Self learn calculus for uk a-levels?

Question

I am currently about to begin self studying for UK maths a-levels, however I am also wanting to gain a solid understanding of calculus. I know that calculus is covered in a-levels, but, the books for a-levels seem to be not as dense or as good as the US books I believe.

My question is this. Would a calculus book better explain calculus than general maths a-level books? And would it be a wise decision to study primarily off a calculus book and fill in all extra gaps required for a-leave in the a-level books?

Any advice would be very helpful. Thanks.

Answer 1

An undergraduate university level textbook will give a much deeper and fuller explanation of calculus, whereas an a-level textbook may be quite superficial. I would recommend learning at a university level and then get a realistic view of what you need for your exam afterwards.

Answer 2

It is probably best to have a both an up to date text so you are clear what exactly is in the syllabus and a more thorough reference for calculus with lots of worked examples and exercises (with answers at the back which is essential to build confidence when self-studying). I still have a copy of G.W. Caunt's "Introduction to Infinitesimal Calculus", Oxford University Press, which was used for decades in British schools from the 1950's through to the 1980's. Older reference works can be bought cheaply on one of the second hand book sites, and if you don't like one you can always search out another.

I also had a Data Tables and Formulae book which I annotated quite a lot with what I wanted to remember. My Reference was by Greer and Hancox, but I am sure there are more modern books now.

(I am around 50 now so my experience of school maths is a long time ago now.)

Answer 3

You said you are about to start studying A-Level Maths, so I think it might be slightly early to think about undergraduate calculus books, such as Spivak. I would recommend 'Pure Mathematics $1$' and 'Pure Mathematics $2$' by Bostock and Chandler. Despite being written a long time ago, these are the best A-Level textbooks I have ever seen; newer books tend to omit a lot of important proofs.

You are also right to point out that high school calculus in the US (such as AP Calc. BC) tends to cover more calculus than is taught in A-Level Maths and Further Maths. Elementary calculus/real analysis topics not covered in A-Level Maths and Further Maths include continuity, techniques for evaluating limits, and convergence and divergence of sequences and series. In the UK, such topics are typically taught in the first year of an undergraduate maths degree.