italian version

Aims :

Knowledge of the basic elements of differential and integral calculus for functions of several variables with applications. Study and solution of some kind of ordinary differential equations

Topics :

Infinitesimal and differential calculus for functions of several variables: limits and continuity, partial derivatives, gradient, directional derivatives, differentiability, Taylor formula, maxima and minima, implicit functions and Dini Theorem.
Multiple integrals: normal domains, reduction formulas, change of variables.
Curves in R2 and R3 : curves simple, closed, regular, tangent line and vector, lenght, abscissa on a curve, curvature, torsion, Frenet formulas; integration on a curve.
Vectorial fields: work along a curve, conservative fields and their characterization by means of potentials.
Green formulas and applications.
Ordinary differential equations: local and global existence and uniqueness theorems; linear differential euqations of the first order and second order with constant coefficients; solution of some kind of nonlinear equations, qualitative study of the solutions.


Textbooks :

N. Fusco - P. Marcellini - C. Sbordone “Elementi di Analisi Matematica 2” (Liguori Editore)
P. Marcellini - C. Sbordone “Esercitazioni di Matematica” vol. 2 (Liguori Editore)

Exam :

The exam consists of a written part (with solution of exercises) and an oral part

Tutorial Session :

Two hours per week, in accordance with students