Resources for a Modern Differential Equations Course

Henry J. Ricardo
Department of Mathematics
Medgar Evers College (CUNY)
1150 Carroll Street
Brooklyn, NY 11225
(718) 270-6118
herme@cunyvm.cuny.edu

After teaching calculus for several semesters using the CCH materials, I felt it was time to consider teaching a modern, reform differential equations course. I attended conferences and workshops. I read the journals and examined every recent textbook I could find. I learned about the power and limitations of graphing calculators and various software products. Finally I developed the picture of the kind of course I would try to teach.

To me, a "modern" differential equations course is one that develops a lean and lively group of topics from a dynamical systems perspective and uses technology to treat these topics graphically, numerically, and analytically. Such a course acknowledges that many (most?) differential equations cannot be solved in closed form and uses qualitative and numerical methods to analyze solutions. With emphasis on a student's ability to analyze problems orally and in writing, such a differential equations course is a natural successor to a reform calculus sequence.

What follows is a (partially annotated) list of resources that I hope will help others devise their own modern differential equations course. These resources are grouped into four categories: books, journal articles, software, and Internet sites. I welcome comments and additions.

BOOKS:

ARTICLES:

SOFTWARE:

See the College Mathematics Journal Special Issue on Differential Equations, pp. 458- 461, for brief reviews of a dozen ODE solvers. Issues of the C*ODE*E newsletter (see ARTICLES) sometimes contain reviews of software. ODE Architect has been developed with NSF support by C*ODE*E and is available through John Wiley & Sons and Intellipro, Inc. Page xi of Zill's book (mentioned above) has a list of nineteen programs and their publishers/distributors. Also, Interactive Differential Equations (IDE), a CD-ROM with workbook by B. West, S. Strogatz, J. McDill, and J. Cantwell, will be published in July, 1996 by Addison-Wesley Interactive. (See the first item under INTERNET SITES for further information.)

INTERNET SITES:

http://awi.aw.com/products.html#mathematics
Addison-Wesley Interactive page advertising Interactive Differential Equations (IDE). (See reference under SOFTWARE heading.)
http://brillig.nebrwesleyan.edu/~glarose/delabs/
Bill McClung, Gavin LaRose, and Dick Vogt at Nebraska Wesleyan U....Course material (including 9 Mathematica labs), 3 projects, and the Spring 1996 syllabus; plain TeX and PostScript files; physical configuration of computer lab
http://cross.sewanee.edu
Clay Ross at The U. of the South...on-line supplements to his DE book (see above)...Mathematica notebooks...DOS and Mac formats
http://math.bu.edu/odes/
Boston U. Differential Equations Project...information about the Blanchard/Devaney/Hall text (see above)...Instructor's Manual, errata...workshop information...sample syllabus; articles on teaching differential equations
http://math.bu.edu/INDIVIDUAL/bob/
Bob Devaney's home page at Boston U....other ODE information and syllabi for various dynamical systems courses taught (or planned to be taught) at BU
http://www.cms.uncwil.edu/~herman/detech.htm
Eric R. Kaufmann at U. of North Carolina at Wilmington...Differential Equations Lab Manual...classroom examples (theory and applications)...PostScript and Maple V files...traditional approach, but with technology
http://www.ma.iup.edu/MathDept/Projects/CalcDEMma/Summary.html
Indiana University of Pennsylvania...description of computerized learning environment...Mathematica notebooks for calculus and differential equations
http://www.math.arizona.edu/software/uasft.html
U. of Arizona...extensive software for calculus, ode's, and other topics, including "Are You Ready for Ordinary Differential Equations?" and other diagnostic programs
http://www.math.hmc.edu/codee/home.html
Home page (at Harvey Mudd College) for C ODE E (Consortium for Ordinary Differential Equations Experiments)...on-line issues of the newsletter, reviews of DE solvers, graphics
http://www.math.rpi.edu/~boycew/index.html
William Boyce's home page at Rensselaer Polytechnic Institute...course information, including assignments and class handouts...excellent Maple worksheets
http://www.math.scarolina.edu/~meade/math242
Doug Meade, U. of South Carolina...course notes, syllabus, exams, projects, homework assignments (and solutions)...Maple worksheets; guest lectures; material from other universities
http://www.math.unl.edu/
Glenn Ledder, U. of Nebraska (Lincoln)...DE course materials...Maple and Mathematica files; other math course materials
http://www.uidaho.edu/~calvert/
Jim Calvert at the U. of Idaho (Moscow)...course information, Maple worksheets...traditional, but with technology
http://www.wam.umd.edu/~stuck/schol/scholhome.html
The SCHOL Project at the U. of Maryland (College Park)--using mathematics software to enhance undergraduate education...samples from the texts Differential Equations with Maple [Mathematica] (see above), PostScript images of M/M solutions
http://zelda.thomson.com/rcenters/diffeq/diffeq.html
Differential Equations Resource Center (PWS Publishing Co.)...discussion threads, exercises, problems, lab projects, applications...software...on-line courses and course notes...information on workshops, symposia, conferences...labs at Rose- Hulman Inst. of Tech., Nebraska Wesleyan, et al....labs to accompany Differential Equations with Boundary Value Problems (Third Ed.) by Zill and Cullen; the Electronic J. of Differential Equations; Mathematics Archives (U. of Tennessee)


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