions. Economic applications.
Part III: Ordinary differential equations and systems:
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.

• Mastroeni L. e Mazzoccoli A.: “Matematica per le applicazioni economiche” ed. Pearson.
or
• Simon & Blume: “Matematica per le scienze economiche” ed. Egea.