Fiches de cours 2018-2019

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Mathematical methods for physicists

PHYS-216

Enseignant(s) :

Brunner Stephan
Graves Jonathan

Langue:

English

Summary

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

Content

Introduction to Hilbert spaces. Solving linear 2nd order Ordinary Differential Equations (ODEs): 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

Analysis: basic theory of ODEs, vector calculus. Linear algebra: Vector spaces, inner product spaces, linear operators, eigenvalue problems, matrix diagonalisation. Complex algebra.

Learning Outcomes

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

• Apply the methods presented in the course for solving physical equations.

Teaching methods

Ex cathedra lecture and 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

• Mathematical Methods for Physicists, A Comprehensive Guide

Moodle Link

• http://moodle.epfl.ch/course/view.php?id=14376