italian version

Aims :

It is planned to give basic knowledge concerning functions of several real
variables and series of functions and their applications to concrete
problems.

Topics :

Limits and contiuity. Directional derivatives. Differentiable
functions. Tangent space. Differentiability and contynuity. Gradient
formula. Higher order derivatives. Schwartz theorem. Max and min, necesary
and sufficient conditions. Curves and curve lenght. Tangent vector. Chain
rule. Dini's theorem. Max/min with constraints. Lagrange multipliers.
Integration in several variables. Reduction formula. Functions in R^n.
Jacobian matrice and its determinant. Changing variables and integration.
Integration in R^3. Polar, cilindrical and spherical coordinates. Improper
integrals. Integrals on curves. Integration of vector fileds. Gauss Green
theorem. Functions series. Types of convergence. Fourier coefficients.
Bessel and Parseval theorem. Convergence of Fourier series


Textbooks :

Bramanti, Pagani, Salsa; Matematica; Zanichelli
Fusco, Marcellini, Sbordone; Elementi di Analisi Matematica 2; Liguori

Exam :

Written test continuation from oral test.

Tutorial Session :

To contact the teacher.