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:

• Differential Equations with Mathematica - M. Abell and J. Braselton
  (Academic Press Professional, Orlando, FLA: 1993) ISBN 0-12-041539-9
• Differential Equations with Maple - M. Abell and J. Braselton
  (Academic Press Professional, Orlando, FLA: 1994) ISBN 0-12-041548-8
• Modern Differential Equations: Theory, Applications, Technology - M. Abell and J. Braselton [+ Instructor's Resource Manual, Student Resource Manual]
  (Saunders, Orlando, FLA: 1996) ISBN 0-03-098337-1
• Differential Equations with Derive - D. C. Arney
  (MathWare, Urbana, IL: 1993) ISBN 0-9623629-3-X
• Exploring Differential Equations with DERIVE - D. C. Arney [+ Solutions Manual]
  (Addison-Wesley, Reading, MA: 1993) ISBN 0-201-50723-4
• Differential Equations (Preliminary Ed.) - P. Blanchard, R. Devaney, and G. Hall
  (PWS, Boston: 1996) ISBN 0-534-95004-3
• Differential Equations: A Modeling Approach - R. Borrelli and C. Coleman [+ Instructor's Manual]
  (Prentice-Hall, Englewood Cliffs, NJ: 1987) ISBN 0-13-211533-6
• Differential Equations: A Modeling Perspective (Preliminary Ed.) - R. Borrelli and C. Coleman [+ Instructor's Manual]
  (Wiley, NY: 1996) ISBN 0-471-04181-5
• Differential Equations Laboratory Workbook: A Collection of Experiments, Explorations and Modeling Projects for the Computer - R. Borrelli, C. Coleman, and W. Boyce
  (Wiley, NY: 1992) ISBN 0-471-55142-2
• Elementary Differential Equations and Boundary Value Problems (Sixth Ed.) - W. Boyce and R. DiPrima [+ Student Solutions Manual, ODE Architect]
  (Wiley, NY: Aug., 1996) ISBN 0-471-08955-9
• Differential Equation Models - ed. by M. Braun, C. Coleman, and D. Drew
  (Springer-Verlag, NY: 1983) ISBN 0-387-90695-9
• Explorations in Differential Equations Using Maple - P. Bugl
  (Prentice-Hall, Englewood Cliffs, NJ: 1995) ISBN 0-13-374752-2
• Introduction to Differential Equations with Boundary Value Problems - S. Campbell and R. Haberman [+ Instructor's Manual]
  (Houghton Mifflin, Boston: 1996) ISBN 0-395-70828-1
• Differential Equations with Mathematica - K. Coombes, B. Hunt, R. Lipsman, J. Osborn, and G. Stuck [+ Instructor's Manual]
  (Wiley, NY: 1995) ISBN 0-471-10874-X [See new edition, Fall 1996]
• Differential Equations with Maple - K. Coombes, B. Hunt, R. Lipsman, J. Osborn, and G. Stuck [+ Instructor's Manual]
  (Wiley, NY: 1996) ISBN 0-471-10875-8 [See new edition, Fall 1996]
• Differential Equations for Mathematics, Science, and Engineering - P. Davis
  (Prentice-Hall, Englewood Cliffs, NJ: 1992) ISBN 0-13-211236-1
• Modeling with Ordinary Differential Equations - T. P. Dreyer
  (CRC, Boca Raton, FLA: 1993) ISBN 0-8493-8636-5
• Differential Equations: Computing and Modeling - C. Edwards, Jr. and D. Penney [+ Computing Projects Manual, Student Solns. Manual]
  (Prentice-Hall, Englewood Cliffs, NJ: 1996) ISBN 0-13-382102-1
• An Introduction to Differential Equations and Their Applications - S. Farlow
  (McGraw-Hill, NY: 1994) ISBN 0-07-020030-0
• Ordinary Differential Equations with Mathematica: A Media Approach - A. Gray, M. Mezzino, and M. Pinsky [+ CD-ROM]
  (Springer-Verlag, NY: 1996) ISBN 0-387-94481-8 [Forthcoming]
• Differential Equations: A Dynamical Systems Approach (Vol. 1: Ordinary Differential Equations; Vol. 2: Higher-Dimensional Systems) - J. Hubbard and B. West
  (Springer-Verlag, NY: 1991, 1995) ISBN 0-387-97286-2, 0-387-94377-3
• Calculus (Chapter 9) - D. Hughes-Hallett, A. Gleason, et al.
• Differential and Difference Equations Through Computer Experiments (Second Ed.) - H. KoŘak [+ Phaser software and lab manual]
  (Springer-Verlag, NY: 1989) ISBN 0-387-96918-7
• Introductory Differential Equations: From Linearity to Chaos (Preliminary Ed.) - E. Kostelich and D. Armbruster
  (Addison-Wesley, Reading, MA: 1996) ISBN 0-201-82475-2
• Exploring Differential Equations via Graphics and Data (Preliminary Ed.) - D. Lomen and D. Lovelock [+ Soln. Manual, Resource Manual, and DOS-based programs]
  (Wiley, NY: 1996) ISBN 0-471-07649-X
• Fundamentals of Differential Equations and Boundary Value Problems - R. Nagle and E. Saff [+ Instructor's Guide, Student Solution Manual]
  (Addison-Wesley, Reading, MA: 1996) ISBN 0-201-80875-X
• Using MATLAB for Differential Equations - J. Polking
  (Prentice-Hall, Englewood Cliffs, NJ: 1995) ISBN 0-13-13394-2
• Calculator Enhancement for Differential Equations: A Manual of Applications Using the HP-48S and HP-28S Calculators - T. G. Proctor
  (Saunders, Orlando, FLA: 1992) ISBN 0-15-092730-7
• Maple ODE Lab Book - D. Redfern and E. Chandler [+ Diskette]
  (Springer-Verlag, NY: 1996) ISBN 0-387-94733-7 [Forthcoming]
• Differential Equations: An Introduction with Mathematica - C. Ross [+ Instructor's Manual and Answer Book, on-line electronic supplement]
  (Springer-Verlag, NY: 1995) ISBN 0-387-94301-3
• Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering - S. Strogatz
  (Addison-Wesley, Reading, MA: 1994) ISBN 0-201-54344-3
• Introduction to Differential Equations and Dynamical Systems - R. Williamson
  (McGraw-Hill, NY: 1997) ISBN 0-07-070594-1 [Forthcoming]
• Differential Equations with Computer Lab Experiments - D. Zill [+ Computer Lab Experiments, Complete Solns. Manual, Student Solns. Manual, Maple and Mathematica notebooks, assorted numerical and graphical software]
  (PWS, Boston: 1995) ISBN 0-534-93785-3

ARTICLES:

• Any issue of C*ODE*E -- newsletter published quarterly and available gratis from C*ODE*E, Math. Dept., Harvey Mudd College, Claremont, CA 91711 (See reference in INTERNET SITES.)
• Special Issue on Differential Equations - The College Mathematics Journal (Vol. 25, No. 5, November 1994)
• "Interactive Texts and a Virtual Environment for Exploring Spring-Mass Systems," M. Branton and M. Hale, Primus VI (No. 1, March 1996), 59-67
• "Modelling Mixing Problems with Differential Equations Gives Rise to Interesting Questions," B. J. Winkel, Int. J. Math. Educ. Sci. Technol. 25 (1994), 55-60
• "A Project Component for a Differential Equations Course," M. McDonald, Primus IV (No. 3, Sept. 1994), 219-228
• "Technology, Cooperative Learning, and Assessment in the Teaching of Ordinary Differential Equations," F. Barber and J. Narayan, Primus IV (No. 4, December, 1994), 337-346
• "Using a Computer Algebra System to Enhance a Traditional Undergraduate Course in Ordinary Differential Equations," A. P. Ferzola, Primus IV (No. 4, December 1994), 383-395
• "Student Research Papers in Freshman Calculus - Modelling with Differential Equations," T. Sherman, Primus III (No. 1, March 1993), 19-34
• "Pendulum Motion - The Value of Multiple Solution Methods," W. Barker, Primus III (No. 3, Sept. 1993), 225-244
• "PHASER-Based Courseware for Ordinary Differential Equations," L. Zia, Primus I (No. 1, March 1991), 49-64

SOFTWARE:

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)

The Electronic Proceedings of Fifth Conference on the Teaching of Mathematics are maintained by the Mathematics Archives as a service to the mathematics community.