## 21210228 - Matematica per le applicazioni economiche

The aim of the course is to broaden and consolidate the acquisition of the mathematical method as a fundamental investigation tool for economic, financial and business disciplines. To this end, we will first provide notions of linear algebra and tools to deal with constrained and unconstrained optimization problems. Then, the fundamental tools for the study of discrete and continuous dynamical systems will be addressed.
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Fruizione: 21210028 Matematica per le applicazioni economiche in Economia L-33 GUIZZI VALENTINA

Programme

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.

Core Documentation

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

Type of delivery of the course

Frontal lesson. Homeworks. Use of graphics tablet and recordings of lectures available at the end of the course.

Type of evaluation

The exam consists in a written and an oral test. The written test will consist of exercises or theoretical questions concerning the entire program of the course including any demonstrations carried out during lectures. The oral test will consist of one or more questions about the entire program. It is possible to take the exam in English.