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Università degli Studi di Parma Università degli Studi di Parma
Degree course in
Physics
Università degli Studi di Parma
Department of Mathematical, Physical and Computer Sciences

INTRODUCTION TO MATHEMATICAL PHYSICS
cod. 14758

Academic year 2013/14
3° year of course - First semester
Professor
Academic discipline
Fisica matematica (MAT/07)
Field
Attività formative affini o integrative
Type of training activity
Related/supplementary
52 hours
of face-to-face activities
6 credits
hub: PARMA
course unit
in - - -
lectures timetable unavailable
exam calls
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Learning objectives

The student will achieve a good knowledge of advanced analytical mechanics, as well as of boundary problems for second order linear equations, and partial differential equations arising from problems of physical interest.

Prerequisites

Knowledge of classical Physics

Course unit content

- Analytical mechanics.


- Series developments of ortogonal functions.


- 2nd order differential equations: contour problems.


- Sturm-Liouville problems.


- Partial differential equations of Mathematical Physics.

Full programme

Elements of calculus of variations,
Variational principles of classical Mechanics.
Canonical and completely canonical transformations.
Poincaré-Cartan differential form. Lie condition. Poisson brackets.
Infinitesimal canonical transformations.
Hamilton-Jacobi theory.
Expansion in series of orthogonal functions.
Boundary value problems for 2nd order ODE.
Sturm-Liouville problems, eigenvalues and eigenfunctions.
Non-homogeneous boundary value problems and Green's function.
Laplace and Poisson equations. Dirichlet and Neumann problems.
The heat equation.
The wave equation.
Cauchy problems.

Bibliography

A. Fasano - S. Marmi, Meccanica analitica, Bollati-Boringhieri.
E. Persico, Introduzione alla Fisica Matematica; Zanichelli.
G. Spiga, Problemi matematici della Fisica e dell'Ingegneria, Pitagora.
A.N. Tichonov - A.A. Samarskii, Equazioni della Fisica Matematica, MIR.
F.G. Tricomi, Equazioni differenziali, Boringhieri.

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

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