.js-id-current, .js-id-previous
Math 222 Differential Equations

Math 222 Differential Equations

I coordinated and taught this class between 2017 and 2022.

Supplements to Sections 10.1 & 10.4 of Boyce

Supplement to 10.1 Supplement to 10.4

Math 450H & Math 451H Capstone 1 & 2

Math 450H & Math 451H Capstone 1 & 2

Spring 2005, Spring 2006, Spring 2010, Fall 2012, Spring 2013

2013 Project Waves in a Chain of Pendulums

The goal of this project was to observe and understand oscillating patterns in a large array of pendulums. This system provides a simple experimental model in which solitons, or something much like them, can be observed.

MATLAB Projects

MATLAB Project 1: Complete the Onramp tutorial, due 1/28/2022 MATLAB Project 2: Slope Fields, due 2/11/2022 MATLAB Project 3a, due 3/4/2022 MATLAB Project 3: Euler’s Method, due Sunday, 3/11/2022 MATLAB Project 4: Computational Exploration of the SIR Model, due 5/5/2022

Dynamical Bias in the Coin Toss

2005-2006 Project In a celebrated article in SIAM Review1, Diaconis, Holmes, and Montgomery show that under general conditions, a coin is inherently biased to land heads-up if it leaves the hand heads-up.

Determining $g$ with a basketball, a videocamera, and a yardstick

Everyone knows that objects falling under the influene of gravity near the surface of the earth experience constant acceleration of about 32 ft/s^2^, neglecting air resistance. Anyone who has taken elementary physics knows that the speed of a ball after it collides with the floor will be equal to its speed before impact, multiplied by ts coefficident of restitution.

A Mechanical Analog of the Two-Bounce Resonance

A Mechanical Analog of the Two-Bounce Resonance

In Spring 2010, the course featured several experiments in chaotic scattering, including, pictured above, the scattering of a laser beam off a system of three cylinders. The highlight of the class was an experiment to reproduce the chaotic dynamics of a soliton colliding with a localized defect (previously studied by Goodman and Haberman) in a simplified experimental setting: the motion of a ball rolling on a specially engineered surface.