# ISTITUZIONI DI FISICA MATEMATICA

Academic Year 2021/2022 - 1° Year - Curriculum APPLICATIVO
Teaching Staff
Credit Value: 12
Scientific field: MAT/07 - Mathematical physics
Taught classes: 70 hours
Exercise: 24 hours
Term / Semester: 1° and 2°

## Learning Objectives

• MODULO II

The objectives of the course are:

1. Give the basic elements of continuum mechanics and fluid dynamics (II module).

2. Understanding the mechanics of continuous physical phenomena and fluid dynamics.

3. Understanding of the different solution methods: why it has been proposed a solution method? What are some alternative methods? Understanding how the analytical solutions obtained are related to the physics of the problem.

4. It will be privileged the understanding of the physical part,the methods and the analytical resolution.

• MODULO I

1. Give the basic elements of the partial differential equations of mathematical physics.

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

• MODULO II

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.

• MODULO I

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, inline with the programme planned and outlined in the syllabus.

## Detailed Course Content

• MODULO II

(Form II)

Continuum Mechanics

Ideal fluids, Stokesian fluids, Navier Stokes equations

The complete program is here:

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

• MODULO I

Partial differential equations of mathematical physics.

Waves equations

Heat equations

Laplace's equation and Poisson.

Schroedinger equation

## Textbook Information

• MODULO II

[1] G. MULONE, Appunti di elementi di meccanica dei continui.

[2] T. RUGGERI, Introduzione della termomeccanica dei continui, II edizione riveduta e corretta, Monduzzi Editoriale, 2014.

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

[4] T. MANACORDA, Introduzione alla termomeccanica dei continui, QUMI, ed. Pitagora.

[5] S. RIONERO, Lezioni di Meccanica Razionale, ed. Liguori.

[6] J. SERRIN, Mathematical principles of Classical Fluid Mechanics, Handbuk der Phisick VIII/1, 1959.

[7] C. TRUESDELL, The elements of continuum Mechanics, ed. SpringerVerlag.

• MODULO I

[1] M.M. SMIRNOV, Second-Order partial differential equations, ed. Noordhoff.
[2] F.JOHN, Partial differential equations, Springer-Verlag.
[3] V.I. SMIRNOV, Corso di matematica superiore II, Editori Riuniti.
[4] N.S.KOSHLYAKOV, M.M.SMIRNOV, E.B.GLINER, Differential equations of mathematical physics, ed. North-Holland.