Revisiting Single-Variable Calculus after Multi-

[feynman_fan]

Hello all! I was thinking about strengthening my knowledge of Calculus after I finish the course I am taking in Multivariable Calculus. I am in a particularly unique situation, as I am only going to enter high school next year.

I took the AP Calculus BC Exam last year and got a 5. The course I took was through John Hopkins Center for Talented Youth, and the textbook was Stewart. I also used Stewart for Multi, but I would love to revisit all of the topics in a more rigorous and proof-focused manner.

I have heard many good things about Spivak and Apostol, but I am open to other possibilities as well. I have recently been reading Linear Algebra Done Right by Axel after watching Gil Strang's 18.06 lectures, and am finding the proofs very enlightening. What would you recommend for my situation? I eagerly await all responses!

 

[MidgetDwarf]

Maybe try either Apostol/Courant/Spivak? Out of these, I find Apostol easier to read.

However, you can start learning Analysis if you find Linear Algebra Done Right readable. A good intro is Understanding Analysis by Abbot.

Once you get up the section before the generalized Reiman Integral (or you can cover it too), have a look at the multivariable Analysis book by Hubbard and Hubbard.