For university level physical applied mathematics, Boas: (http://www.amazon.co.uk/Mathematical-Methods-Physical-Scienc...)

I'd also recommend Riley, Hobson and Bence, which has all the benefits and disadvantages of being bigger: (http://www.amazon.co.uk/Mathematical-Methods-Physics-Enginee...)

For A-level, most students I've taught want me to follow their school course, so I've mostly taught out of an array of textbooks of varying quality. On the whole, the standard A-level course books for EdExcel, AQA, OCR and the like are adequate, but only really as part of a taught course. If I cast my mind back, Bostock and Chandler was quite good, although I suspect it will be a bit retro by now with respect to syllabus changes - it was old when I was learning this stuff for the first time. That said, mathematics is one of the more stable subjects and the fundamentals don't change very much, so I'd definitely recommend looking at it. Obviously, if you're not looking for something to pass an exam with, classic books become a lot more appealing.

For a good grounding in a lot of maths, I have somewhat fond memories of Boas: http://www.amazon.com/Mathematical-Methods-Physical-Sciences...

Arfken was also tough, but excellent: http://www.amazon.com/Mathematical-Methods-Physicists-Sixth-...

Yes, these books are fucking expensive.

PS: I did a physics degree, so my favourite books are maths for physicists... maybe former Maths students will have "purer" books to recommend. Anyway, between these two, you'll have a good year or two of hard studying before you need to buy another one :-)