This is a collection of links gleaned
from the WWW and from colleagues and graduate students at UNC. I have not
checked them out thoroughly. Some of them look superb, and others may be
of questionable value. I have added my first impressions with the links.
There does not seem to be many sites devoted to linear algebra. If you
find more, let me know. There are a few scattered ones using Maple or Mathematica
that are not listed here.
Please check them out and send me
comments. Ultimately I will winnow (and extend) the list and add more incisive
comments, with your help.
Send comments to
Ted Scheick scheick@math.unc.edu
Differential Equations
1. Internet Differential Equations Activities
http://www.sci.wsu.edu/idea/
Supported by NSF and Brookes-Cole.
Has java software to run the applications. Now has 9 projects, mostly done?
Has a "java code generator" to help in writing applets. The second package
is a more sophisticated graphics package for Microsoft Windows machines.
It is called DynaSys. It is posted in a self-extracting compressed form
(using PKZIP 2.04). The file is smaller than 200KB.
DynaSys can perform the following
tasks.
Two dimensional
phase portraits;
Three dimensional
phase portraits;
Two dimensional
iterated maps and stair-step diagrams;
Text displays;
May be used either with MS Windows 3.1, or with Windows
95.
"The third package is a demonstration of certain aspects
of chaos, fractals and Julia sets, developed by C. J. Kentler. It examines
the behavior of the logistic map, and shows how it becomes chaotic as µ
increases. The package also includes java applets for bifurcation, and
Julia sets."
2. Math Forum Internet Resource Collection - Outline Version.
Outstanding!!
Ordinary differential Equations
http://forum.swarthmore.edu/~steve/steve/ode.html
Partial differential Equations
http://forum.swarthmore.edu/~steve/steve/pde.html
A Vast number of links.
3. Penn State: A phase plane plotter on line.
http://www.math.psu.edu/melvin/phase/newphase.html
Nullclines, direction field and orbits.
Click the screen for initial conditions. Java applet. Do screen capture
to print. Cannot adjust the time range, so only bits of orbits are plotted.
4. Java applets to plot phase planes from Scott Herod
at the University of Colorado.
http://amath-www.colorado.edu/appm/faculty/sherod/classes/Phasor/phase.html
Point and click initial conditions.
No nullclines. Can control t range. Printing is not working??
5. The Differential Equations Resource Center
http://diffeq.brookscole.com/
There are 6 project ideas here that
look good. A good review of software.
The Boston University Differential Equations Project:
http://math.bu.edu/odes/
Their book is published by Brooks-Cole.
Some references are here. You are referred to Brooks-Cole.
6. The Consortium for Ordinary Differential Equations
Experiment
http://www.math.hmc.edu/codee/home.html
"The goal of the Consortium of ODE
Experiments is to share the rapidly growing wealth of computational instruction
techniques with as many teachers of differential equations as is possible.
We feel that the computer is a vital tool in helping students understand
and visualize concepts in differential equations, and we would like to
help stimulate interest in computer experiments as an aid to teaching differential
equations."
At first sight, it looks like a newsletter
with articles about using computers in ODE courses. Has a review of popular
ODE solvers (e.g. ACSL, DSTOOL, MDEP, Mathematica, Maple, Phaser).
7. NWU Differential Equations Resource Page Nebraska Wesleyan
University
http://www.mathcs.NebrWesleyan.edu/delabs/
This page documents the course materials
(labs and projects). There are 10 labs and many projects. It looks like
an excellent resource. Mathematica is used. The files are in DVI and Postscript
form. You will need a DVI viewer or Ghostview/Ghostscript for viewing Postscript
files. Instructions for obtaining these are at this site. Some projects
can be read without all this hassle.
8. Rose-Hulman Institute of Technology. Problem sets in
ODEs and other topics.
http://www.rose-hulman.edu/Class/CalculusProbs/Problems/catlist.html#DEs
Searchable lists of problems. The
problems, solutions and discussions are given. Mathematica worksheets can
be downloaded by email.
9. Differential Equations - Mathematica files
http://www.math.utep.edu/classes/3226/Mathematica/mathematica.html
A collection of Mathematica worksheets
for ODEs.
10. Ordinary Differential Equations using MATLAB, by John
C. Polking. Published by Prentice Hall.
http://math.rice.edu/~polking/odesoft/
This is a manual for using MATLAB
in a course on Ordinary Differential Equations. It can be used as a supplement
of almost any textbook.
DFIELD and PPLANE can be downloaded
here.
11. IDEA Internet differential equations activities
http://www.sci.wsu.edu/idea/
12. The Stat/Math Center at Indiana University
http://www.indiana.edu/~statmath/bysubject/differential.html
This site has instructions on solving
differential equations using Matlab, Maple and Mathematica.
13. Penn State: Course home pages and other instructional
material.
http://www.math.psu.edu/PSUmathhome/courses/
Here are a number of teaching aids,
including an archive, for calculus and ODEs.
14. Differential Equations - Mathematica files
http://www.math.utep.edu/classes/3226/Mathematica/mathematica.html
A collection of Mathematica notebooks
for ODEs to go along with the book "Differential Equations" by Blanchard,
Devaney and Hall.
Linear Algebra
Two relevant books that I have asked
to be purchased for the library:
Linear
Algebra Labs With Matlab, David R. Hill, Prentice-Hall
"Using a variety of class-tested exercises
and the "discovery" method, this supplement reinforces key concepts in
linear algebra and can be used with any text. They also offer opportunities
for experimentation, encourage students to think about algebraic relationships,
and provide geometric foundations where appropriate.
Matlab Project Book for Linear Algebra, Rick L. Smith, Prentice-Hall.
1. Math Forum – linear algebra
http://forum.swarthmore.edu/linear/linear.html
Classroom material, software, projects.
2. ATLAST Project
A project to Augment the Teaching of Linear Algebra through
the use of Software Tools
http://www.umassd.edu/SpecialPrograms/Atlast/welcome.html
3. EigenExplorer
http://www.cs.gordonc.edu/~senning/Java/EigenExplorer.html
A java applet that plots x and Ax
(two dimensions). The author is working on more materials.