Advanced mathematical methods of physics (code 61843) has credit value 6 and it is taught in the first semester of the first or second year of the LM.
Lectures are usually given in Italian. Should it be requested, they can be given in english.
The calculus of variations is a general method to derive differential and partial differential equations
used in physics.
We will show how to solve these equations using the theory of distributions and the Green's function method.
The course is divided in two parts:
The first part is on the applications of calculus of variations to mechanics and classical field theory.
The second one is on the introduction of the distributions and the Green's functions.
Mathematical methods of Physics.
Teaching is done in the traditional (chalk and blackboard) way. Students are (very) strongly suggested to attend the class.
Functionals. Variation of a functional. Simple examples.
Euler-Lagrange equations.
Symmetries and Noether's theorem.
The vibrating string.
Klein-Gordon Lagrangian. Retarded, advanced and Feynmann Green's functions.
Introduction to the theory of distributions.
Examples: Dirac's Delta function and its derivatives.
Green's formulae.
Dirichlet and Neumann problem.
The wave equation.
Vibrations of a circular membrane.
Gross-Pitaevskii Lagrangian. Gross-Pitaevskii equations.
U(1) symmetry and conserved current.
Suggested textbooks
Elsgolc, Calculus of variations.
Butkov, Mathematical physics.
Ricevimento: The teacher meets with students everyday from 14,00 to 16,00 (please contact the teacher by mail).
NICODEMO MAGNOLI (President)
ANDREA AMORETTI
PIERANTONIO ZANGHI' (President Substitute)
First semester, usually last week of September
ADVANCED MATHEMATICAL METHODS IN PHYSICS
Written examination.Optional oral examination.
Methodology of ranking
The explicit aim of the course is to carry the students to the level of making calculations and solving problems. This is why the essential part of the exam is the written one, where the student is asked to make calculations and to solve explicitly problems.
The text is divided into three levels, each level corresponds to a range of marks. (These ranges of marks are clearly indicated in the text given to each student).
The oral part is typically a small correction of the written examination and it is not mandatory.
