PHYS 30672 Mathematical Methods for Physics

• The unit survey is now available via Blackboard

• Syllabus and textbooks. I recommend Arfken & Weber Mathematical Methods for Physicists or Riley, Hobson & Bence Mathematical Methods for Physics and Engineering for this course. Another good book is Mathews & Walker Mathematical Methods of Physics; it covers much the same ground and I find it particularly readable.

• Contour integration is used only in the lecture notes on Green's functions, as an alternative to the method used in lectures. No exam question for this course will require knowledge of contour integration, either to understand the question or obtain a solution. Nevertheless, the calculus of functions of a complex variable is both fascinating and useful. If you have never met complex variables before, the Green's function notes may provide some motivation to find out more: the Appendix (by Niels) is a very brief introduction to contour integration.

• Lecture notes (PDF file) are an on-going project and may be updated as the course progresses. Check back occasionally for updates.
• Another edition of the notes is available for those who prefer to see angled brackets (rather than round brackets) in the notation used for the scalar product. You can use any popular notation in the exam.

• The lectures are supported by examples classes, held on alternate Tuesdays, 14.00-15.30. Final examples class: 2pm, Tuesday 17 May 2016, in room L1 of the Braddick Library. You can also hand in solutions to examples sheet questions, or (preferred) ask me directly about them: my office is 7.17, Schuster Laboratory, and my pigeonhole is in the kitchen area, close to my office.

• Examples sheets and worked solutions:
• Examples 1 (released 2016), Solutions 1 (released 2016) (warning: Q.2 and its solution use different Fourier transform conventions, but this doesn't affect the method)
• Examples 2 (released 2016), Solutions 2 (released 2016)
• Examples 3 (released 2016), Solutions 3 (released 2016)
• Examples 4 (released 2016), Solutions 4 (released 2016)

• There is no special merit in doing long, error-prone analytical calculations by hand, any more than there is in doing floating-point arithmetic using a pencil and paper. Every theoretical physicist should therefore get to know a computer algebra package, such as Mathematica. To get you started, here are some Mathematica notebooks (by Niels) that relate closely to the course material:
  • Introduction to Mathematica: Introduction.nb
  • Review of linear algebra: LinearAlgebra.nb
  • Orthonormalization of vectors: Orthonormal.nb
  • Linearly dependent sets of functions: OverlapGaussian.nb
  • Representations of the Dirac delta function: dirac.nb
  • Construction of a 1D Green's function: GreenFunc1.nb
  • Review of contour integration: Contour.nb and Contour.pdf
  Less beautiful (by me):
  • Numerical solution of an integral equation: MolecularFlow.nb (updated April 2016)
  Let me know if any of these notebooks don't work.

• Bottom-line numerical answers for Q2 of the 2012 exam.

• 2014/15 exam paper (version in the School archive is missing Q2)

• Thanks go to those students who have helped to eliminate bugs in the lecture notes and solutions to problems. No doubt there are still errors to be found, so let me know if you find anything puzzling.