I've taken the single and multivariate calculus classes at my school, (college class offered in my high school for accelerated students). I'm currently a junior, but in the summer of my senior year, I plan to read a book on proofs, brush up on math glossed over by the american education system (combinatorics and geometry), and do spivak's calculus book and hubbards vector calc book simultaneously. Will spivak's book and hubbard's book cover all that would be covered in a standard college calculus track (this is rather vague, I'm not sure how to express this in words. What i am trying to ask is whether or not i could potentially replace an entire multivariate calculus course in college with hubbard's book or if his book is good, but lacking in content in some areas) The book is arrive some time in the next two weeks, and I'll compare the table of contents to a college syllabus when i get time. for now i rely on all you helpful peeps in physics forums. any comparisons with spivak's calculus on manifolds, and trombas vector calculus book would be helpful too. I am planning on majoring in ee and at least minoring in physics, but I do not mind focusing on the pure math side of calculus, as i find math equally as interesting.