Calculus: A Comedy

March 23, 2010 Shawn Cornally

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.

• Manifesto
• Logistics

• 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):

• Dating Range vs. Available Singles

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:

• Why Spammers Keep Using the Word “Nigeria.”