Continue on to elementary real analysis or review calculus?

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Reviewing calculus concepts, particularly limits, continuity, sequences, and series, is beneficial before self-studying basic real analysis. While techniques for calculating integrals and derivatives are less critical for this purpose, a solid understanding of foundational calculus is essential. Multivariable calculus is not necessary for elementary real analysis. Engaging with theoretical calculus texts like Spivak's or Apostol's is recommended, as they serve as effective reviews while also introducing key real analysis concepts. Working through these books can provide a comprehensive understanding of both calculus and analysis.
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Im kind of rusty on my calculus II and III and I was wondering if I should review it before I try to self teach myself basic real analysis? I have some experience with basic proofs.
 
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It's a good idea to review concepts like limits, continuity, sequences, and series. For basic real analysis this will be more important than the various techniques for calculating integrals and derivatives, which make up the bulk of most calculus courses. Also, multivariable calculus is not a prerequisite for elementary real analysis.

Getting your hands on a theoretical calculus book such as Spivak's or Apostol's might be the most productive way to "review" calculus if your goal is to study real analysis. Indeed these books are gentle introductions to real analysis as much as they are calculus books.
 
I also think it might be a good idea to work through a book like Spivak or Apostol at this point. It will be a very thorough review of calculus and it will introduce you to the ideas of analysis.
 

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