28382 - Mathematical Physics 3

Learning outcomes

Upon successful completion of this course, students will know the fundamental knowledge of classical mechanical systems within a more general analytic context. The students will be able to solve theoretical and applied problems in physics, and other sciences. The students will be equipped with a high learning skill that facilitates the comprehension of second-level-degree courses.

Course contents

- Lagrangian Mechanics: D'Alembert's Principle; Hamilton's Principle; Euler-Lagrange Equations; Noether's Theorem. - Hamiltonian Formalism: Legendre Transformation; Modified Hamilton's Principle; Hamiton's Equations; Canonical Transformations; Liouville's Theorems; Integrable systems; Hamilton-Jacobi Equation.

Readings/Bibliography

H. GOLDSTEIN, C. POOLE and J.L. SAFKO: Classical Mechanics, III ed., Pearson 2001;
G. GRIOLI: Lezioni di Meccanica Razionale Libreria Cortina;
C. CERCIGNANI: Spazio, tempo, Movimento: Introduzione alla Meccanica Razionale, Zanichelli, Bologna 1976;
V. I. ARNOLD: Mathematical Methods of Classical Mechanics, II ed., Springer-Verlag, 1989;
M. BRAUN: Differential Equations and their Applications, IV ed., Springer-Verlag, 1993.
F. R. GANTMACHER: Lezioni di Meccanica Analitica, Editori Riuniti, 1980;

Teaching methods

Face-to-face Lectures.

Assessment methods

Oral exam that includes solving exercises. An oral exam is extremely important. It allows the student to demonstrate her/his comprehension of the syllabus and to dialogue with the professor by using the appropriate scientific terminology. Moreover, during the oral exam the student is able to correct a wrong statement by means of the interaction with the professor who stimulates her/him to reason. The length of the exam is directly proportional to the student's emotional feelings and inversely proportional to her/his knowledge of the syllabus.

Office hours

See the website of Maria Clara Nucci

See the website of André Georges Martinez