I’ve struggled with how to write about calculus. The standard techniques seem to be:
- The “bag of formulas”: memorize ‘em and move on
- The anal-retentive, rigorous treatment: written by math robots, for math robots!
- The happy smiles tour: oversimplifications without examples (Calculus helps scientists solve problems!)
No, nyet, nein! I know what I need: intuition (What does it really mean?) followed by examples to back it up. I want a calculus series that lets calculus be calculus — wild, interesting, and fun.
The Explanatory Approach
I started writing in a vacuum, but realized I don’t remember calculus. I need a refresher — in fact, I need the insights I want to share! These articles are for us both (it’s what I’d want to relearn the subject), and here’s my approach:
- I’m reading Elementary Calculus: An Infinitesimal Approach [free pdf]. It teaches calculus using its original approach (infinitesimals), not the modern limit-based curriculum. My goal is intuition, so this works well.
- As I study the chapters, I’ll share the insights I find and the concepts I struggled with.
- I’ll sprinkle examples along the way. They’re a gut check, not the focus (if you want practice problems, the book has plenty).
It’s a lack of insights, not information, that makes calculus hard. We don’t need another course repeating the definitions that confused us the first time (Here’s the definition of a limit, again!).
We shouldn’t be struggling with the true meaning of a subject centuries after its invention. This is my intuition-laced hat in the ring.
The Calculus Articles
The goal is to be concise, informal, and fun. Dabble, skim and ignore the examples if needed — focus on the insights. The elegance of calculus can be appreciated progressively: we don’t need astrophysics to enjoy a starry night.
Small numbers: Limits and Infinitesimals
- Learning Calculus: Overcoming Our Artificial Need for Precision
- Understanding the need for small numbers (in progress)
Measuring Changes: Derivatives
Accumulating Changes: Integrals
This post is the table of contents for the series. Happy math.