CODE 60235 ACADEMIC YEAR 2026/2027 CREDITS 6 cfu anno 2 INGEGNERIA CIVILE, EDILE E AMBIENTALE 11949 (L-7 R) - GENOVA 6 cfu anno 2 INGEGNERIA CHIMICA E DI PROCESSO 11918 (L-9 R) - GENOVA 6 cfu anno 2 INGEGNERIA ELETTRICA 11879 (L-9 R) - GENOVA 6 cfu anno 2 INGEGNERIA MECCANICA 11881 (L-9 R) - GENOVA SCIENTIFIC DISCIPLINARY SECTOR MAT/05 LANGUAGE Italian TEACHING LOCATION GENOVA SEMESTER 1° Semester PREREQUISITES Propedeuticità in ingresso Per sostenere l'esame di questo insegnamento è necessario aver sostenuto i seguenti esami: Obbligatori: Electrical Engineering 11879 (coorte 2025/2026) MATHEMATICAL ANALYSIS 1 A 115519 2025 Mechanical Engineering 11881 (coorte 2025/2026) MATHEMATICAL ANALYSIS 1A 115453 2025 INGEGNERIA CIVILE, EDILE E AMBIENTALE 11949 (coorte 2025/2026) MATHEMATICAL ANALYSIS 1 A 115519 2025 In alternativa: INGEGNERIA CIVILE, EDILE E AMBIENTALE 11949 (coorte 2025/2026) GEOMETRY 56716 2025 FISICA GENERALE 115338 2025 Propedeuticità in uscita Questo insegnamento è propedeutico per gli insegnamenti: INGEGNERIA CIVILE, EDILE E AMBIENTALE 11949 (coorte 2025/2026) TRANSPORT SYSTEMS AND ROAD INFRASTRUCTURES 84523 FONDAMENTI DI TECNICA DELLE COSTRUZIONI 115346 LABORATORIO DI STRUTTURE E GEOTECNICA 115356 LABORATORIO DI COMPOSIZIONE ARCHITETTONICA 115354 PROGETTAZIONE ESECUTIVA DELLE COSTRUZIONI E FONDAMENTI DI BIM 115351 HYDROLOGY & HYDRAULIC INFRASTRUCTURES 115293 PRINCIPLES OF ECOLOGY 83950 ECOHYDROLOGY FUNDAMENTALS 115304 GEOTECHNICAL APPLICATIONS 115361 SANITARY AND ENVIRONMENTAL ENGINEERING 115360 STRUCTURAL MECHANICS II 66285 GEOTECHNICAL PRINCIPLES 115532 URBAN PLANNING 84525 GEOTECHNICS MODULE 1 99063 LABORATORIO DI COSTRUZIONI IDRAULICHE 115357 ELETTROTECNICA 115350 FONDAMENTI DI COMPOSIZIONE ARCHITETTONICA 115353 FONDAMENTI DI COSTRUZIONI METALLICHE 115347 MODULES Questo insegnamento è un modulo di: MATHEMATICAL ANALYSIS 2 AND MATHEMATICAL PHYSICS TEACHING MATERIALS 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. RECOMMENDED READING/BIBLIOGRAPHY C. Canuto e A. Tabacco, Analisi Matematica 2, 2nd ed., Springer-Verlag Italia, 2014. TEACHERS AND EXAM BOARD LAURA BURLANDO Ricevimento: At the end of lectures or by appointment. FILIPPO DE MARI CASARETO DAL VERME Ricevimento: Weekly office hours, typically 2-hours per week, will be communicated. Meetings upon E-mail requests will also be considered compatibly with the teacher's availability. ALESSANDRO TOIGO LESSONS LESSONS START https://corsi.unige.it/en/corsi/11881/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.
