ODE Resources

Updated 6 October 2006

The following is a list of sites that may be useful to ODE teachers and students. As participants of the Undergraduate Faculty Program (UFP), Mike Breen and Meg Dillon started the list during the Park City Mathematics Institute 2001. Other participants in the UFP contributed sites to the list.

Recent Additions

Open source Mathematica Addon 700 new functions, 60 packages, also parts of a book, ``Structure and Interpretation of Computer Programs.''

Online text (pdf) by Harry Watson, Jr.

Animations

Resources for Differential Equations, Maple and Mathematica resources, demonstrations, explorations, some small executable downloads, from the School of Mathematics at Georgia Tech

Animations for the Differential Equations Course, Bob Devaney, Boston University

Bifurcations

Saddle Node Classroom Demo, Bob Devaney, Boston University

Special Problem: Describe the Bifurcations, Bob Devaney, Boston University

Eigenvalues and Bifurcations, a project or lab, Rick Wicklin, formerly of The Geometry Center

Circuits

The van der Pol System, module, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

Classroom Demos

Introduction to Differential Equations, PowerPoint Show, Meg Dillon, SPSU

Origins of Differential Equations, PowerPoint Show, Meg Dillon, SPSU

Laplace Transforms, PowerPoint Show, Meg Dillon, SPSU

Growth and Decay, PowerPoint Show, Meg Dillon, SPSU

Growth and Decay 2, PowerPoint Show, Meg Dillon, SPSU

Resources for Differential Equations, Maple and Mathematica resources, demonstrations, explorations, some small executable downloads, from the School of Mathematics at Georgia Tech

Phase Line Motion: Quick Time Movie, Bob Devaney, Boston University

Saddle Node Classroom Demo, Bob Devaney, Boston University

Sink, Source, Node: Quick Time Movie, Bob Devaney, Boston University

Data Sets

Arizona Mathematical Software Data Files, David Lomen, et. al., University of Arizona

Explorations, Labs, Modules

(Extended activities for students to work through)

Maple Worksheets, numerical methods, direction fields, projects, by Joe Fadyn, Southern Polytechnic State University

Resources for Differential Equations, Maple and Mathematica resources, demonstrations, explorations, some small executable downloads, from the School of Mathematics at Georgia Tech

Cholesterol Levels in Humans, S. F. Ellermeyer, Kennesaw State University

Chemical Reactions, S. F. Ellermeyer and L. L. Combs, Kennesaw State University

An Epidemiology Model, Part I, Meghan Burke, Kennesaw State University

An Epidemiology Model, Part II, Meghan Burke, Kennesaw State University

Numerical Solutions of Differential Equations, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

World Class Sprints, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

Logistic Growth Model, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

Predator-Prey Models, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

Second-Order Linear Homogeneous Differential Equations with Constant Coefficients, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

Spring Motion, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

Forced Spring Systems, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

Trajectories of Linear Systems, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

The Pendulum, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

Lead in the Body, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

Gain and Phase Shift, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

The van der Pol System, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

Simulating the Battle of Trafalgar, Jim Marsalis, et. al., Woodrow Wilson Leadership Program in Mathematics

Differential Equations and Oscillations, Rubin H. Landau, the Krell Institute

Mass Transport Module, Contact person, Project Links, Rensselaer Polytechnic Institute

Variable Force and Mass: Rocket Liftoff, for use with Maple, Boyd Gatlin, Mississippi State University

Draining a Tank: Some Real-World Fluid Mechanics, for use with Maple, Boyd Gatlin, Mississippi State University

NASA Aquatics Lab Loading, Ed Chandler, Scottsdale Community College, Scottsdale, Arizona

A Chaotic Pendulum in Phase Space with Java, Hans Kowallik, Oregon State University

Eigenvalues and Bifurcations, a project or lab, Rick Wicklin, formerly of The Geometry Center

General Resources

Online text (pdf) by Harry Watson, Jr.

Resources for Differential Equations, Maple and Mathematica resources, demonstrations, explorations, some small executable downloads, from the School of Mathematics at Georgia Tech

The Boston University Differential Equations Project, Paul Blanchard, Bob Devaney, Glen R. Hall

Connected Curriculum Project: Materials for Differential Equations, projects, labs, and tutorials for using Mathcad, Maple, Mathematica and Matlab, Lawrence Moore, David Smith, et.al., Duke University

Gavin's DiffEq Resource Page, projects and labs employing Mathematica, Gavin LaRose, University of Michigan

The Mathematical Atlas: Ordinary Differential Equations, good information of a general nature, many bad links as of 23 July 2001, Dave Rusin, Northern Illinois University

S.O.S. Mathematics Differential Equations, Math Medics, L.L.C. Warning: this site has commercial support and insists that you accept cookies.

IDE (Interactive Differential Equations software)

Interactive Differential Equations, Addison Wesley Longman, publishers

Glider Project, Paul Blanchard, Boston University

Java Applets

Beta Java Applet version of Dfield and Pplane, John C. Polking, Rice Univesity

Phase Portraits for ODEs, Richard Mansfield, Pennsylvania State University, and Frits Beukers

Damped Harmonic Oscillator, Contact person, University of Alberta

Applet Demo Gallery, Mark Sutherland, Fun @ Learning

Interactive Math Programs, Professor Richard Williamson, Dartmouth College

A Chaotic Pendulum in Phase Space with Java, Hans Kowallik, Oregon State University

Predator Prey, difference equations, RUNS BETTER IN NETSCAPE, David Zachman, Colorado State University

Autonomous System, et. al., IES, Japanese software company

Linear Algebra Supplements

Matrix Operations, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

Eigenvalues and Eigenvectors, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

Maple

Waterloo Maple, Inc.

Maple Tutorials, from Wake Forest University

Maple Worksheets, numerical methods, direction fields, projects, by Joe Fadyn, Southern Polytechnic State University

Documents, Demos, and Examples, Maple V Resources from Jeff Lawson, Trinity University

Resources for Differential Equations, Maple and Mathematica resources, demonstrations, explorations, some small executable downloads, from the School of Mathematics at Georgia Tech

Spring Motion, module, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

Forced Spring Systems, module, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

Numerical Solutions of Differential Equations, module, for use with Maple, Mathematica or Matlab, module, Lawrence Moore, David Smith, et.al., Duke University

World Class Sprints, module, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

Logistic Growth Model, module, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

Predator-Prey Models, module, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

Second-Order Linear Homogeneous Differential Equations with Constant Coefficients, module, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

The Pendulum, module, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

Trajectories of Linear Systems, module, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

Lead in the Body, module, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

Gain and Phase Shift, module, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

The van der Pol System, module, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

Variable Force and Mass: Rocket Liftoff, module, Boyd Gatlin, Mississippi State University

Draining a Tank: Some Real-World Fluid Mechanics, module, Boyd Gatlin, Mississippi State University

Elementary Differential Equations Maple Worksheets, some for use with Differential Equations by Blanchard, et. al., Doug Meade, University of South Carolina

Some MAPLE exercises for Differential Equations, these are old but with some editing could be a valuable resource, Peter Monk, University of Delaware

Mathematica

Open source Mathematica Addon 700 new functions, 60 packages, also parts of a book, ``Structure and Interpretation of Computer Programs.''

Wolfram Research, Inc., purveyors of Mathematica

Resources for Differential Equations, Maple and Mathematica resources, demonstrations, explorations, some small executable downloads, from the School of Mathematics at Georgia Tech

Spring Motion, module, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

Forced Spring Systems, module, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

Numerical Solutions of Differential Equations, module, for use with Maple, Mathematica or Matlab, module, Lawrence Moore, David Smith, et.al., Duke University

World Class Sprints, module, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

Logistic Growth Model, module, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

Predator-Prey Models, module, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

Second-Order Linear Homogeneous Differential Equations with Constant Coefficients, module, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

The Pendulum, module, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

Trajectories of Linear Systems, module, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

Lead in the Body, module, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

Gain and Phase Shift, module, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

The van der Pol System, module, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

Gavin's DiffEq Resource Page, projects and labs employing Mathematica, Gavin LaRose, University of Michigan

Ordinary Differential Equations: Mathematica Computer Laboratory Projects, John H. Mathews, California State University Fullerton

Matlab

The MathWorks, developers of Matlab

A Practical Introduction to Matlab, Mark S. Gockenbach, Michigan Technological University

Introduction to Matlab, Kadin Tseng, Boston University

Matlab Summary and Tutorial, University of Florida

Spring Motion, module, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

Forced Spring Systems, module, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

Numerical Solutions of Differential Equations, module, for use with Maple, Mathematica or Matlab, module, Lawrence Moore, David Smith, et.al., Duke University

World Class Sprints, module, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

Logistic Growth Model, module, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

Predator-Prey Models, module, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

Second-Order Linear Homogeneous Differential Equations with Constant Coefficients, module, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

The Pendulum, module, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

Trajectories of Linear Systems, module, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

Lead in the Body, module, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

Gain and Phase Shift, module, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

The van der Pol System, module, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

Pedagogy

Articles about Differential Equations, this is a list of articles with bibliographic information but no links, John H. Mathews, California State University Fullerton

Pendulum

Nonlinear Pendulum Problem, Bob Devaney, Boston University

The Pendulum, module, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

Behavior of a Damped Pendulum, ideas for a project, Scott Sutherland, Stony Brook Institute for Mathematical Sciences

A Chaotic Pendulum in Phase Space with Java, Hans Kowallik, Oregon State University

Projects

Maple Worksheets, numerical methods, direction fields, projects, by Joe Fadyn, Southern Polytechnic State University

Differential Equations Resource Center Labs, laboratory and project ideas from Brooks/Cole publishers

Mass and Spring with Rubber Band, Paul Blanchard, Boston University

Tacoma Narrows Bridge, Paul Blanchard, Boston University

Cantilever Beam Project, Paul Blanchard, Boston University

Forced Cantilever Beam Project, Paul Blanchard, Boston University

Glider Project (for use with IDE), Paul Blanchard, Boston University

Sample Projects for Differential Equations, Art Heinricher, Worcester Polytechnic Institute

Simulating the Battle of Trafalgar, Jim Marsalis, et. al., Woodrow Wilson Leadership Program in Mathematics

A Chaotic Pendulum in Phase Space with Java, see especially Suggested Explorations, Hans Kowallik, Oregon State University

Eigenvalues and Bifurcations, a project or lab, Rick Wicklin, The Geometry Center

Short Problems

Describe Bifurcations as a Parameter Varies, Bob Devaney, Boston University

Nonlinear Pendulum (determine the motion of the pendulum from the solution curve; uses QuickTime), Bob Devaney, Boston University

Solvers

Winplot, Rick Parris, Phillips Exeter Academy

Instructions for Using Winplot, Al Lehnen, Madison Area Technical College in Madison, Wisconsin

Beta Java Applet version of Dfield and Pplane, John C. Polking, Rice Univesity

Phase Portraits for ODEs, Richard Mansfield, Pennsylvania State University, and Frits Beukers

Springs

Mass and Spring with Rubber Band, project, Paul Blanchard, Boston University

Spring Motion, module, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

Forced Spring Systems, module, for use with Maple, Mathematica or Matlab, Lawrence Moore, David Smith, et.al., Duke University

Damped Harmonic Oscillator, Contact person, University of Alberta

Tutorials

Maple Tutorials, from Wake Forest University

Are You Ready for Ordinary Differential Equations? Brian Hassard, State University of New York at Buffalo

Why Study Differential Equations?, Charles Tier, University of Illinois at Chicago

Calculus Review, a short quiz, Charles Tier, University of Illinois at Chicago

Serious Algebra and Calculus Errors, a short list, Charles Tier, University of Illinois at Chicago

Bifurcations, Equilibria, and Phase Lines: Modern Topics in Differential Equations Courses, Bob Devaney, Boston University

Simple ODE Solvers, a tutorial on Euler, Improved Euler, and Runge-Kutta with Java applet, Joel Feldman, University of British Columbia

S.O.S. Mathematics Differential Equations, Math Medics, L.L.C.

SPSU Mathematics

Direct corrections and contributions to Meg Dillon.

Updated 28 August 2006