CODE 60235 2024/2025 6 cfu anno 2 INGEGNERIA CHIMICA E DI PROCESSO 10375 (L-9) - GENOVA 6 cfu anno 2 INGEGNERIA CIVILE E AMBIENTALE 8715 (L-7) - GENOVA 6 cfu anno 2 INGEGNERIA ELETTRICA 8716 (L-9) - GENOVA 6 cfu anno 2 INGEGNERIA MECCANICA 8720 (L-9) - GENOVA MAT/05 Italian GENOVA 1° Semester Questo insegnamento è propedeutico per gli insegnamenti: Civil and Environmental Engineering 8715 (coorte 2023/2024) HYDROLOGY & HYDRAULIC URBAN INFRASTRUCTURES 66097 Questo insegnamento è un modulo di: AULAWEB

## AIMS AND CONTENT

### LEARNING OUTCOMES

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.

### AIMS AND LEARNING OUTCOMES

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.

### TEACHING METHODS

Lecture and exercise classes

### SYLLABUS/CONTENT

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.

## LESSONS

### LESSONS START

https://corsi.unige.it/8720/p/studenti-orario

### Class schedule

The timetable for this course is available here: Portale EasyAcademy

## EXAMS

### EXAM DESCRIPTION

Written exam, requiring the solution of exercises.

An oral exam may optionally be taken as well.

### ASSESSMENT METHODS

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.