In the Analysis module we provide the tools for the comprehension and computation of double and triple integrals, of curvilinear integrals of scalar and vector functions, and we introduce the related theorems (divergence, Gauss-Green). We show how to deal with constrained optimization problems in several variables.
The first goal is the understanding of integral calculus for functions of two or three real variables: double and triple integrals, line and surface integrals of scalar and vector fields. We will discuss the divergence theorem. The second objective is a general understanding of constrained optimization problems for functions of two or more variables.
Lecture and exercise classes
Integration theory for functions of several variables. Double and triple integrals, changes of variables in multiple integrals. Polar, cylindrical, spherical coordinates. Parametric curves. Line integrals of scalar functions, length of a curve. Vector fields, line integrals of differential forms, closed and exact forms, potentials. Divergence theorem and Gauss Green formulas in the plane. Parametric surfaces in space, area of a surface, surface integrals. Flow of a field through a surface. Divergence theorem in space. Constrained optimization theory for functions of several variables. Constrained maximum and minimum points. Lagrange multipliers.
C. Canuto e A. Tabacco, Analisi Matematica 2, 2nd ed., Springer-Verlag Italia, 2014.
Ricevimento: By appointment, to be scheduled by e-mail
Ricevimento: At the end of lectures or by appointment.
EDOARDO MAININI (President)
LAURA BURLANDO
FRANCO BAMPI (President Substitute)
MAURIZIO CHICCO (President Substitute)
ANDREA POGGIO (Substitute)
https://corsi.unige.it/en/corsi/8720/studenti-orario
Written exam, requiring the solution of exercises.
An oral exam may optionally be taken as well.
The written exam verifies the knowledge of the main techniques of integral caluclus and optimization for functions of several variables.
The optional oral exam verifies the theoretical knowledge and possibly requires the solution of exercises.
