I am from Pakistan where I have completed the A level mathematics in my first year of a level. I plan on taking the further mathematics Course this year. I am looking for a good book to self teach my self differential integral calculus in the next two months. I am extremely worried that calculus in a level mathematics is too basic as compared to what a math oriented student might learn in the USA, where I plan to apply for university for physics. The problems i have come across are a walk in the park, with only the most basic Of integrals and little to nothing about their application ( other than areas..)
I am looking for a book which can provide me with a good understanding of calculus, different techniques and tricks integral and Differential calculus, and good quality questions, preferably without getting bogged down too deep in theory ( like spivak’s book, from what ive read). Also, would MIT open courseware be a good place to start,
I Know that this isn’t a math question but I thought this would be the best place to seek help From experienced people, rather than something like quora where people Randomly give their opinion.
P.S i am already done with what be called pre calculus
My guess is that, under the parameters you define, your A-level would be adequate to take on a University degree.
As for a self-study book, I highly recommend "Mathematical Analysis" and "Calculus", both by K.G. Binmore (1977 and 1983 respectively). He is clear and thorough, and does not overcomplicate things unnecessarily. He also includes comprehensive solutions in the back, which in the case of "Mathematical Analysis" are just about complete.
"Mathematical Analysis" does include Calculus in it, but single-variable only, and it is limited to real numbers and functions. It covers trigonometric, exponential and logarithmic functions, and as a final flourish explores the Gamma function.
"Calculus" takes on multi-variable functions, and covers partial differentiation and multiple integrals, as well as (very briefly and un-thoroughly) complex functions and differential equations.
EDIT: Re-reading your question, "Mathematical Analysis" would actually probably just be revision for you -- although I do still recommend it.