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.

We introduce mathematical techniques for the construction of a mathematical model, for its formalization, and for the study of its behavior. In order to illustrate such methods, the following topics are developed:

• Systems modeled by ordinary differential equations: Population dynamics, Lotka-Volterra predator-prey models.
• Systems modeled by partial differential equations: transport equation, Laplace equation, wave and heat equations. Simple Cauchy and boundary value problems: formulation and main techniques: separation of variables (and related techniques: Fourier series and transform), fundamental solutions.
• Matlab exercises

• lecture notes
• E.Beltrami Mathematics for dynamic modelling Academic Press
• O.Caligaris - P.Oliva lecture notes at : //sv.inge.unige.it/DidRes/Analisi/

Traditional lectures, lab exercises with matlab.

Students can choose among the following possibilities:

1) traditional examination: it consists in answering a number of questions about the syllabus

2) writing a report: it consists in writing an essay on a topic of interest for the student. It should be structured as follows: explanation of the process/phenomenon under consideration, writing of the equations modeling it, solution (analytical and/or numerical), explanation and interpretation of the solution

For those students who attended all the laboratories and delivered all the lab reports in due time, a simpler version of the exam is required, in which they have to solve a matlab exercise similar to one assigned during the labs.

1) "Traditional" examination: the student is asked to prove his understanding of the program by answering questions about the syllabus

2) Writing a report: students agree with the teacher about the topic and the structure of the essay. Once the essay has been written, it must be submitted to the teacher before the day of the examination. 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.

3) if the student attended all the labs and delivered all the lab reports in due time, he is asked to solve a Matlab exercise similar to one of those he has faced during the labs.