Important! To run these apps, follow instructions below.
Windows (.exe) apps: Click on the link, then double-click the downloaded file (if you can’t find it check the downloads folder). You may get a warning that looks like
Click on the More info link and then choose
Mac (.zip) apps: Click on the link, then double-click the downloaded file (if you can’t find it check the downloads folder, which Safari uses by default). With Chrome browser you choose where to put the downloaded .zip file; double clicking it creates the executable file. Now double click the executable file to run the app (Safari unzips automatically, so one less step).
Starter Mathlets
First Order Differential Equation Grapher: An applet for graphing first order differential equations. There is one graph window. Opens with the standard logistic differential equation.
Windows (.exe): First Order
Macintosh (.zip): First Order
Differential Equation System Grapher: An
applet for graphing systems of two differential equations. There are three
graph windows for viewing a phase plot and two time
plots at the same time. Can be used to graph second order equations by
rewriting them as systems. Opens with a standard mass-spring equation written
as a system.
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Windows (.exe): Systems |
Macintosh (.zip): Systems
More Complex Mathlets for
Differential Equations (Windows)
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Trace-Determinant Plane Three views of a linear second-order DE (written as a first-order system) with the trace and determinant of the corresponding matrix plotted in the trace-determinant plane. Bifurcations can be observed as parameters are changed. |
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Fit Mass-Spring Data was taken on a real mass spring system. The applet contains the data and the equation of a linear second-order DE (written as a first-order system). Adjust the parameters of the DE to fit the data. Because the data set is so large, the user cannot see both the beginning and end of the data clearly with one window setting. |
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Beats Time plots and phase plots for an undamped, driven mass-spring system. Opens with a plot that could be mistaken for resonance, but is in fact beats using Euler’s method with a too large step size. Switching to RK2 or RK4 one observes the beats, and by interactively changing the driving frequency one can see the transition from beats to resonance and back. |
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Mass-Spring vs Pendulum Includes two different second-order DE’s (written as first-order systems); one for a linear mass-spring system and one for a pendulum. There are three graph windows for phase plots and time plots. One can observe how the two systems match up: near the origin they are similar, but diverge as one zooms out. |
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Period Doubling Graphs solutions to the standard logistic DE (often used to model population growth) using both Euler’s method and RK2 superimposed. As the growth rate parameter is increased, one observes period doubling first in the Euler graph and then in the RK2 graph (and some other cool relationships). |
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Bifurcate Bifurcations of a logistic DE with harvesting. Two graph windows; one for graphing solutions to the DE and one for graphing the right-side of the DE as a function of the dependent variable. As the havesting parameter is changed one observes two views of the bifurcation point. |
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Poincare Illustrates the idea of a Poincare map which can be used to identify periodic solutions to periodic DE’s. Also works with autonomous DE’s (since they are periodic for any period)
Mathlets for iterated maps (discrete dynamical systems, Windows) Iterated
Map Grapher with Bifurcation Diagram and Lyapunov
Exponent Graph: An applet for a
first-order iterated map in one window, bifurcation diagram in a second, and
Lyapunov exponent graph in a third. Starts with the standard iterated
logistic map with one parameter.
Iterated
Map Systems Grapher: An applet for iterating systems of two maps.
Starts with the Henon map.
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Generic blank mathlets (Windows)
The mathlets below start out blank. You can customize your mathlet for a specific application or concept.