justcalculus
Multivariable calculus notes, slideshows, and explorations
Blog
Can You Bake the Optimal Cake Using Calculus?
Solving FiveThirtyEight's Riddler: maximize the volume of a three-tiered cake that fits inside a cone using multivariable calculus.
Does a Lampshade Cast a Hyperbolic Shadow?
Using parametric plotting and Mathematica to prove that the shadow a lampshade casts on a wall is a pair of hyperbolas.
Modeling the Rolling Shutter Effect
Using Mathematica to simulate how a rolling shutter distorts a spinning propeller, from polar plots to contour plots to animated distortion.
The Riemann Sphere as a Stereographic Projection
Visualizing stereographic projection and the extended complex plane with an interactive Wolfram Demonstration.
Parameterized Families of Elliptic Curves with Large Rational Torsion Subgroups
Exploring one-parameter families of elliptic curves with rational torsion points of order 4 through 12, with an interactive Wolfram Demonstration.
Lecture Notes
All 13 lessons are available as interactive HTML5 slideshows, downloadable PDFs, or video lectures. Topics range from parametric plotting through Stokes' Theorem.