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