CODE 60235 2023/2024 6 cfu anno 2 INGEGNERIA CHIMICA E DI PROCESSO 10375 (L-9) - GENOVA 6 cfu anno 2 INGEGNERIA ELETTRICA 8716 (L-9) - GENOVA 6 cfu anno 2 INGEGNERIA CIVILE E AMBIENTALE 8715 (L-7) - 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 2022/2023) URBAN PLANNING AND TRANSPORTATION ENGINEERING 84522 Civil and Environmental Engineering 8715 (coorte 2022/2023) STRUCTURAL ENGINEERING I 72543 Civil and Environmental Engineering 8715 (coorte 2022/2023) GEOTECHNICS 99062 Civil and Environmental Engineering 8715 (coorte 2022/2023) HYDROLOGY & HYDRAULIC URBAN INFRASTRUCTURES 66097 Civil and Environmental Engineering 8715 (coorte 2022/2023) STRUCTURAL MECHANICS II 66285 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 linear systems of differential equations (considering in particular the case of constant coefficients).

### 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.

## TEACHERS AND EXAM BOARD

### Exam Board

EDOARDO MAININI (President)

ROBERTO CIANCI

ELENA RIZZO

FRANCO BAMPI (President Substitute)

LAURA BURLANDO (President Substitute)

MAURIZIO CHICCO (President Substitute)

## 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.

### Exam schedule

Data Ora Luogo Degree type Note
22/01/2024 09:00 GENOVA Scritto
13/02/2024 09:00 GENOVA Scritto
26/06/2024 09:00 GENOVA Scritto Per gli studenti di INGEGNERIA NAVALE fuori corso contattare il docente di riferimento.
16/07/2024 09:00 GENOVA Scritto
30/08/2024 09:00 GENOVA Scritto