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## How I Teach Calculus: A Comedy in

# Calculus: A Comedy

## How I Teach Calculus: A Comedy in *n* acts

This is the table of contents for my ongoing series on the lessons I give in my Honors Calculus course. This list is not exhaustive of my classroom behaviors or activities, but they are the lessons I’ve had time to write about.

- Power Rule Families
- L’amuse Bouche
- Rates, Hubble, YOLO (Intro to class)
- Man v Food (Diff Eq)
- Programming Loops
- xkcd Dating Pool (Optimization)
- Drubbles (related rates)
- Exponentials and Glow sticks
- Trig Sub
- Differential Equations.
- Fugues and Exponents?
- Natural Exponent.
- Natural Logarithm.
- Numerical Integration.
- U-Substitution.
- Parabolic Arch
- The Papoose is Imminent
- Definite Integral.
- Area.
- Concavity.
- Optimization.
- Rates and Gas Tanks.
- Related Rates.
- Implicit Differentiation.
- Conics.
- Product and Quotient Rule Equivalence.
- The Chain Rule.
- The Product Rule.
- Income Taxes.
- The Power Rule.
- The Limit Definition of the Derivative.

# Rich Ideas

These are things that students sometimes bite into. I like them because I can see all sorts of calculus and math in them, but sometimes the students don’t, or do, who knows!

**xkcd (gets its own category):**

**YouTube Statistics:**

- Compare average views (integration)
- Compare views attained in comparable intervals (Bieber-Black, not relevant anymore)
- Function fitting fun

**Glowsticks**

- Temperature dependence
- pH dependence
- Exponentials

**Garden Hose**

- Flow and force (fireman’s hose style)
- Fill rates
- Pressure and flex in rubber
- Use it to propel objects (big, wheeled trash cans work great)

**Sailboats**

- Easily built from two Gatorade bottles (or human-sized from grocery store cardboard cantaloupe crates)
- Wind speed and kinematics of the boat
- Keel size
- Dependence of sail angle on whatever you want to measure.

**The Stock Market**

- Fourier and sine and cosine and slopes and oh my gosh it’s endless.
- How much crying does Mark Zuckerberg do on any given night?

**Motivating Trigonometry:**

- Find the “sine” and “cosine” of random shapes, like rhombus, squares, ellipses, whatever the kids want.
- Plan a camera pan using forced perspective (Hobbits!)

**Academic Papers Students Should Read:**

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