Portale di Ateneo - En.Unibs.it

Differential calculus for functions of several variables.
Limits, continuity, partial and directional derivatives, differentiability.
Extremal points, classification of stationary points, test by Hessian matrix
and Hessian determinant. Lagrange multipliers.

Curves and line integrals.
Definition of curve parametrization, length, arc length. Vector-valued
functions of several variables. Curvilinear integrals of the first and second
species. Vector-valued functions, potentials, gradients.

Integration and differentiation of vector-valued functions.
Differentiability of vector fields; derivation of composite functions.
Multiple integrals: definitions, reduction formulas, change of variables.
Gauss-Green formula in the plan. Operators rotor, gradient and
divergence. Surfaces, area of a surface, surface integrals. Stokes'
theorem. Gauss' divergence theorem.

Sequences and series of functions.
Sequences: pointwise and uniform convergence. Series of functions:
pointwise, uniform, total convergence; derivation and integration term by
term. Power series and Taylor series expansions.

Fourier series.
Trigonometric series. Fourier series: definition, mean convergence, pointwise and uniform convergence.