I got myself a copy of Spivak's Calculus because I wanted to learn Calculus right & as far as the text goes, it's marvellous. It's very fresh, especially for a 30-40 year old text, & the main body of the text, so far, has helped me a lot. I've learned a lot of calculus from other books, apart from some integration stuff which I'm going over in Thomas' Calculus concurrently.
I know enough Calc to get away with doing well in Physics, so far, and am continuing to learn.
But, my problem comes from the end of chapter questions. As you would expect, a lot of people complain about the difficulty of these questions due to the demands they place on the student to "shape up" & I don't mean to be one of them but I've only been studying mathematics for about 8-9 months after a lifetime of failing basic math in school.
I don't want to skimp on Spivak as I know that the rewards will be great but how can I be expected to give three analogous proofs to the Schwarz Inequality? How can I obtain the Lagrange Interpolation formula? I can't even do Lagrangians in mechanics yet, let alone Interpolations...
I've never been exposed to any kind of book that explains how to go about doing these things. You can't do abstract algebra without precursors & you can't do calculus without precursors.
I've heard W.G. Hardy's book A Course in Pure Mathematics would teach me some of what I'm looking for. Can you sympathise with my situation & perhaps give some guidance?
A Course of Pure Mathematics - Wikipedia, the free encyclopedia