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 at the use of differential equations for the modeling of physical phenomena. Traditional lectures at the blackboard are complemented by lab sessions in which the student has to implement simple exercises with Matlab on the topics covered by the lectures. In order to become familiar with Matlab, a review of the matrix formalism is performed, which is of interest by itself.

MODALITA' DIDATTICHE

Traditional lectures, lab exercises with matlab.

PROGRAMMA/CONTENUTO

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:

• Simple systems modeled by ordinary differential equations.
• Systems modeled by partial differential equations: transport equation, 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

TESTI/BIBLIOGRAFIA

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

DOCENTI E COMMISSIONI

Commissione d'esame

CLAUDIO CARMELI (Presidente)

OTTAVIO CALIGARIS

LEZIONI

Orari delle lezioni

MATHEMATICAL MODELING FOR ENERGY SYSTEMS

ESAMI

MODALITA' D'ESAME

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.

MODALITA' DI ACCERTAMENTO

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 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.

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.

Calendario appelli