Mathematics (2020/2021)

Course partially running (all years except the first)

Course code
4S003790
Name of lecturers
Letizia Pellegrini, Alberto Peretti
Coordinator
Letizia Pellegrini
Number of ECTS credits allocated
7.5
Academic sector
SECS-S/06 - MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES
Language of instruction
Italian
Location
VERONA
Period
A.A. 20/21 dottorato dal Oct 1, 2020 al Sep 30, 2021.

Lesson timetable

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Learning outcomes

Requirements
You are expected to be familiar with standard calculus in one variable.

Objectives
This course is intended to review some concepts of linear algebra and calculus for several variables and develop the most important topics on unconstrained and constrained optimization.

Syllabus

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.
Unconstrained optimization: first order optimality conditions, second order optimality conditions.
Constrained Optimization: the Weierstrass Theorem. Constrained optimization with equality constraints, Lagrange theorem. Lagrangian function and optimality conditions. Constrained optimization with inequality constraints, Kuhn-Tucker theorem. Convex problems.

Reference books
Author Title Publisher Year ISBN Note
C.P. SIMON, L.E. BLUME Mathematics for Economists New York, London: Norton & Company Press, Cambridge 1994 0-393-95733-0

Assessment methods and criteria

Written exam. Intermediate tests are proposed during the course.