â¢GUIDA ECONOMIA 07-08 - Università degli studi di Udine
â¢GUIDA ECONOMIA 07-08 - Università degli studi di Udine
â¢GUIDA ECONOMIA 07-08 - Università degli studi di Udine
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222 prospectus u<strong>di</strong>ne<br />
point in the plane. Continuity for a function<br />
of two variables. Partial derivatives.<br />
The tangent plane. Local and global minima<br />
and maxima. The gra<strong>di</strong>ent and critical<br />
points. The Hessian matrix, necessary<br />
con<strong>di</strong>tions and sufficient con<strong>di</strong>tions for<br />
local extrema. Saddle points. Local<br />
extrema with constraints, Lagrange’s<br />
multipliers.<br />
Bibliography<br />
Course textbook<br />
- M. GAUDENZI, Matematica Generale (provided<br />
by the lecturer).<br />
Rea<strong>di</strong>ng list<br />
- A. AMBROSETTI, I. MUSU, Matematica<br />
Generale e Applicazioni all’Economia,<br />
Liguori E<strong>di</strong>tore.<br />
- G.C. BAROZZI, C. CORRADI, Matematica<br />
Generale per le Scienze Economiche, Il<br />
Mulino.<br />
- P. MARCELLINI, C. SBORDONE, Calcolo,<br />
Liguori E<strong>di</strong>tore.<br />
MATHEMATICS<br />
ADVANCED COURSE 1<br />
Prof. Marcellino Gaudenzi<br />
Contents<br />
- The n-<strong>di</strong>mensional space, metrical and<br />
topological properties.<br />
- Functions of several real variables.<br />
- Differential calculus for functions of<br />
several variables.<br />
- Local and global maxima and minima.<br />
- Functions of several real variables<br />
assuming vector values.<br />
- Differential calculus for functions<br />
assuming vector values.<br />
- The implicit function theorem.<br />
Bibliography<br />
- SIMON-BLUME, Matematica 2 per l’Economia<br />
e le Scienze Sociali, Univ. Bocconi E<strong>di</strong>tore.<br />
- M. GAUDENZI, Lecture notes (provided<br />
by the lecturer).<br />
MATHEMATICS<br />
ADVANCED COURSE 1<br />
(CdL CSBM)<br />
Prof. Marcellino Gaudenzi<br />
Contents<br />
- The n-<strong>di</strong>mensional space, topological<br />
and geometrical properties.<br />
- Functions of several real variables.<br />
- Differential calculus for functions of<br />
several variables.<br />
- Quadratic forms.<br />
- Convex functions.<br />
- Local and global maxima and minima.<br />
- Optimization.<br />
- Jordan and Lebesgue measures.<br />
- Multi-<strong>di</strong>mensional integrals.<br />
Bibliography<br />
- M. GAUDENZI, Lecture notes (provided<br />
by the lecturer).<br />
MATHEMATICS<br />
ADVANCED COURSE 2<br />
Prof. Luciano Sigalotti<br />
Contents<br />
- Quadratic forms.<br />
Symmetric matrices and quadratic forms.<br />
Sign-based classification of quadratic<br />
forms.<br />
Characterization of positive and negative<br />
definite quadratic forms. Quadratic<br />
forms with linear constraints and their<br />
characterization.<br />
- Unconstrained optimization.<br />
First order necessary con<strong>di</strong>tions for optimal<br />
points. Second order sufficient con<strong>di</strong>tions<br />
for optimal points.<br />
- Constrained optimization. Equality constraints.<br />
The Lagrange multipliers theorem. Geometric<br />
and synthetic analysis of stationarity<br />
points. Second order sufficient con<strong>di</strong>tions<br />
for constrained optimal points.<br />
- Constrained optimization. Inequality<br />
and mixed constraints.
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