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File containing challenge description.
First, follow through the general theory of solving differential equations:
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Solving an ODE Some basic methods for solving a differential
equation by computer.
then play with a simple Matlab code until you understand how it works:
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A simple oscillator A Matlab code to simulate a swinging pendulum.
This code demonstrates a simple method for solving an ODE.
Next, read through the general theory of modeling diffusion:
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Modeling Diffusion Explains how we model diffusion and its
connection to diffusion equations
and run + alter the relevant Matlab code below,
again making sure you understand how it works.
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A model of diffusion in 2D A Matlab code to simulate basic diffusion.
For the challenge, you will select one of the following three projects,
each of which combine spatial diffusion with a system that can produce oscillations.
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Predator-prey system Extending the Lotka-Volterra model for
ecological interactions.
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Fitzhugh-Nagumo Model Producing a neural model for cardiac waves.
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Belousov-Zhabotinsky Reaction A reaction diffusion system. (toughest challenge)
