Mathematical Methods and Modeling
A.Y. 2016/2017
Lesson for
Learning objectives
Students will learn advanced mathematical techniques and how to use them to model and solve problems in economics and finance.
Course structure and Syllabus
Active edition
Yes
Responsible
Unita' didattica Dynamical Systems
SECSS/06  MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES  University credits: 3
Lessons: 20 hours
Professor:
La Torre Davide
Unita' didattica Optimization
SECSS/06  MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES  University credits: 6
Lessons: 40 hours
Professor:
La Torre Davide
ATTENDING STUDENTS
Unita' didattica Optimization
Syllabus
Topics in linear algebra. Review of basic linear algebra. Linear independence. The rank of a matrix. Main results on linear systems. Eigenvalues. Diagonalization. Quadratic forms. Quadratic forms with linear constraints. Linear programming. A simple maximization problem. Graphical solution procedure. Extreme points and the optimal solution. Special cases. General linear programming notation. Sensitivity analysis and interpretation of solution.
Multivariable calculus. Gradients and directional derivatives. Convex sets. Concave and convex functions. Quasiconcave and quasiconvex functions. Taylor's formula. Implicit and inverse function theorems. Degrees of freedom and functional dependence. Differentiability. Existence and uniqueness of solutions of systems of equations. Static optimization. Extreme points. Local extreme points. Equality constraints: the Lagrange problem. Local secondorder conditions. Inequality constraints: nonlinear programming. Sufficient conditions. Comparative statics. Nonnegativity constraints. Concave programming. Precise comparative statics results. Existence of Lagrange multipliers.
Unita' didattica Dynamical Systems
Syllabus
Differential equations I: Firstorder equations in one variable. Introduction. The direction is given, find the path. Separable equations. Firstorder linear equations. Exact equations and integrating factors. Transformation of variables. Qualitative theory and stability. Existence and uniqueness. Differential equations II: Secondorder equations and systems in the plane. Introduction. Linear differential equations. Constant coefficients. Stability for linear equations. Simultaneous equations in the plane. Equilibrium points for linear systems. Phase plane analysis. Stability for nonlinear systems. Saddle points. Control theory: basic techniques. The basic problem. A simple case. Regularity conditions. The standard problem. The maximum principle. Sufficient conditions.
Unita' didattica Optimization
Syllabus
Topics in linear algebra. Review of basic linear algebra. Linear independence. The rank of a matrix. Main results on linear systems. Eigenvalues. Diagonalization. Quadratic forms. Quadratic forms with linear constraints. Partitioned matrices and their inverses.
Linear programming. A simple maximization problem. Graphical solution procedure. Extreme points and the optimal solution. Special cases. General linear programming notation. Sensitivity analysis and interpretation of solution. Multivariable calculus. Gradients and directional derivatives. Convex sets. Concave and convex functions. Quasiconcave and quasiconvex functions. Taylor's formula. Implicit and inverse function theorems. Degrees of freedom and functional dependence. Differentiability. Existence and uniqueness of solutions of systems of equations. Static optimization. Extreme points. Local extreme points. Equality constraints: the Lagrange problem. Local secondorder conditions. Inequality constraints: nonlinear programming. Sufficient conditions. Comparative statics. Nonnegativity constraints. Concave programming. Precise comparative statics results. Existence of Lagrange multipliers.
Unita' didattica Dynamical Systems
Syllabus
Differential equations I: Firstorder equations in one variable. Introduction. The direction is given, find the path. Separable equations. Firstorder linear equations. Exact equations and integrating factors. Transformation of variables. Qualitative theory and stability. Existence and uniqueness. Differential equations II: Secondorder equations and systems in the plane. Introduction. Linear differential equations. Constant coefficients. Stability for linear equations. Simultaneous equations in the plane. Equilibrium points for linear systems. Phase plane analysis. Stability for nonlinear systems. Saddle points. Control theory: basic techniques. The basic problem. A simple case. Regularity conditions. The standard problem. The maximum principle. Sufficient conditions.
Lesson period
First trimester

Lesson period
First trimester
Professor(s)
Reception:
On leave. Office hours are suspended.
Room 30, DEMM