# Mathematical methods for physicists

## Summary

This course complements the Analysis and Linear Algebra courses by providing further mathematical background and practice required for 3rd year physics courses, in particular electrodynamics and quantum mechanics.

## Content

Review of essential linear algebra concepts and their application to function spaces. Solving Ordinary Differential Equations (ODEs), in particular linear 2nd order: Frobenius method, boundary value problems, Sturm-Liouville problems. Fourier analysis: Fourier Series and Fourier Transforms. Special functions. Methods for solving Partial Differential Equations (PDEs).

## Learning Prerequisites

## Required courses

Analyse I, II and III. Linear algebra I and II Physics I, II, and III.

## Recommended courses

Computational Physics I.

## Important concepts to start the course

**Linear algebra**: Vector spaces, inner product spaces, linear operators, eigenvalue problems, matrix diagonalisation.**Analysis**: basic theory of ODEs, vector calculus. Complex algebra and towards the end of the course, complex analysis.

## Learning Outcomes

By the end of the course, the student must be able to:

- Apply the methods presented in the course for solving (differential) equations met in various fields of physics.

## Teaching methods

Ex cathedra lecture and assisted exercises in the classroom

## Assessment methods

written exam

## Resources

## Bibliography

The main reference for the course is the book by Arfken:

G. B. Arfken, H. J. Weber, and F. E. Harris

"Mathematical Methods for Physicists, A Comprehensive Guide"

7th edition, Academic Press 2013.

Hard copies and electronic version available through EPFL library.

## Ressources en bibliothèque

## Moodle Link

## In the programs

**Semester:**Spring**Exam form:**Written (summer session)**Subject examined:**Mathematical methods for physicists**Lecture:**2 Hour(s) per week x 14 weeks**Exercises:**2 Hour(s) per week x 14 weeks