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.

**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

- 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

- 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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