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Paul's Online Math Notes: Modeling with Differential Equations
Notes explaining basic modeling with first order differential equations, looking at specific examples of Mixing Problems, Population Problems, and Falling Bodies.
Modeling, ODE
COMAP Collection of ILAPs
These student Interdisciplinary Lively Applications Projects developed over seven years are collected at the COMAP website (comap.com)Â
Modeling, ODE
Diffusion, Fick's Law
Graphs solutions of diffusion equations over time. Interface could be smoother. You have to click at different points on the timeline to get things graphed - animation would be helpful.
Modeling, ODE
Laplace Transforms IDE
Eleven interactive activities from the definition to solutions of ODEs
Laplace Transforms
Poles of the Laplace Transform and Behavior of Solutions
Applet that shows the poles of the Laplace transform in the frequency domain and the graph of the solution in the time domain simultaneously.
Laplace Transforms
First-Order Linear Systems
Enter (constant) coefficients for a first order autonomous system.
Graphic Methods
Free and Forced Motion Lab
User can enter (constant) coefficients for a second order differential equation with cosine forcing function and see the graph of the solution.
Graphic Methods
Scriptable ODEs
CLICK ON "SYSTEMS OF ODES" IN LEFT PANEL TO BEGIN. The first thing done is to rewrite the second order equation as a first order system and then the applet traces the solution through time.
Graphic Methods
Java Applet for Phase Plane
Plots the solution curves of a user-input two dimensional system of autonomous differential equations. It has a reasonable parser, flexibility, and speed.
Graphic Methods
CalcTool 3
This java applet provides a variety of graphing functionality supporting multivariable calculus.
General Tools, Vector Operations, Graphing Multivariable Functions, Partial Derivatives, Differentiability, Double Integrals, Vector Fields and Flowlines, Line Integrals

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