CODE 86630 ACADEMIC YEAR 2024/2025 CREDITS 6 cfu anno 1 ENERGY ENGINEERING 10170 (LM-30) - SAVONA SCIENTIFIC DISCIPLINARY SECTOR MAT/07 LANGUAGE English TEACHING LOCATION SAVONA SEMESTER 1° Semester TEACHING MATERIALS AULAWEB OVERVIEW The course aims to provide general mathematical and numerical techniques for the implementation of a mathematical model, for its formalization, and for the study of its behavior. AIMS AND CONTENT LEARNING OUTCOMES 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. AIMS AND LEARNING OUTCOMES 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 and numerical 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. PREREQUISITES Basic Calculus (suggested) Basics of PDEs and ODEs (suggested) TEACHING METHODS Traditional lectures, with both theory and exercises in class, and MATLAB labs. Attendance (and active participation) in the course is strongly recommended. SYLLABUS/CONTENT 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. RECOMMENDED READING/BIBLIOGRAPHY J. David Logan, Applied Mathematics: A Contemporary Approach, Wiley 1987 Jon H. Davis, Methods of Applied Mathematics with a MATLAB Overview, Springer Science 2004 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 TEACHERS AND EXAM BOARD VINCENZO VITAGLIANO Ricevimento: Office hours by appointment, please contact in advance vincenzo.vitagliano@unige.it Exam Board VINCENZO VITAGLIANO (President) CLAUDIO CARMELI LESSONS LESSONS START https://corsi.unige.it/en/corsi/10170 Class schedule The timetable for this course is available here: Portale EasyAcademy EXAMS EXAM DESCRIPTION The exam consists of two parts: a Matlab exercise and a written test. The written test typically consists of a problem and three theoretical questions. Each part carries a mark, the total mark will be given by the sum of the five. Students who have a valid physical or learning disability certification and wish to discuss possible accommodations for classes and exams must get in contact with the instructor. ASSESSMENT METHODS 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. Exam schedule Data appello Orario Luogo Degree type Note 10/01/2025 10:00 SAVONA Laboratorio 10/01/2025 10:00 SAVONA Scritto 05/02/2025 10:00 SAVONA Laboratorio 05/02/2025 10:00 SAVONA Scritto 05/06/2025 10:00 SAVONA Laboratorio 05/06/2025 10:00 SAVONA Scritto 02/07/2025 10:00 SAVONA Laboratorio 02/07/2025 10:00 SAVONA Scritto 04/09/2025 10:00 SAVONA Laboratorio 04/09/2025 10:00 SAVONA Scritto Agenda 2030 - Sustainable Development Goals Quality education Gender equality Decent work and economic growth Reduce inequality