Preparation for Advanced Calculus?

[SMA_01]

I'm signed up to take Advanced Calculus 1 for the Fall semester, I think it's the equivalent of an intro Real Analysis course. I want to prepare ahead of time, especially because I heard it's challenging, does anyone know any books I can use to get a feel for the topic? I'm not too good with proofs, so I would like to really improve that skill.

 

[Jorriss]

Spivak. Calculus.

A phenomenal book on 'advanced' calculus - calc I but with rigor.

 

[micromass]

Second for Spivak.

A good book is also https://www.amazon.com/dp/052171978X/?tag=pfamazon01-20 (on proofs and writing mathematics)

 

[SMA_01]

Thank you, will look into it!

 

[mathwonk]

When I asked Lynn Loomis what I needed to brush up on before taking his advanced calculus class he said I should learn the proof that a continuous function on a closed bounded interval has a maximum and minimum value. I learned it from the advanced calculus book by David Widder. Of course that was in 1963, before Spivak wrote his book. That proof is one the the "three big theorems" in Spivak's Calculus book.