ISTITUZIONI DI FISICA MATEMATICA

12 CFU - 1° and 2° Semester

GIUSEPPE MULONE - MODULO II - MAT/07 - 6 CFU
ORAZIO MUSCATO - MODULO I - MAT/07 - 6 CFU

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.

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.

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

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.

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