scheick1

Calculus 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.
    Please check them out and send me comments. Ultimately I will winnow (and extend) the list and add more incisive comments, with your help.
Statements in quotes are from the site in question.
    Send your comments to
    Ted Scheick scheick@math.unc.edu

1. Calculus with Mathematica.
http://www.ma.iup.edu/projects/CalcDEMma/Summary.html
This site has a collection of notebooks in Mathematica.

2. From the Indiana University Stat/Math Center (http://www.indiana.edu/~statmath/)
http://www.indiana.edu/~statmath/bysubject/calculus.html
A number of links to Mathematica (and Maple) notebooks for use in calculus.
http://www.indiana.edu/~statmath/bysubject/plotting.html
Here are instructions on plotting using Matlab, Maple and Mathematica.

3. The University of Tennessee has an extremely rich site.                                         Outstanding
http://www.math.utk.edu
    The entryway site. Teaching materials, software, topics, links. At UT, the calculus text is "Brief Calculus: Applications + Technology", by Tomastik, Saunders College Publishing. Evidently this book has student projects.
http://archives.math.utk.edu/
    There are math archives here, interesting. Much good stuff here. Teaching materials, topics, links. Some of them are listed below.
http://archives.math.utk.edu/visual.calculus/
    "Visual Calculus is a collection of modules which can be used in the study or teaching of calculus. Originally, this collection was designed for instructors to give some ideas how technology, in particular, computers, can be used in the teaching of calculus. Detailed instructions on implementing these ideas with various public domain, shareware and commercial software packages are provided. The collection has been expanded to include tutorials, interactive modules (MathView, Java, and Javascript) which can be used by either students or faculty and now also includes detailed instructions for TI-85 and TI-86 graphing calculators. As an additional aid for students, modules containing quizzes and drill problems have also been added."
http://archives.math.utk.edu/software.html#MathArch
    A collection of Math software and reviews. DOS, windows, Mac, commercial. Has categories in terms of course subject matter. Public domain, shareware, commercial and demos. Looks like lots of good stuff is there, free.
Calculus Resources On-line:
http://archives.math.utk.edu/calculus/crol.html
    "This area contains information and links to numerous Internet resources, which could be used for teaching and learning of calculus." There are links here to many other universities that are using computers in calculus courses.

4. Math Forum Internet Resource Collection - Outline Version.                                                     Outstanding
    One variable calculus:
http://forum.swarthmore.edu/~steve/steve/mathcalc.html
    Multivariable calculus:
http://forum.swarthmore.edu/~steve/steve/sevvarcalc.html
    There are a vast number of links here to sites involving the teaching of calculus.

5. Wolfram Research (Mathematica)
http://www.mathsource.com/         home page, searchable.
http://www.mathsource.com/cgi-bin/MathSource/Applications
    Here there are applications in many areas, by area
http://www.mathsource.com/cgi-bin/MathSource/Applications/Mathematics
    This has math apps, advanced.
http://www.mathsource.com/cgi-bin/MathSource/Applications/Education
http://www.mathsource.com/cgi-bin/MathSource/Applications/Education/Calculus
    Look at the
    Knox package         $30
    Lafayette College calculus packages. Many notebooks used in calculus labs (once per week).
    Lecture Labs in Ordinary Differential Equations. Some notebooks for a first ODE course.

6. Gavin's Calculus Projects by P. Gavin LaRose at Nebraska Wesleyan University.
http://brillig.nebrwesleyan.edu/~glarose/classes/calc/calcprojects.html
Here are many creative projects for calculus using Mathematica. Links to other sites with calculus projects or other calculus materials. Some of these look good to follow up on. Also, see his home page at
http://www.mathcs.nebrwesleyan.edu/~glarose/

7. The Mathematics Department at Indiana University of Pennsylvania (IUP)
Interactive calculus with applications, based on Mathematica.
http://www.ma.iup.edu/projects/CalcDEMma/Summary.html

8. International education softtware
http://www.ies.co.jp/math/java/calcjava.html
A few java calculus applets that illustrate some calculus ideas. Some are animated.

9. "The MathServe Calculus Toolkit" (Vanderbuilt)
http://mss.math.vanderbilt.edu/~pscrooke/toolkit.shtml
These look interesting. Some java applets and a variety of stuff.

10. On line calculus tutorials. (For student use only?)
Finite Mathematics and Applied Calculus Resource Page, Hofstra University.
http://www.hofstra.edu/~matscw/realworld.html
    A few tutorial topics in calculus and finite math.
Java Powered Calculus (and Mathematica):
http://www.usm.maine.edu/~flagg/jpc/
    Offered for credit by the University of Southern Maine. You can enter as a guest, read the course material, which is like a brief book, and run the software which illustrates calculus topics.
Karl's calculus tutor   ($5 donation):
http://www.netsrq.com/~hahn/calculus.html

11. Penn State. Several sites.
Course home pages and other instructional material is at
http://www.math.psu.edu/PSUmathhome/courses/
There are are a number of teaching aids, including an archive, for calculus and ODEs.
Graphics for the Calculus Classroom, by Douglas Arnold. (Penn State)
http://www.math.psu.edu/dna/graphics.html
Animated demos for 1) differentials and differences, 2) Computing the volume of water in a tipped glass, 3) Archimedes' calculation of p, 4) how the ball bounces, 5) secants and tangents, 6) zooming in on a tangent line, 7) a trigonometric limit, 8) the limit, 9) a nowhere differentiable function, 10) e, 11) the intersection of two cylinders. These consist of animated GIFs, but there is a JAVA version. They may be viewed on a web browser.

12. "Calculus Resources"
http://www.seresc.k12.nh.us/alvirne/apresc.html
A collection of resources for calculus using technology. Many have been listed in these pages.

13. Shodor Education Foundation
http://www.shodor.org
"The Shodor Foundation is a non-profit research and education organization dedicated to the advancement of science and math education, specifically through the use of modeling and simulation technologies. Included on this site are instructional resources and software ready to be used in the classroom". Much remains to be done, it seems. However, at
http://www.shodor.org/master/gnuplot/software/
You can use Gnuplot for 2D, 3D online plotting and animations. Cannot be downloaded.

14. Mathematics Connections On The Www Compiled by M. Alsani.
http://www.acsu.buffalo.edu/~alsani/mathonwww.html
Calculus mostly. Here is a good place to see what other people are doing. Some on line courses. Some other schools are using Maple or MathCad. Not much of immediate use??

15. The University of Minnesota Calculus Initiative
http://www.geom.umn.edu:80/education/calc-init/
Four detailed calculus labs.

16. Rose-Hulman University: Complex, Technology Based Problems in Calculus Home Page.
http://www.rose-hulman.edu/Class/CalculusProbs/
"We offer complex, technology-based problems in calculus with applications in science and engineering. These problems have a higher level of complexity than traditional text book problems and foster use of a computer algebra system. Each problem set includes discussions of related teaching issues and solutions worked in Mathematica."

17. DAU Math Refresher. George Mason University.
http://www.cne.gmu.edu/modules/dau/math/
Modular review of precalculus and calculus through integrals. Possible tutorial for students?

18. The Stat/Math Center at Indiana University
http://www.indiana.edu/~statmath/bysubject/calculus.html
A number of links to Mathematica (and Maple) notebooks for use in calculus.

19. Mathematics Education Technology Research at Imperial College
(a.k.a. Imperial College's Transitional Mathematics Project)
http://othello.ma.ic.ac.uk/
Pre-calculus: a book and some Mathematica notebooks.

20. 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.

21. H. Halpern's Mathematica notebooks
http://math.uc.edu/~halpern/
Notebooks for linear algebra are also available.

22. Rob Pratt's calculus page
http://www.math.unc.edu/Grads/rpratt/ma31fa98.html
Rob has a lot of good stuff and a list of good links. Some have been listed above.

23. Calculus and Mathematica, by Jerry Uhl, Bill Davis, Horacio Porta, University of Illinois at Urbana-Champaign
http://www-cm.math.uiuc.edu/
Here is a description of the course, and how to get it or samples.

24. Project CALC at Duke University.
http://www.math.duke.edu/modules/projcalc/
The first edition of Calculus: Modeling and Application is now available. There are lab manuals for a variety of computing tools, including Mathematica (commercially available).

25. Calculus@internet:
http://www.calculus.net/
http://www.calculus.net/mathview/
In construction, some reference stuff coming, but has the "top 20 calculus web sites" now and some labs, projects, homework, applications. Uses Maple. There may be a Mathamatica track coming.

26. Mathematics Connections On The WWW
http://www.acsu.buffalo.edu/~alsani/mathonwww.html
Calculus, Differential equationsXX, Linear Algebra, Statistics, Computer Science and other math links. Not much using Mathematica? Some good examples of what others do in Calculus with Maple, MathCad

27. Calculus & Differential Equations with Maple V (Interactive, developed at NCSU)
http://www2.ncsu.edu/eos/info/maple_info/www/
Could be interesting to look at, if you have Maple V. Not examined.

28. Computer-based Calculus, Old Dominion University
http://claymore.math.odu.edu/~web/cbii/calculus.html
The math department here has labs for calculus based on Maple and MathCad in pdf format. They can be downloaded and used by individuals, but are copyrighted and permission must be obtained for class use. I list this here as a sample of what folks are doing.