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 :

Laplace trensform and its properties. Differential equations and Laplace transform.Functions of several variables. Differential equations of the first order and their general solution. 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 :

Marcellini, Sbordone; Elementi di Analisi Matematica 1, Liguori.

Exam :

Written and oral proof.

Tutorial Session :

To be defined.