This second-year course introduces the basic mathematical machinery needed for quantum mechanics and for solving the most important differential equations that arise in undergraduate physics.

**MT2017:** this year’s lectures will start with linear algebra; there will be no revision of probability theory.

- Notes (version of 25 Nov 2017. Changes: appendix numbering; convergence in sec.8; YST corrections)

Problems: (updated on 4 Oct 2017: first problem set is revision; second is mostly new)

- Problems 1 on finite-dimensional vector spaces (mostly revision)
- Problems 2 on applications of linear algebra (material covered in wk 1’s lectures) (
**Update**25 Oct: correct statement of Reynolds’ transport theorem) - Problems 3 on Fourier methods (material covered in wk 2 lectures)
- Problems 4 on linear operators (covered in wk 3, approx)
- Problems 5 on PDEs (covered wks 4-6)

### Reading

I strongly recommend Fabian Essler’s notes and problems for this course from MT2009. My lectures cover broadly the same topics, but in a different order and with different mistakes.

*Mathematical methods for physics and engineering*by Riley, Hobson & Bence covers practically all of the material in this course and – most importantly – offers plenty of exercises.*Mathematics for physicists*by Dennery & Krzywicki has no exercises, but it provides accessible accounts of the concepts developed in this course.

### Revision lecture Friday week 4 TT 2018

I’ll work through the following past paper questions:

- 2013 A1 Q11
- 2012 A3 Q4
- 2011 A1 Q7, 11