PRESENTAZIONE

The course aims to provide an introduction to foundations of continuum mechanics with applications to fluid mechanics and a presentation of the most common partial differential equations (PDE) and their solution techniques.

OBIETTIVI E CONTENUTI

OBIETTIVI FORMATIVI

L'insegnamento fornisce un'introduzione ai fondamenti della meccanica del continuo con applicazioni alla meccanica dei fluidi e una introduzione alle equazioni differenziali parziali più comuni e ad alcune delle loro tecniche di soluzione.

OBIETTIVI FORMATIVI (DETTAGLIO) E RISULTATI DI APPRENDIMENTO

Active participation in lectures and individual study will enable the student to:

-learn the main fundamentals of continuum mechanics;

- be able to classify the main partial differential equations;

- calculate the analytical solution of some problems related to partial differential equations of elliptic, parabolic and hyperbolic types;

PREREQUISITI

prerequisites of the course are: linear algebra, geometry, mathematical analysis and rational mechanics.

MODALITA' DIDATTICHE

The module is based on theoretical lessons.

PROGRAMMA/CONTENUTO

1. Introduction to continuum mechanics

2. Kinematics and dynamics of marine craft

3. Added mass theory

4. Introduction to partial differential equations (PDE).  Classification and normal form. Elliptic, hyperbolic and parabolic PDE.

5. Series and Fourier transform.

6. Elliptic equations. The harmonic functions. Dirichlet and Neumann boundary conditions. Resolution of some related problems 

7. Parabolic differential equations. The diffusion and heat equations. Resolution of some related problems.

8. Hyperbolic equations. The equation of D'Alembert. The method of characteristics. Resolution of some related problems. 

TESTI/BIBLIOGRAFIA

• Lewandowski: The dynamics of marine craft.
• Milne-Thomson: Theoretical Hydrodinamics.
• Newman: Marine Hydrodinamics.
• L.I. Sedov: A course in continuum mechanics, Volume 1.
• W. Jaunzemis: Continuum Mechanics.
• A.N.Tichonov, A.A.Samarskij: Equazioni della Fisica matematica, Problemi della fisica matematica, Mosca,1982;
• R. Courant, D. Hilbert, Methods of Mathematical Phisics vol I e II, Interscience, NY, 1973;
• R. Bracewell, The Fourier Transform and Its Applications, New York: McGraw-Hill, 1999;
• P. V. O’ Neil, Advanced engineering mathematica, Brooks Cole, 2003;
• H. Goldstein, Meccanica Classica, Zanichelli, Bologna, 1985;
• V. I. Smirnov. Corso di Matematica superiore, Vol. 3. MIR (1978).

DOCENTI E COMMISSIONI

LEZIONI

INIZIO LEZIONI

https://corsi.unige.it/9268/p/studenti-orario

Orari delle lezioni

L'orario di questo insegnamento è consultabile all'indirizzo: Portale EasyAcademy

ESAMI

MODALITA' D'ESAME

The examination mode consists of an oral test to verify learning of the course content.

MODALITA' DI ACCERTAMENTO

The assignment of the exam grade will take into account: knowledge and understanding of the covered topics, ability and clarity of exposition, ability to solve problems related to the covered topics