italian version

Aims :

Knowledge of the theory of functions with several variables and geometric applications. Study and solutions of ordinary differential equations.

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, Dini's theorems 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,
qualitative study of the solutions.

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 :

At least three hours for week.