## 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.