Lecture Notes on Mathematical Methods PH2130 - 2015/2016 Glen D. Cowan Physics Department ROYAL HOLLOWAY UNIVERSITY OF LONDON
Last revised: September 10, 2015
Preface The main goal of PH2130 is to learn how to use the mathematical tools that underpin a number of the core physics courses in the undergraduate programme, especially electromagnetism and quantum mechanics. To a large extent this amounts to learning more about differential equations, especially partial differential equations, which involve partial derivatives with respect to more than one variable. The lecture notes contain 10 chapters and several appendices. The main body of the course covers: 1. Review of ordinary differential equations 2. Introduction to partial differential equations 3. Orthogonal functions 4. Fourier series 5. Sturm-Liouville theory 6. The Laplace equation 7. Series solutions to differential equations 8. Special functions 9. Nonhomogeneous problems 10. Fourier transforms We will work through roughly one chapter per week with the notable exception of Chapter 8 (Special Functions), which will occupy more than two weeks. Appendix A concerns numerical methods, and we will try to make links between this and your computing course PH2150. The other appendices include useful background information and some further examples. Useful supplementary materials for this course are the texts by Riley et al. [1], Arfken [2], Boas [3], Boyce and DiPrima [4], Haberman [5], as well as the notes from the earlier PH2130 course by B. Cowan [6] and those by K. Howell at University of Alabama, Huntsville [7]. These references as well as valuable discussions with Brian Cowan, James Nicholls, Veronique Boisvert and Stephen West have have provided the basis for the present set of notes. i