italian version

Aims :

Knowledge of the theory of functions with several variables. Study and solutions of ordinary differential equations and algebraic systems.

Topics :

Functions of several variables: continuity and differentiability, the chain rule, Taylor expansion, changes of variables and jacobian matrix; maxima, minima and other critical points: hessian matrix, constrained extrema and Lagrange multiplies.Implicit functions and geometric applications.
Regular curves: arc lenght and line integrals. Multiple integrals: calculus, geometric meaning. Regular surface and surface integrals.
Ordinary differential equations: initial value problem and boundary value problem, existence and uniqueness of solution. Study and solution of some differential equations, linear equations with constant coefficients or not, first order linear systems. Fourier series
Matrix algebra, determinants, algebric equations, systems of simultaneous equations.

Textbooks :

M. Bramanti, C.D.Pagani, S.Salsa "Matematica", Zanichelli
R. Adams, "Calcolo differenziale 2", Editrice Ambrosiana
P.Marcellini, C. Sbordone, "Esercitazione di Matematica" vol.2, Editore Liguori

Exam :

The exam consists of a written and a oral part.

Tutorial Session :

Da concordare con gli studenti.