I am here for an unusual book recommendation request.
So, I have been studying contest math for a while now but now I also want to start learning Physics, partly because I have to (INDIA'S JEE EXAM), and partly because I think I'll also enjoy Physics Olympiad.
I have had an algebraic introduction to mechanics, but now that I want to study from good/advanced physics books, one of the first things I need is Calculus.
Now, as I have been preparing for (and will continue to prepare for) Math Olympiads, I feel like I have covered the necessary pre req's for calculus.
So, some weeks ago, I had started this book called Thomas' Calculus, which is by all means a very good book, but it is also over $1000$ pages long.
Now, I will hopefully complete the book within the next 12-15 months, and the basic portions within 4-5 months, but I don't think I want to/ have the luxury to wait for that long before starting physics.
Now, I have also read (tried, anyway) some calculus intro's in physics books, but , they are not very .... $nice$ . They usually just tell you the formulas and don't even often tell the proofs/ tell how to use them in Physics. Now, I do not think I can read Maths this way. (which is why I'm posting on MSE and not Physics SE)
Also, because I know calculus (real analysis) is a really important part of mathematics, I do not want to spoil my interest / intuition for it by reading a Physicists' guide to math, and a lot of people have told me it is much tougher to relearn some thing as compared to learning it.
So, now the thing I am looking for is a good guide to Calculus, mainly the amount needed for physics. But I do not want it to be like 3 pages (like most physics books calculus intro), and neither do I want it to be like 1000 pages. I am looking for something I can hopefully finish in, say a month. It does not need to be very easy either.
Any handouts/ books/ online resources would work.
Thank you!