CODICE 86630 ANNO ACCADEMICO 2021/2022 CFU 6 cfu anno 1 ENERGY ENGINEERING 10170 (LM-30) - SAVONA SETTORE SCIENTIFICO DISCIPLINARE MAT/07 LINGUA Inglese SEDE SAVONA PERIODO 1° Semestre MATERIALE DIDATTICO AULAWEB PRESENTAZIONE The course aims to provide general mathematical techniques for the implementation of a mathematical model, for its formalization, and for the study of its behavior. OBIETTIVI E CONTENUTI OBIETTIVI FORMATIVI The aim of the course is to provide students with an overview of the basic mathematical methods used for the solution and the qualitative study of certain types of ordinary and partial differential equations of interest in engineering. At the end of the course, the student acquires the ability to study the behavior of complex systems through the formulation of a simplified mathematical model capable of describing and predict the salient features of the phenomenon. OBIETTIVI FORMATIVI (DETTAGLIO) E RISULTATI DI APPRENDIMENTO The course introduces the use of differential equations for modelling of physical phenomena. We will introduce mathematical techniques for the construction of a differential mathematical model, its formalization, and, by means of appropriate mathematical methods, the analysis of its qualitative (and sometimes quantitative) behaviour. Natural phenomena will be scrutinised under the magnifying glass of rigorous mathematical analysis. By the end of the course, we will introduce and study several examples and applications of engineering interest (e.g., traffic flow, diffusion of a pollutant, population dynamics, heat conduction, dynamics of electrical circuits). Armed with mathematical methods, we will then either obtain explicit solutions or analyse qualitatively these phenomena, highlighting their properties and their emergent behaviours. MODALITA' DIDATTICHE Traditional lectures, with both theory and exercises in class. Attendance (and active participation) in the course is strongly recommended. PROGRAMMA/CONTENUTO Introduction to mathematical modelling: aspects of the modelling process; representations scales; dimensional analysis. Ordinary differential equations (ODEs): ODEs classification; mathematical statement of ODEs problems; qualitative analysis of dynamical systems; regular and singular perturbation methods; introduction to the problem of bifurcation. Partial differential equations (PDEs): elementary models of mathematical physics (wave propagation, thermal diffusion); analytic methods for linear problems; discretization of continuous models. TESTI/BIBLIOGRAFIA N.Bellomo, E. De Angelis, M. Delitala, Lecture Notes on Mathematical Modelling From Applied Sciences to Complex Systems, SIMAI Notes 2010 S Strogatz, Nolinear Dynamics and Chaos, CRC Press 2018 S Farlow, Partial Differential Equations for Scientists and Engineers, Dover 1982 E Beltrami, Mathematics for Dynamic Modeling, Academic Press 1987 Further references will be suggested, time by time, during the course DOCENTI E COMMISSIONI VINCENZO VITAGLIANO Ricevimento: Savona: Monday 4pm - 6pm Genova: Friday 10am - 12am It is strongly recommended to book in advance via email: vincenzo.vitagliano@unige.it Commissione d'esame VINCENZO VITAGLIANO (Presidente) CLAUDIO CARMELI LEZIONI INIZIO LEZIONI https://courses.unige.it/10170/p/students-timetable Orari delle lezioni MATHEMATICAL MODELLING FOR ENERGY SYSTEMS ESAMI MODALITA' D'ESAME Students can choose among the following possibilities: 1) traditional examination: It consists of a written test and an oral examination. The written test (open questions and problems) has a duration of three hours and the oral one a maximum of 30 minutes. A student is admitted to the oral exam only if s/he has achieved at least 50% of the maximum score (15 marks). 2) writing a report: It consists in writing an essay on a topic of interest for the student (to be agreed in advance with the lecturer). It should be structured as follows: explanation of the process/phenomenon under consideration, equations modeling it, explanation and interpretation of the solution. Once the essay has been written, it must be submitted to the teacher in due time. If the report is approved, students must prepare a set of slides and present them. During the presentation, the students are required to prove their understanding of the topic by answering questions. MODALITA' DI ACCERTAMENTO The exam verifies the student's ability to write the equations that model simple phenomena, to set the solution and to analyze the salient qualitative aspects. Calendario appelli Data appello Orario Luogo Tipologia Note 14/01/2022 10:00 GENOVA Scritto + Orale 04/02/2022 10:00 GENOVA Scritto + Orale 09/06/2022 10:00 GENOVA Scritto + Orale 08/07/2022 10:00 GENOVA Scritto + Orale 08/09/2022 10:00 GENOVA Scritto + Orale