# EQUAZIONI DIFFERENZIALI DELLA FISICA MATEMATICA

Academic Year 2020/2021 - 1° Year - Curriculum APPLICATIVO
Teaching Staff: Giuseppe MULONE
Credit Value: 6
Scientific field: MAT/07 - Mathematical physics
Taught classes: 35 hours
Exercise: 12 hours
Term / Semester:

## Learning Objectives

1. Give the basic elements of the partial differential equations of mathematical physics (I module).

2. Understanding of physical phenomena governed by partial differential equations; Construction of mathematical models: equations of the waves, heat, Laplace equation.

3. Understanding of the different solution methods: why it has been proposed a solution method? What are some other alternative methods? Understanding how the analytical solutions obtained are interpreting the physical real situations (wellposedness of the models or paradoxes).

4. It will be privileged the undertsnding the physical part, the models and their analytical solution.

## Course Structure

Lectures and exercises done by students at home and in class.

Should teaching be carried out in mixed mode or remotely, it may be
necessary to introduce changes with respect to previous statements, in
line with the programme planned and outlined in the syllabus.

## Detailed Course Content

Partial differential equations of mathematical physics.

Waves equations

Heat equations

Laplace's equation and Poisson.

The complete programme here:

http://www.dmi.unict.it/~mulone/IFM2021.pdf

## Textbook Information

[1] G. MULONE, Appunti di equazioni a derivate parziali della fisica matematica.

[2] M.M. SMIRNOV, Second-Order partial differential equations, ed. Noordhoff.

[3] F.JOHN, Partial differential equations, Springer-Verlag.

[4] V.I. SMIRNOV, Corso di matematica superiore II, Editori Riuniti.

[5] J. FLAVIN, S. RIONERO, Qualitative estimates for partial differential equations. An introduction. Boca Raton, Florida: CRC Press, 1996.

[7] N.S.KOSHLYAKOV, M.M.SMIRNOV, E.B.GLINER, Differential equations of mathematical physics, ed. North-Holland.

[8] A.N.TICHONOV, A.A. SAMARSKIJ, Equazioni della fisica matematica, ed. Mir.

[9] L.C. EVANS, Partial differential equations, American Mathematical Society, 1998.

[10] H. LEVINE, Partial differential equations, American Mathematical Society, 1997.