Copies of lecture notes will be placed here after lectures. If you wish to read ahead then please read the text book. The lecture plan shows which sections of the book we cover and lectures will follow the book closely.
- Lectures 1 & 2: Introduction, linear operators.
- Lectures 3 & 4: Physical derivation of the heat/diffusion equation.
- Lectures 5 & 6: Steady state solutions, separation of variables, plotting solution with Matlab. Matlab file, graph.
- Lectures 7, 8, 9: Fourier Series, plotting solution with Matlab. Matlab file.
- Lectures 10, 11, 12: Complex Fourier Series, Sturm-Liouville Theory.
- Lecture 13: More Sturm-Liouville Theory, application to the heat equation.
- Lectures 14 & 15: Laplace transforms; Definition, transforms of derivatives, convolutions.
- Lecture 16: More Laplace transforms, solving differential equations.
- Lectures 17 & 18: Fourier integral and
Fourier Transform.
Some old Notes which you might find useful:
Introduction to PDEs and Separation of Variables
Fourier Series 1: Preliminaries.
Matlab files: myfourier.m, myfourier1.m.
Fourier Series 2.
Fourier Series 3 (L2 convergence),
Fourier Series 4 (Complex Fourier Series).
Sturm-Liouville problems.
Course guide