Notes on Calculus 1

These are notes for 1st semester calculus - Limits, derivatives, applications of derivatives, basic integration.

Comments: The section on limit theorems contains a lot of epsilon-delta proofs, which are usually not covered in a first-term calculus course. The related rates examples are complete, but need reworking. I need to show a graphing example step-by-step, the way I would do one in class. I need to write up proofs of L'Hôpital's rule and the "only one critical point" theorem that is used in the max-min word problems section; this will require sections on the extended Mean Value Theorem and the Intermediate Value Theorem for derivatives. The extended Mean Value Theorem is usually proved using Rolle's Theorem, which is proved using the existence of maxima and minima for a continuous function on a closed interval. That result in turn requires foundational stuff; you can use completeness for the reals, the Nested Interval Theorem, or Dedekind cuts [which are all equivalent]. That's a lot of writing! So this is my excuse for not having done it yet.

I need to write up the section on hyperbolic functions.

[September 8, 2022] I corrected some typos in the notes on limit theorems.


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