A Java Applet for Studying Ordinary Differential Equations

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Instructions on using and downloading the Applet

Tasks:

• Slope fields and solutions of equations of the form y'=f(x,y)
• same as above, but using variables y'=f(t,y) instead
• Direction fields and solutions of equations of systems of equations of form x'=f(x,y), y'=g(x,y)
• 3D systems x'=f(x,y,z), y'=g(x,y,z), z'=h(x,y,z)
• 4D systems x'=f(x,y,z,w), y'=g(x,y,z,w), z'=h(x,y,z,w), w'=k(x,y,z,w)
• 2D,3D,4D,5D,6D,7D,8D systems with choice of names of dependent variables (and choice of window size)
• y=y(x) Solution Verifier for comparing numerical solutions to exact and approximate formulas
• x=x(t), y=y(t) Solution Verifier for systems of 2 equations

Examples:

• Population Dynamics: Elks, Coyotes and Wolves in Yellowstone Park
• Circuit
• Simple Model of Sunami
• Two-Body Problem
• Limit cycle for the Van der Pol equation (another version one here)
• Hodgin-Huxley equations (includes a student assignment)
• Chemostat (includes a student assignment)
• Species competition (includes a student assignment)
• Gardner/Cantor/Collins Synthetic E.Coli Toggle Switch equations (includes a student assignment)

Contributions

• Jason Miller's tutorial on using the Applet