OVERVIEW

The module 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 module 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 module, 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 module 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 module, 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 module is strongly recommended.

Working students and students with certified Specific Learning Disorders (SLD), disabilities, or other special educational needs are advised to contact the instructor at the beginning of the module to agree on teaching and examination methods that, while respecting the module objectives, take into account individual learning styles.

Students with a valid certification of physical or learning disabilities filed with the University who wish to discuss possible accommodations or other circumstances related to lectures, modules, and exams should speak with both the instructor and Professor Federico Scarpa (federico.scarpa@unige.it), the School of Engineering’s disability coordinator.

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 module

TEACHERS AND EXAM BOARD

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.

FURTHER INFORMATION

Contact the instructor for further information not included in the module syllabus