Learning objectives

The course aims to provide students with the tools needed to quantitatively address the main problems that arise in the economic and financial fields. The basic notions of Linear Algebra and Calculus for functions of one variable are essential prerequisites. After an introduction to some more advanced notions of Linear Algebra and Calculus for functions of several variables, the unconstrained and constrained optimization problems and their applicability in the economic-financial field are presented. The resolution of optimization problems will be addressed with the classic results deriving from the conditions of optimality of the first and second order and from the properties of the Lagrangian function.

Prerequisites and basic notions

Familiarity with standard calculus in one variable

Program

Linear algebra: matrix algebra, determinants, rank, quadratic forms, sign of a quadratic form and definite matrices. Calculus: functions of several variables, level sets, differential calculus for functions of several variables, convex functions. Free optimization: first-order optimality conditions, second-order optimality conditions. Constrained optimization: Weierstrass theorem. Constrained optimization with equality constraints, Lagrange's theorem. Lagrangian function and optimality conditions. Constrained optimization with inequality constraints, Kuhn-Tucker theorem. Convex problems.

Didactic methods

Frontal teaching.

Learning assessment procedures

Written exam

Assessment

The ability to solve exercises, knowledge of basic definitions and important theorems, and critical attitude will be considered fundamental.

Criteria for the composition of the final grade

Overall assessment of knowledge of the different topics presented during the course

Scheduled Lessons

Sustainable Development Goals - SDGs

This initiative contributes to the achievement of the Sustainable Development Goals of the UN Agenda 2030. More information on sustainability