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.
scheda docente
materiale didattico
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)
Other materials will be available in the course Moodle class
Other Textbooks:
Mastroeni L. and Mazzoccoli A.: “Matematica per le applicazioni economiche” ed. Pearson.
Fruizione: 21210028 Matematica per le applicazioni economiche in Economia L-33 GUIZZI VALENTINA
Programma
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)
Testi Adottati
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.
Modalità Erogazione
Frontal lesson. Homeworks. Use of graphics tablet and recordings of lectures available at the end of the course.Modalità Valutazione
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 poofs of the results indicated in the program with "(w.p.)". The oral test will consist of one or more questions about the entire program. It is possible to take the exam in English.