I'll be finishing Calculus by Spivak somewhat soon, and want to continue into linear algebra and multivariable calculus afterwards. My current plan for learning the two subjects is just to read and work through Apostol volume II; is this a good idea, or would it be better to get a dedicated Linear Algebra book? Are there better books for multivariable calculus? (I don't think I want to jump right into Calculus on manifolds.)
EDIT: I'd like to add, as part of my question, something I mentioned in a comment below. Namely, is it useful to learn multivariable calculus without differential forms and the general results on manifolds before reading something like Calculus on Manifolds or Analysis on Manifolds? That is, do I need to learn vector calculus as it is taught in a second semester undergraduate course before approaching differential forms?
Best Answer
Try Multivariable Mathematics: Linear Algebra, Multivariable Calculus, and Manifolds by Theodore Shifrin. It shows how the two subjects are related.