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.
teacher profile teaching materials
Vectorial functions and the Jacobian matrix. Chain rule. Implicit function theorem. Secon property of the gradient (w.p.). Constrained optimization: equality constraints and inequality constraints. Lagrange multiplier theorem NC (w.p. geometrical). Second order conditions for constrained local problems (bordered Hessian matrix). Hint on Khun-Tucker NC. Global case with compact constraint. Geometric representation of the constrained problem. Economic applications. The problem of the consumer.
Part II: Ordinary differential equations and systems
Definitions and examples. Malthusian growth model. Cauchy problem. General existence theorem and uniqueness of the solution (hint). First order linear differential equations: structure of solutions, the case with constant coefficients, the general formula for solutions. Separable variable equations. Second-order linear differential equations: structure of solutions, the constant coefficient case, the homogeneous case and the similarity principle. Logistic growth model. Economic applications. Systems of two-dimensional first-order differential equations. Systems of linear first order differential equations with constant coefficients: solving by eigenvalues, steady states and their stability.
(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.
Fruizione: 21210028 Matematica per le applicazioni economiche in Economia L-33 GUIZZI VALENTINA
Programme
Part I: Functions of several variables – Constrained optimizationVectorial functions and the Jacobian matrix. Chain rule. Implicit function theorem. Secon property of the gradient (w.p.). Constrained optimization: equality constraints and inequality constraints. Lagrange multiplier theorem NC (w.p. geometrical). Second order conditions for constrained local problems (bordered Hessian matrix). Hint on Khun-Tucker NC. Global case with compact constraint. Geometric representation of the constrained problem. Economic applications. The problem of the consumer.
Part II: Ordinary differential equations and systems
Definitions and examples. Malthusian growth model. Cauchy problem. General existence theorem and uniqueness of the solution (hint). First order linear differential equations: structure of solutions, the case with constant coefficients, the general formula for solutions. Separable variable equations. Second-order linear differential equations: structure of solutions, the constant coefficient case, the homogeneous case and the similarity principle. Logistic growth model. Economic applications. Systems of two-dimensional first-order differential equations. Systems of linear first order differential equations with constant coefficients: solving by eigenvalues, steady states and their stability.
(w.p. = with proof)
Core Documentation
Textbook:• 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.
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 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. The course will include intermediate tests. It is possible to take the exam in English.