I've been working through Spivak's Calculus for a few weeks; however, I am stuck on Chapter 5 (limits, epsilon-delta, etc.). I'm finding that I need to reference his earlier chapters (on inequalities) to follow the introductory proofs. Furthermore, I don't understand how he comes up with his methods for proving the theorems. Ideally, I would like to just 'grind' through the difficulties, but I am pressed for time--2 months+other daily activities--to learn the topics covered in high school BC calculus (AP curriculum). Due to these reasons, I am considering switching to another text, Art of Problem Solving Calculus, and coming back to Spivak later down the road. Based on my situation, would you recommend staying with Spivak or switching to the latter text?
A bit of auxiliary information: Spivak is my first introduction to Calculus; I need to learn BC calculus because the course I'm taking following the 2 months is multi-variable calculus.
In my opinion, I think people should stick with the common college texts to learn calculus: either go for Stewart or Thomas. They are always my go-to if I have to remember something.
Spivak is nice but it feels like a prop for the advanced student. Many of the analysis (epsilon-delta, inequalities, etc.) are used in a course in advanced calculus (typically in your third year of college) so you can ignore it.
For a typical multivariable calculus class, you should know
how to evaluate limits by squeezing, evaluation, or l'Hopital.
what continuity is.
what derivatives are and how to compute them.
how to use derivatives in optimization.
the chain rule.
how to integrate.
how to find areas and volumes via integration.
Most, if not, all of this, is used in Calculus BC.
TL;DR, find easier texts. The proofs can wait. Your local bookstore should have some decently priced material - a shop like Half Price Books is good for low cost calculus texts.