# Mathlab Math 221 Support Page

The lab consists primarily of dual booting Windows 2000/Linux Pentium 4 machines. There are also 4 old Macs.

Linear algebra capable programs to support Math 221 in the lab include:

Maple
is installed on all Windows and linux machines with support notes at http://www.mathlab.cornell.edu/support/maple.html.
Some linear algebra samples for getting started include:
linalg: html format | Basiclinalg.mws (more symbolic support)
LinearAlgebra: html format | BasicLinearAlgebra.mws (faster numerical support)
Entering Matrices: html format | EnteringMatrices.mws
Matlab
is installed on all pentium 4 linux and windows 2000 machines with support notes at http://www.mathlab.cornell.edu/support/matlab/using_matlab.html.
Mathematica
is installed right now on two machines; the linux side of indian and the Windows 2000 side of tahoe.

We have a number of reference books in the lab on using Maple and Matlab within linear algebra courses. (Specific List Forthcoming)

A general listing of references in the lab is at http://mathlab.cit.cornell.edu/references/references.html.

The lab also has much support for differential equations. For the moment you might refer to our Math 420 support page http://mathlab.cit.cornell.edu/support/m420_support/m420_support.html and the differential equation ideas below.

### Some Ideas for Computer Usage to Enhance a Differential Equations Course:

• 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

At most times when the lab is open, consultants have ready access to immediate support by telephone, so please don't hesitate to ask questions when you have them.