The aim of the course “Mécanique Analytique” (Classical Mechanics) is to provide the mathematical foundations for most of the subsequent physics courses.
The Lagrangian, Hamiltonian and Hamilton-Jacobi formalisms will be introduced and their basic features described. No specific systems will be studied. Rather, the mission of this course is to give the students the tools to write down a mathematical description of any mechanical physical system and to understand the formal, mathematical basis of quantum mechanics, field theory, hydrodynamics and so on.
This is a very mathematical course where good computational skills are required. Also, all the notions of the first year are considered as well acquired.
A standard reference for this course is:
H. Goldstein (with C. Poole & J. Safko in the International Edition)
The notes of the course, in French, and the exams of the previous years can be found here.
Here are a couple of pages about Noether’s Theorem (pdf file).