Calculus I/II

Some programs I have written for use while teaching introductory calculus courses.

Riemann Sums

Lets the user enter a function, and adjust the parameters for various left/right/midpoint Riemann sums.

Disks And Washers

The user may enter a function and visualize the disks-and-washers decomposition of its volume of revolution.

Cylindrical Shells

The user may enter a function and visualize the cylindrical shells decomposition of its volume of revolution.

Calculus III/IV

Some programs I have written for introducing parametric equations and fields.

Parametric Curves

A graphing calculator for parametric curves.

Parametric Surfaces

A graphing calculator for parametric surfaces.

Vector Fields

A graphing calculator for vector fields in 3-space.

Line Integrals

A graphing calculator for line integrals.

Differential Geometry

Some programs potentially useful in teaching Differential Geometry.

Geodesics on a Gaussian

Numerically solving the geodesic equation for the metric on the graph of $\exp(-x^2-y^2)$ from $\mathbb{R}^3$.

Geodesics on a Torus of Revolution

Solving the geodesic eqatuion on a torus of revolution in $\mathbb{R}^3$ with the induced metric. Adjust the initial location and direction to explore the positively curved exterior, negatively curved interior, and the effect of the umbilic points.

Fourier Analysis

Some programs from teaching analysis.

The Ptolemaic System

In some sense the precursor to sinusoidal expansions, this Greek geocentric cosmological system successfully modeled non-circular motion as a sum of two circular motions.

A Square Orbit?

A configuration of many epicycles, giving a square orbit!

Sinusoidal Expansion

A static visualization of a square wave and its expansion into sinusoids

Complex Valued Fourier Series

What does a fourier series look like, as a function from R to C?

PDEs

Some programs from introductory PDEs.

The 1D Wave Equation

Solving the wave equation on a line with Fourier Series.

The Wave Equation on a Rectangle

Sliders allowing you to move about within a finite dimensional subspace of sinsusoidal soltuions.

The Wave Equation on a Disk

Illustrating the Bessel function basis.