** Next:** Algebra and Number Theory
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** Previous:** Linear Algebra

- Errors in ODE integration schemes as a function of
method and step size. Empirical measures of the order of a method.
- Experiment with graphical integrators and then argue
for the correctness of some of the results seen. (e.g. fences,
vertical asymptotes, behavior at infinity.)
- Bifurcations of 2d homogeneous linear systems.
- Matrix exponential and applications.
- Computer assistance for variation of parameters.
- Computer assistance for change of coordinates.
- Logistic, predator-prey and generalizations as a
function of parameter.
- Computer algebra systems in scratchpad mode to
assist with power series and Frobenius methods solutions.
- Use computers to bring some special functions to life.
- Study some basic low codimension bifurcations (e.g.
saddle node, pitchfork, hopf.)
- Sensitive dependence on initial conditions.
- Study attractive periodic points as a function of
parameter in the 1d discrete logistic equation to see chaotic behavior.
- Explore the restricted 3 body problem numerically.
**Web Resources:**
**Java and Matlab versions of Dfield and Pplane:**
- http://math.rice.edu/polking
**Dynamics Solver Source:**
- http://tp.lc.ehu.es/JMA/ds/ds.html
**Interactive Differential Equations:**
- http://awlonline.com/ide/
* (All labs available online in pdf
format!)*
**IDEA:**
- http://www.sci.wsu.edu/idea
**CODEE**
- http://www.math.hmc.edu/codee/main.html
**Mathlab: **
- http://www.mathlab.cornell.edu/computer_and_portfolio/index.html#ODE

*root*

*2002-08-26*