Enrollment year
2019/2020
Academic discipline
MAT/07 (MATHEMATICAL PHYSICS)
Department
DEPARTMENT OF PHYSICS
Curriculum
PERCORSO COMUNE
Period
1st semester (05/10/2020 - 20/01/2021)
Lesson hours
84 lesson hours
Activity type
WRITTEN AND ORAL TEST
Prerequisites
Necessary mathematical tools are from the courses of Calculus (Analisi) and Linear Algebra of the first year. It is required also an appropriate knoledge of classical mechanics in Newton's formulation.
Learning outcomes
Aim of the course is to convey essential concepts and make the familiar the mathematical tools typical of the analytical formulation (Lagrangian and Hamiltonian) of classical mechanics.
The contents of this course are necessary to address properly the sequel of the curriculum in Physics, in particular quantum mechanics, relativity and field theory. If necessary, short reviews of topics not addressed previously will be recalled.
Attendance is not mandatory but highly recommended.
Course contents
Remainders on the fundamental principles of Newtonian mechanics. Lagrange formulation: D' Alembert's principle; Euler-Lagrange equations from the Hamilton variational principle.
conservation laws and symmetry properties (Noether theorem). Applications: motion in a central fforce field; the 2-body problem and Kepler laws; oscillators and normal modes. Hamiltonian formulation: phase space, Legendre thansformation; modified Hamilton principle snd deduction of Hamilton equations; canonical trasformations; Poisson brackets; Hamiltonian flow and invariance of the volume in the phase space (Liouville theorem). Infinitesimal canonical trasformations and conservation laws. Angular momentum algebra and SO(4) symmetry in the Kepler problem. Lagrangian formulation in continuum mechanics and field theory.
There will be a few introductory lessons on the theory of Special Relativity.
Teaching methods
Lectures, complements and exercises at the blackboard. There will be also two teaching assistants.
*Lectures will be in presence, complements online*
Reccomended or required readings
H Goldstein, C Poole, J Safko
"Classical Mechanics", Pearson New International Edition (third edition 2011).
Notes will be made avalaible
Assessment methods
A written and an oral examination. The written part (3 exercises) is evaluated with marks from "insufficient" to"excellent". The written test must be passed (at least "sufficient") before the admittance to the oral examination. The latter is aimed to verify the assimilation of the basic concepts and of their interconnections. For Erasmus students special modalities will be set upon request.
Further information
A written and an oral examination. The written part (3 exercises) is evaluated with marks from "insufficient" to"excellent". The written test must be passed (at least "sufficient") before the admittance to the oral examination. The latter is aimed to verify the assimilation of the basic concepts and of their interconnections. For Erasmus students special modalities will be set upon request.
Sustainable development goals - Agenda 2030
Università di Pavia - Offerta formativa