Differential Equations, Linear Algebra and Technology

    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.