CODE 60243 ACADEMIC YEAR 2022/2023 CREDITS 6 cfu anno 2 INGEGNERIA CHIMICA E DI PROCESSO 10375 (L-9) - GENOVA SCIENTIFIC DISCIPLINARY SECTOR MAT/05 TEACHING LOCATION GENOVA SEMESTER 1° Semester PREREQUISITES Propedeuticità in ingresso Per sostenere l'esame di questo insegnamento è necessario aver sostenuto i seguenti esami: Civil and Environmental Engineering 8715 (coorte 2021/2022) MATHEMATICAL ANALYSIS I 72290 2021 GENERAL PHYSICS 56686 2021 GEOMETRY 56721 2021 CHEMICAL AND PROCESSES ENGINEERING 10375 (coorte 2021/2022) MATHEMATICAL ANALYSIS I 56594 2021 Propedeuticità in uscita Questo insegnamento è propedeutico per gli insegnamenti: Civil and Environmental Engineering 8715 (coorte 2021/2022) HYDROLOGY & HYDRAULIC URBAN INFRASTRUCTURES 66097 Civil and Environmental Engineering 8715 (coorte 2021/2022) STRUCTURAL ENGINEERING I 72543 Civil and Environmental Engineering 8715 (coorte 2021/2022) GEOTECHNICS 99062 Civil and Environmental Engineering 8715 (coorte 2021/2022) STRUCTURAL MECHANICS II 66285 Civil and Environmental Engineering 8715 (coorte 2021/2022) URBAN PLANNING AND TRANSPORTATION ENGINEERING 84522 MODULES Questo insegnamento è un modulo di: MATHEMATICAL ANALYSIS II AND PHYSICS TEACHING MATERIALS AULAWEB OVERVIEW The module Mathematical Analysis II (code 60243) deals with some issues of Mathematical Analysis with the aim to complete the basic learning and introduce some theoretical tools used in engineering science. The main topics concern with the study of maximum and minimum constrained for functions of more real variables, the integration for functions of two and three variables, the theory of differential forms and the Fourier's series. AIMS AND CONTENT AIMS AND LEARNING OUTCOMES This module aims to provide the student with the knowledge of the following mathematical conceps: 1) Maximum and minimum constrained for functions of more real variables 2) Integration on R^2 and R^3. Integration of differential forms. Gradient, divergence, curl and their properties. 3) Fourier series. The main learning outcomes consist of technical skills about the following issues: Calculation of maximum and minimum constrained of functions of more real variables. Evaluation of integrals on R^2 and R^3. Integration of differential forms. Calculus of gradient, divergence, curl. Fourier series expansions. TEACHING METHODS Both theory and exercises are presented by the teacher in the usual way. Moreover some tutorial exercitations can be carried out during the semester. SYLLABUS/CONTENT - maximum and minimum constrained for functions of more real variables - integrals on R^2 and R^3 - curves and surfaces in R^3. Vector analysis: differential forms and path integrals, closed and exact differential forms, gradient, curl, divergence. Stokes Theorem. - Fourier series. RECOMMENDED READING/BIBLIOGRAPHY G. Anichini, G. Conti, M. Spadini - Analisi matematica 2 - Pearson O. Caligaris, P. Oliva - Analisi matematica 2 - E.C.I.G. O. Caligaris, P. Oliva - Complementi di analisi matematica W. Rudin - Real and Complex Analysis - McGraw-Hill 1970 N. Fusco, P. Marcellini, C. Sbordone - Lezioni di analisi matematica 2 - Zanichelli (2020) M. Chicco, F. Ferro - Esercizi di Analisi matematica II - E.C.I.G. M. Boella, Analisi matematica 2, Esercizi - Pearson TEACHERS AND EXAM BOARD ADA ARUFFO Ricevimento: At the end of lectures or by appointment. Exam Board ADA ARUFFO (President) PIERRE OLIVIER MARTINETTI (President) LAURA BURLANDO CRISTINA CAMPI MAURIZIO CHICCO MARC ALEXANDRE MUNSCH EDOARDO MAININI (President Substitute) SIMONE MURRO (President Substitute) LESSONS LESSONS START The class will start according to the academic calendar. Class schedule The timetable for this course is available here: Portale EasyAcademy EXAMS EXAM DESCRIPTION Written and oral tests. Oral test, which students can access only if the grade of written test is at least 10, has to be taken in the same exam session of written test. If the University introduces again the obligation to perform even partially online exams (as happened in part of the academic years 2019-20, 2020-21 and 2021-22), the exam will consist only of oral test. Students with DSA certification ("specific learning disabilities"), disability or other special educational needs are advised to contact the teacher at the beginning of the course to agree on teaching and examination methods that, in compliance with the teaching objectives, take account of individual learning arrangements and provide appropriate compensatory tools. ASSESSMENT METHODS The written examination consists in some exercises about the topics covered in this course. In this test the ability to apply theoretical results in concrete situations is evaluated. In the written test it is possible to consult the notes and textbooks. In the oral exam a discussion of the written examination is done; moreover some questions are asked on the course content and/or about the solution of some exercises about the topics covered in this course. In such way they are assessed the understanding, the knowledge of the concepts, and the skills in using them, acquired by the students. Exam schedule Data appello Orario Luogo Degree type Note 12/01/2023 09:00 GENOVA Orale 23/01/2023 09:00 GENOVA Scritto 02/02/2023 10:00 GENOVA Scritto 07/02/2023 09:00 GENOVA Orale 14/02/2023 09:00 GENOVA Scritto 08/06/2023 10:00 GENOVA Scritto 14/06/2023 09:00 GENOVA Orale 26/06/2023 09:00 GENOVA Scritto 06/07/2023 14:30 GENOVA Scritto 14/07/2023 09:00 GENOVA Orale 18/07/2023 09:00 GENOVA Scritto 01/09/2023 09:00 GENOVA Scritto 04/09/2023 10:00 GENOVA Scritto 13/09/2023 09:00 GENOVA Orale FURTHER INFORMATION Attendance is recommended. Students are suggested to enroll in AulaWeb, in order to be able to get further information by the teachers about the course.