MATHEMATICAL PHYSICS
cod. 00421

Academic year 2016/17
1° year of course - First semester
Professor
Marzia BISI
Academic discipline
Fisica matematica (MAT/07)
Field
Formazione modellistico-applicativa
Type of training activity
Characterising
72 hours
of face-to-face activities
9 credits
hub: PARMA
course unit
in - - -

Learning objectives

The student will learn mathematical tools to tackle and solve different types of PDEs, appearing in fundamental problems of Mathematical physics.

Prerequisites

Knowledge of topics of mathematical courses of class L-35 (first degree).

Course unit content

Functions of a complex variable.
Fourier and Laplace transforms.
Green function and Sturm-Liouville problems.
Classification of second order PDEs.
Fundamental equations of mathematical physics: Laplace equation, heat equation, wave equation.
Conservation laws.

Full programme

Functions of a complex variable: Cauchy-Riemann conditions, types of singularities, residues and integration, Laurent series.
Fourier and Laplace transforms: definitions and basic properties, transforms of the fundamental functions, transform of Dirac delta, inverse transforms.
Introduction to the Green function and to Sturm-Liouville problems.
Classification of linear second order PDEs with two independent variables; Cauchy problem.
Fundamental equations of mathematical physics: Laplace equation, heat equation, wave equation (physical derivation, mathematical properties, methods of solution).
Conservation laws.

Bibliography

F. Gazzola, F. Tomarelli, M. Zanotti, Analisi complessa - Trasformate - Equazioni Differenziali, Esculapio, Milano.

S. Salsa, Equazioni a derivate parziali, Springer, Milano.

G. Spiga, Problemi matematici della Fisica e dell'Ingegneria, Pitagora, Bologna.

A. N. Tichonov, A. A. Samarskij, Equazioni della fisica matematica, MIR, Mosca.

Teaching methods

During class lectures, the topics will be proposed from a formal point of view, and equipped with meaningful examples and applications.

Assessment methods and criteria

The examination is based on an oral discussion, where the level of knowledge and understanding of the topics is valued, as well as the mathematical accuracy of exposition.

Other information

- - -

2030 agenda goals for sustainable development

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Contacts

Toll-free number

800 904 084

Segreteria studenti

E. segreteria.scienze@unipr.it
T. +39 0521 905116

Quality assurance office

Education manager
dott.ssa Giulia Bonamartini

T. +39 0521 906968
Office E. smfi.didattica@unipr.it
Manager E.giulia.bonamartini@unipr.it

President of the degree course

Prof. Luca Lorenzi
E. luca.lorenzi@unipr.it

Faculty advisor

Prof. Luca Lorenzi
E. luca.lorenzi@unipr.it

Career guidance delegate

Prof. Francesco Morandin
E. francesco.morandin@unipr.it

Tutor Professors

Prof.ssa Alessandra Aimi
E. alessandra.aimi@unipr.it

Prof. Luca Lorenzi
E. luca.lorenzi@unipr.it

Prof. Adriano Tomassini
E. adriano.tomassini@unipr.it

 

Erasmus delegates

Prof. Leonardo Biliotti
E. leonardo.biliotti@unipr.it

Quality assurance manager

Prof.ssa Alessandra Aimi
E. alessandra.aimi@unipr.it

Internships

Prof. Costantino Medori
E.
 costantino.medori@unipr.it

Tutor students

Dott.ssa Fabiola Ricci
E. fabiola.ricci1@studenti.unipr.it