Worcester Polytechnic Institute

MA2051 - Ordinary Differential Equations
Maple Worksheets - C98



Worksheet Description
Introduction #1 Brief introduction to dsolve and DEplot for first-order equations.
Introduction #2 Brief introduction to dsolve and DEplot for second-order equations.
Euler's method Maple worksheet illustrating Euler's method
Heun's method Maple worksheet illustrating Heun's method
Euler #1 Simple blocks of Maple instructions that will do Euler's method for you.
Undetermined Coefficients #1 A simple block of Maple commands that will do all of the dirty work of undetermined coefficients for you. (A great way to check your answers.)
Euler #2 This turns the second-order equation into a system and runs Euler's method to build an approximate solution. Have fun!
Resonance This worksheet generates handles the "general" damped, forced spring-mass system. It allows you to plot the amplitude as a function of the forcing frequency.
Limiting Behavior This worksheet generates graphs in the phase plane for spring-mass systems. Some of the commands here can be useful when you start work on Project 2.
The REAL Pendulum This worksheet generates solution curves for the real, nonlinear pendulum and allows you to compare the results with the linearized model.
Competing Species This worksheet generates solution curves for a population model where two species compete for limited resources.
Euler's method (systems) This worksheet implements Euler's method for a nonlinear predator-prey model.
Heun's method (systems) This worksheet implements Heun's method for the same predator-prey model.
Euler's method (2nd order eqns.) This worksheet implements Euler's method for a damped mass-spring model.
Heun's method (2nd order eqns.) This worksheet implements Heun's method for the same mass-spring model.



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Maintained by: Nathan Gibson, <gibso@wpi.edu>
Last modified: Mon Apr 20 09:38:09 EDT 1998