MATHEMATICAL METHODS OF PHYSICS
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- Versione italiana
- Academic year
- 2022/2023
- Teacher
- ALESSANDRO DRAGO
- Credits
- 6
- Didactic period
- Primo Semestre
- SSD
- FIS/02
Training objectives
- Knowledge: to learn the basis of the theory of partial differential equations and their physical interpretation.
Abilities: Mastering methods, including numerical ones, to solve differential equations relevant for physics. Prerequisites
- Real and complex calculus. Ordinary differential equations.
Course programme
- Solution of ordinary differential equations with Laplace tecnique. Non-omogeneous differential equations and tecnnique of the variation of the parameters. (14 hours)
Partial differential equations: classification and examples (5 hours). Time independent boundary condition problems (10 hours). Equation of diffusion (10 hours). Equation of waves (8 hours). Green method (7 hours).
Numerical techniques for the solution of ordinary and of partial differential equations: Runge-Kutta technique, piecewise polynomials, technique of finite elements and of finite differences. (roughly one third of the total time indicated above is dedicated to the discussion of the numerical techniques).
Roughly one fourth of the course will deal with ordinary differential equations and their analytical and numerical solution, the bulk of the course is on partial differential equations. Didactic methods
- Frontal lessons. The course will include numerical techniques: the software Python will be used to solve numerically the equations and for the graphical rendering of the solutions.
Learning assessment procedures
- Oral exam. Students are encouraged to prepare in writing an exercise in which they solve a partial differential equation of physical interest by using one of the techniques (including numerical ones) discussed during the course. The exam will test the ability of the student to deal with a problem based on a partial differential equation and his/her ability to find the best technique (either analytical or numerical) to solve it.
Reference texts
- Main reference: Partial differential equations. Analytical and numerical methods. Mark S. Gockenbach. Second Edition. SIAM (2011).
Further reference: Landau - non relativistic quantum mechanics.
