Portale di Ateneo - En.Unibs.it

Integration of functions of one real variable.
Basic definitions. Fundamental theorems of integral calculus. Integration by substitution, integration by parts.

Differential equations. Equations with separable variables. First order differential equations.
Linear second order differential equations with constant coefficients. Cauchy problems.

Differential calculus for functions of several variables. Domains of definition, limits, continuity.
Definition of partial and directional derivatives, differentiability. Schwarz Theorem. Local minima and maxima, classification of stationary points, Hessian matrix test. Basic notions of global minima and maxima.

Curves and path integrals. Definition of a curve, length, arc length. Vector fields of several variables. Definition of the path integrals for vector fields. Conservative vector fields and path integrals.

Double integrals. Basic definitions. Reductions formulae. Change of variables.