PHY226

Mathematical Methods for Physics and Astronomy

Unit 3: Partial differential equations, 3D coordinate systems, spherical harmonics

Dr Vitaly Kudryavtsev

Department of Physics and Astronomy

University of Sheffield

Dr Vitaly Kudryavtsev: F9b, tel: 0114 2224531; e-mail: v.kudryavtsev@sheffield.ac.uk

Outline:

1. Introduction to partial differential equations.

2. Wave equation.

3. Schrödinger equation.

4. 2D Laplace equation.

5. Diffusion equation.

6. Three-dimensional coordinate systems.

7. Spherical harmonics.

Lecture notes.

Presentations:

Lecture 15 - Introduction to PDE, Wave equation; 16/11, 18/11 2009.

Lecture 16 - Time dependent Schroedinger equation; 23/11/2009.

Lecture 17 - 2D Laplace equation; 25/11/2009.

Lecture 18 - Diffusion equation; 30/11/2009.

Lecture 19 - 3D coordinate systems; 2/12, 7/12/2009.

Lecture 20 - Spherical harmonics; 7/12, 9/12/2009.

Revision lecture, 9/12/2009.

Homework 2 – answers should be handed in to the Office by 16:30, Friday, 4^th December.

Homework 2 – model answer to Question 2.

Tutorial questions – weeks 9-10.