Natural Sciences Tripos Part 1 Mathematics
Mathematical Methods for Physics and Engineering is an indispensible handbook for the second year maths course. It may be worth purchasing a copy, but if not, your library should have it. The solutions manual is also useful, given a lot of the problems are similar to your question sheets.
Mathematical Methods in the Physical Sciences by Mary Boas is also a fine reference, highly recommended by the Mathematics department for their corresponding courses.
Practicalities
Supervisions will be weekly in 31C Churchill. Please hand in work by 5:00 pm the day before your supervision (or by noon if you're handing in on Sunday) to my pigeon hole in the Porters' Lodge.
Work
On the front page of your work, please summarise any issues you had with the problems or questions you have from the lectures. It's much more efficient if I know what we need to go over in advance.
This is only a rough guide; it might have to change depending on the pace of supervisions. Once we've got going, I suggest we cover a Tripos question each week as well.
1B NST mathematics
These are not the standard course question sheets. They're based on them, but have some extra questions to both improve your understanding and cover things that routinely come up in the exam but are absent from the lecturer's sheets.
They're a bit longer than the course sheets, but in exchange I won't be setting loads of extra Tripos questions this year.
| Supervision | Work |
|---|---|
| Michaelmas 1 | Fourier transforms |
| Michaelmas 2 | Suffix notation & vector calculus |
| Michaelmas 3 | Curvilinear coordinate systems |
| Michaelmas 4 | Green's functions for ODEs |
| Michaelmas 5 | Linear algebra #1 |
| Michaelmas 6 | Linear algebra #2 |
| Michaelmas 7 | Complex analysis |
| Michaelmas 8 (carried over to Lent) |
Power series solutions to ODEs |
| Lent 1 | Sturm–Liouville Theory |
| Lent 2 | Variational methods |
| Lent 3 | General solutions to PDEs |
| Lent 4 | Green's functions for PDEs |
| Lent 5 | Cartesian tensors |
| Lent 6 | Residues & Cauchy's theorem |
| Lent 7 | Complex methods |
| Lent 8 (carried over to Easter) |
Fourier transform methods |
| Easter 1 | Normal modes |
| Easter 2 | Group theory #1 |
| Easter 3 | Group theory #2 |
| Easter 4 | Representation theory |