MATHEMATICAL PHYSICS
Course objectives
Knowledge and understanding: Successful students are able to understand mathematical models to study problems arising in Mechanics. In particular, they are able to apply the analytical and qualitative methods of classical mechanics studied in the course. Ability to formulate a mechanical problem in mathematical term, then find its solution and, finally, interpret the obtained results. Skills and attributes: Successful students are familiar with the the use of logical-deductive reasoning. They acquired the rigor needed to achieve mathematically precise and physically significant results. Hence, they are able to provide a physical interpretation of the result they obtain analytically.
Channel 1
EMILIO NICOLA MARIA CIRILLO
Lecturers' profile
Program - Frequency - Exams
Course program
1. Introduction to linear algebra;
2. kinematics of a particle;
3. kinematics of Euclidean spaces;
4. law of mechanics;
5. dynamics and statics of a particle;
6. dynamics of a system of particles;
7. dynamics of holonomic systems: Lagrange equations;
8. oscillatory systems;
9. statics of holonomic systems;
10. conservative one-dimensional mechanical systems;
11. kinematics of the rigid body;
12. mass distribution of a rigid body;
13. dynamics and statics of a rigid body;
14. central motion;
15. interacting oscillators;
16. properties of a system of forces;
17. equations of the dynamics of a rigid body and Euler equations;
18. motion of a rigid body with fixed axis;
19. motion of a rigid body with a fixed point: Poinsot motion and motion
of the top;
20. motion of a rigid body on a fixed friction free surface;
21. motion of a rigid body on a fixed surface with friction.
Prerequisites
In order to understand the topics of the Meccanica Razional lectures,
the studets must have a good knowledge of the following topics:
1. elementary algebra;
2. trigonometry;
3. mathematical analysis;
4. linear algebra;
5. geometry of Euclidean spaces;
6. mechanics of point particle.
Books
Emilio N.M. Cirillo,
``Appunti delle Lezioni di Meccanica Razionale per l'Ingegneria."
Edizioni CompoMat, 2018, Configni (Ri).
Teaching mode
Lessons will be given using a blackboard or a beamer.
Frequency
Attending classes is voluntary and takes place in the classrooms and
according to the schedule published by the Dean office.
Attending classes, although warmly encouraged, does not contribute to the
final mark.
Exam mode
The final exam aims to check the knowldege and understanding
skills achieved by the students. The exam is made of a written
and an oral part on the whole programme.
The written exam consists in one test.
The test is technical in nature and measures the student's capability of
solving problems in Rational Mechanics, applying the methods and the techniques
taught in the Course.
The oral exam is
aimed at a more comprehensive assessment of the understanding of the
fundamental structures of Rational Mechanics.
The exam is administered after the end of the course.
Evaluation criteria:
Minimal knowledge (grade 18-20); average knowledge (grade 21-23); sufficient
capability of applying knowledge (grade 24-25); good capability of applying
knowledge (grade 27-28); optimal capability of applying knowledge (grade 29-30
cum laude).
Bibliography
V.I. Arnold,
``Metodi Matematici della Meccanica Classica."
Editori Riuniti, 1986.
P. Benvenuti, P.G. Bordoni, G. Maschio,
``Lezioni di Meccanica Razionale."
Edizioni CompoMat, 2010, Configni (Ri).
P. Benvenuti, G. Maschio,
``Esercizi di Meccanica Razionale."
Edizioni CompoMat, 2011, Configni (Ri).
W.E. Deskins,
``Abstract Algebra."
The MacMillian Company, 1964, New York.
G. Gallavotti, ``Meccanica elementare."
Boringhieri, Torino, 1986.
H. Goldstein, C. Poole, J. Safko,
``Meccanica Classica."
Zanichelli, 2005, Bologna.
L. Landau, E. Lifchitz,
``Meccanica," tomo 1 della collezione ``Fisica Teorica."
Mir, 1964, Mosca.
T. Levi--Civita, U. Amaldi,
``Lezioni di Meccanica Razionale."
Edizioni CompoMat, 2012, Configni (Ri).
E. Olivieri,
``Appunti di Meccanica Razionale."
UniTor, 1991, Roma.
J.R. Taylor,
``Meccanica Classica."
Zanichelli, 2006, Bologna.
Lesson mode
Lessons will be given using a blackboard or a beamer.
- Lesson code1022388
- Academic year2024/2025
- CourseCivil Engineering
- CurriculumCurriculum unico
- Year2nd year
- Semester1st semester
- SSDMAT/07
- CFU9
- Subject areamatematica, informatica e statistica