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Most of these references have appeared in the College Mathematics Journal. The individual articles are available through JSTOR by clicking on the "Article" link in the reference. Some of the articles have short summaries attached; some of these summaries appeared in *Math Reviews*.

Almost all of the articles are listed at http://www.maa.org/pubs/cmj-index/cmj-index.html under the heading: Differential Equations and Dynamical Systems.

Questions, comments, and future reviews should be sent to [ude.usafs|wtnosduj#ude.usafs|wtnosduj].

# Topics Index

- First order equations
- Higher-order equations and linear systems
- Nonlinear differential equations
- Numerical methods for differential equations
- Other topics in differential equations
- Software for differential equations and dynamical systems
- Pedagogy

# References by Topic

## First order equations

- Transcendental Functions and Initial Value Problems: A Different Approach to Calculus II, Byungchul Cha,
*College Mathematics Journal*, 38:4, 2007, 288–296. Article Summary - Temperature Models for Ware Hall, J. K. Denny and C. A. Yackel,
*College Mathematics Journal*, 35:3, 2004, 162-170. Article Summary - First Order Differential Equations and the Atmosphere, Gerhard Ströhmer,
*College Mathematics Journal*, 35:2, 2004, 93-96. Article Summary - Models for Growth, Elizabeth B. Appelbaum,
*College Mathematics Journal*, 32:4, 2001, 258-259. Article Summary - Some Socially Relevant Applications of Elementary Calculus, Colin Clark,
*College Mathematics Journal*, 4:2, 1973, 1-15. Article Summary - The Homicide Problem Revisited, David A. Smith,
*College Mathematics Journal*, 9:3, 1978, 141-145. Article Summary - Creative Teaching by Mistakes, Andrejs Dunkels and Lars-Erik Persson,
*College Mathematics Journal*, 11:5, 1980, 296-300. Article Summary - Differential Equations and the Battle of Trafalgar, David H. Nash,
*College Mathematics Journal*, 16:2, 1985, 98-102. Article Summary - Both a Borrower and a Lender Be, William Miller,
*College Mathematics Journal*, 16:4, 1985, 284. Article Summary - The Problem of Managing a Strategic Reserve, David Cole and Loren Haarsma and Jack Snoeyink,
*College Mathematics Journal*, 17:1, 1986, 48-60. Article Summary - A Linear Diet Model, Arthur C. Segal,
*College Mathematics Journal*,18:1, 1987, 44-45. Article Summary - The Snowplow Problem Revisited, Xiao-peng Xu,
*College Mathematics Journal*, 22:2, 1991, 139. Article Summary - Four Crotchets on Elementary Integration, Leroy F. Meyers,
*College Mathematics Journal*, 22:5, 1991, 410-413. Article Summary - Physical Demonstrations in the Calculus Classroom, Tom Farmer and Fred Gass,
*College Mathematics Journal*, 23:2, 1992, 146-148. Article - What It Means to Understand A Differential Equation, John H. Hubbard,
*College Mathematics Journal*, 25:5, 1994, 372-384. Article Summary - Teaching Differential Equations with a Dynamical Systems Viewpoint, Paul Blanchard,
*College Mathematics Journal*, 25:5, 1994, 385-393. Article Summary - Asking Good Questions about Differential Equations, Paul Davis,
*College Mathematics Journal*, 25:5, 1994, 394-400. Article Summary - A Balloon Experiment in the Classroom, Thomas Gruszka,
*College Mathematics Journal*, 25:5, 1994, 442-444. Article Summary - Designing a Rose Cutter, J. S. Hartzler,
*College Mathematics Journal*, 26:1, 1995, 41-43. Article Summary - Minimal Time of Descent, Jack Drucker,
*College Mathematics Journal*, 26:3, 1995, 232-235. Article - Discovering Differential Equations in Optics, William Mueller and Richard Thompson,
*College Mathematics Journal*, 28:3, 1997, 217-223. Article Summary - Spirals and Conchospirals in the Flight of Insects, Khristo N. Boyadzhiev,
*College Mathematics Journal*, 30:1, 1999, 23-31. Article Summary - FFF #142. Calculating the Average Speed, Bill Simpson,
*College Mathematics Journal*, 30:3, 1999, 209. Article Summary - Things I Have Learned at the AP Reading, Dan Kennedy,
*College Mathematics Journal*, 30:5, 1999, 346-355. Article Summary - Epidemic Models for SARS and Measles, Edward Rozema,
*College Mathematics Journal*, 38:4, 2007, 246-259. Article Summary - Enhancing Mathematics Understanding through Visualization: The Role of Dynamical Software, Karen Keene and Chris Rasmussen,
*Sometimes Less is More: Examples of Student-Centered Technology as Boundary Objects in Differential Equations*, Chapter 2, IGI Global, 2013, 12-36. Article Summary - Fontaine’s Forgotten Method for Inexact Differential Equations, Aaron E. Leanhardt and Adam E. Parker,
*Mathematics Magazine*, 90:3, 2017, 208-2019. Article Summary

## Higher-order equations and linear systems

- An Elementary Proof of an Oscillation Theorem for Differential Equations, Robert Gethner,
*College Mathematics Journal*, 38:4, 2007, 301–303. Article Summary - Temperature Models for Ware Hall,
*College Mathematics Journal*, 35:3, 2004, 162-170. Article Summary - Harmonic Oscillators with Periodic Forcing, Temple H. Fay,
*College Mathematics Journal*, 28:2, 1997, 98-105. Article Summary - Solving Linear Differential Equations by Operator Factorization,
*College Mathematics Journal*, 27:3, 1996, 199-203. Article Summary - Functions Defined by Differential Equations: A Short Course in Trigonometry, D. Bushaw,
*College Mathematics Journal*, 2:1, 1971, 32-35. Article Summary - Talking About Particular Solutions, Sidney H. L. Kung,
*College Mathematics Journal*, 3:1, 1972, 67-71. Article - On Particular Solutions of Pn(D)Y=0, H. L. Kung,
*College Mathematics Journal*, 4:1, 1973, 14-25. Article - Solving Systems of Linear Differential Equations, Michael Olinick,
*College Mathematics Journal*, 4:1, 1973, 26-30. Article - Factorization of Operators of Second Order Linear Homogeneous Ordinary Differential Equations, Donn C. Sandell and F. Max Stein,
*The Two-Year College Mathematics Journal*, 8:3, 1977, 132-141. Article Summary - Another Approach to a Standard Differential Equation, R.S.Luthar,
*The Two-Year College Mathematics Journal*, 10:3, 1979, 200-201. Article Summary - Differential Operators Applied to Integration, Kong-Ming Chong,
*The Two-Year College Mathematics Journal*, 13:2, 1982, 155-157. Article Summary - Differential Equations and the Battle of Trafalgar, David H. Nash,
*College Mathematics Journal*, 16:2, 1985, 98-102. Article Summary - A General Method for Deriving the Auxiliary Equation for Cauchy-Euler Equations, Vedula N. Murty and James F. McCrory,
*College Mathematics Journal*, 16:3, 1985, 212-215. Article Summary - Predator-Prey Model, David P. Kraines and Vivian Y. Kraines and David A. Smith,
*College Mathematics Journal*, 22:2, 1991, 160-162. Article Summary - Systems of Linear Differential Equations by Laplace Transform, H. Guggenheimer,
*College Mathematics Journal*, 23:3, 1992, 196-202. Article - Fireworks, J.M.A.Danby,
*College Mathematics Journal*, 23:3, 1992, 237-240. Article Summary - Timing Is Everything, J. Thoo,
*College Mathematics Journal*, 23:4, 1992, 308-309. Article - Teaching the Laplace Transform Using Diagrams, V. Ngo and S. Ouzomgi,
*College Mathematics Journal*, 23:4, 1992, 309-312. Article Summary - FFF #63. An Euler Equation, Ed Barbeau,
*College Mathematics Journal*, 24:4, 1993, 343-344. Article Summary - New Directions in Elementary Differential Equations, William E. Boyce,
*College Mathematics Journal*, 25:5, 1994, 364-371. Article Summary - What It Means to Understand A Differential Equation, John H. Hubbard,
*College Mathematics Journal*, 25:5, 1994, 372-384. Article Summary - Teaching Differential Equations with a Dynamical Systems Viewpoint, Paul Blanchard,
*College Mathematics Journal*, 25:5, 1994, 385-393. Article Summary - Computers, Lies, and the Fishing Season, Robert L. Borrelli and Courtney S. Coleman,
*College Mathematics Journal*, 25:5, 1994, 401-412. Article Summary - A New Look at the Airy Equation with Fences and Funnels, John H. Hubbard, Jean Marie McDill, Anne Noonburg, and Beverly H. West,
*College Mathematics Journal*, 25:5, 1994, 419-431. Article Summary - FFF #78. Solving a Second-order Differential Equation, Ed Barbeau,
*College Mathematics Journal*, 25:5, 1994, 432-433. Article Summary - A Progression of Projectiles: Examples from Sports, Roland Minton,
*College Mathematics Journal*, 25:5, 1994, 436-442. Article Summary - Matrix Patterns and Undetermined Coefficients, Herman Gollwitzer,
*College Mathematics Journal*, 25:5, 1994, 444-448. Article Summary - The Lighter Side of Differential Equations, J. M. McDill and Bjorn Felsager,
*College Mathematics Journal*, 25:5, 1994, 448-452. Article Summary - Experiments with Probes in the Differential Equations Classroom, David O. Lomen,
*College Mathematics Journal*, 25:5, 1994, 453-457. Article Summary - Sonnet from the Bard of Peirce-upon-Charles (poem), Ezra Hausman,
*College Mathematics Journal*, 25:5, 1994, 457. Article - Distinguished Oscillations of a Forced Harmonic Oscillator, T. G. Proctor,
*College Mathematics Journal*, 26:2, 1995, 111-117. Article Summary - The Matrix Exponential Function and Systems of Differential Equations Using Derive@, Robert J. Hill and Mark S. Mazur,
*College Mathematics Journal*, 26:2, 1995, 146-151. Article - Projectile Motion with Arbitrary Resistance, Tilak de Alwis,
*College Mathematics Journal*, 26:5, 1995, 361-367. Article - The Falling Ladder Paradox, Paul Scholten and Andrew Simoson,
*College Mathematics Journal*, 27:1, 1996, 49-54. Article Summary - A Home Heating Model for Calculus Students, Prashant S. Sansgiry and Constance C. Edwards,
*College Mathematics Journal*, 27:5, 1996, 394-397. Article Summary - Harmonic Oscillators with Periodic Forcing, Temple H. Fay,
*College Mathematics Journal*, 28:2, 1997, 98-105. Article Summary - Who Cares if X2 + 1 = 0 Has a Solution?, Viet Ngo and Saleem Watson,
*College Mathematics Journal*, 29:2, 1998, 141-144. Article Summary - The Effects of a Stiffening Spring, Sharon Hill and Karen Clark,
*College Mathematics Journal*, 30:5, 1999, 379-382. Article Summary - Another Broken Symmetry, Chuck W. Groetsch,
*College Mathematics Journal*, 36:2, 2005, 109-113. Article Summary

## Nonlinear differential equations

- Synchronizing Fireflies, Ying Zhou, Walter Gall and Karen Nabb,
*College Mathematics Journal*, 37:3, 2006, 187-193. Article Summary - How to Balance a Yardstick on an Apple, Herbert R. Bailey,
*College Mathematics Journal*, 17:3, 1986, 220-225. Article Summary - Bat and Superbat, Herbert R. Bailey,
*College Mathematics Journal*, 18:4, 1987, 307-314. Article Summary - A Rich Differential Equation for Computer Demonstrations, Bernard W. Banks,
*College Mathematics Journal*, 21:1, 1990, 45-50. Article Summary - Newton's Orbit Problem: A Historian's Response, Curtis Wilson,
*College Mathematics Journal*, 25:3, 1994, 193-200. Article - Newton's Principia and Inverse-Square Orbits, N. Nauenberg,
*College Mathematics Journal*, 25:3, 1994, 212-221. Article Summary - New Directions in Elementary Differential Equations, William E. Boyce,
*College Mathematics Journal*, 25:5, 1994, 364-371. Article Summary - What It Means to Understand A Differential Equation, John H. Hubbard,
*College Mathematics Journal*, 25:5, 1994, 372-384. Article Summary - Teaching Differential Equations with a Dynamical Systems Viewpoint, Paul Blanchard,
*College Mathematics Journal*, 25:5, 1994, 385-393. Article Summary - Computers, Lies, and the Fishing Season, Robert L. Borrelli and Courtney S. Coleman,
*College Mathematics Journal*, 25:5, 1994, 401-412. Article Summary - Quenching a Thirst with Differential Equations, Martin Ehrismann,
*College Mathematics Journal*, 25:5, 1994, 413-418. Article Summary - A Progression of Projectiles: Examples from Sports, Roland Minton,
*College Mathematics Journal*, 25:5, 1994, 436-442. Article Summary - A Balloon Experiment in the Classroom, Thomas Gruszka,
*College Mathematics Journal*, 25:5, 1994, 442-444. Article Summary - The Lighter Side of Differential Equations, J. M. McDill and Bjorn Felsager,
*College Mathematics Journal*, 25:5, 1994, 448-452. Article Summary - Experiments with Probes in the Differential Equations Classroom, David O. Lomen,
*College Mathematics Journal*, 25:5, 1994, 453-457. Article Summary - Gudermann and the Simple Pendulum, John S. Robertson,
*College Mathematics Journal*, 28:4, 1997, 271-276. Article Summary - Characterizing Power Functions by Volumes of Revolution, Bettina Richmond and Tom Richmond,
*College Mathematics Journal*, 29:1, 1998, 40-41. Article - Finding Unpredictable Behavior in a Simple Ordinary Differential Equations, Lisa D. Humphreys and Ray Shammas,
*College Mathematics Journal*, 31:5, 2000, 338-346. Article Summary - Using a Gradient Vector to Find Multiple Periodic Oscillations in Suspension Bridge Models, Lisa D. Humphreys and P. J. McKenna,
*College Mathematics Journal*, 36:1, 2005, 16-26. Article Summary

## Numerical methods for differential equations

- A Rich Differential Equation for Computer Demonstrations, Bernard W. Banks,
*College Mathematics Journal*, 21:1, 1990, 45-50. Article Summary - Newton's Principia and Inverse-Square Orbits, N. Nauenberg,
*College Mathematics Journal*, 25:3, 1994, 212-221. Article Summary - Computers, Lies, and the Fishing Season, Robert L. Borrelli and Courtney S. Coleman,
*College Mathematics Journal*, 25:5, 1994, 401-412. Article Summary - Using a Gradient Vector to Find Multiple Periodic Oscillations in a Suspension Bridge, Lisa D. Humphreys and P. J. McKenna,
*College Mathematics Journal*, 36:1, 2005, 16-26. Article Summary

## Other topics in differential equations

- An Alternative Approach to the Vibrating String Problem, James Chew,
*College Mathematics Journal*, 12:2, 1981, 147-149. Article Summary - Computer Graphics for the Vibrating String, Howard Lewis Penn,
*College Mathematics Journal*, 17:1, 1986, 79-89. Article Summary - How Should We Introduce Integration? David M. Bressoud,
*College Mathematics Journal*, 23:4, 1992, 296-298. Article Summary - A New Look at the Airy Equation with Fences and Funnels, John H. Hubbard, Jean Marie McDill, Anne Noonburg, and Beverly H. West,
*College Mathematics Journal*, 25:5, 1994, 419-431. Article Summary - Distinguished Oscillations of a Forced Harmonic Oscillator, T. G. Proctor,
*College Mathematics Journal*, 26:2, 1995, 111-117. Article Summary - Zeroing In on the Delta Function, Joan R. Hundhausen,
*College Mathematics Journal*, 29:1, 1998, 27-32. Article - How to Pump a Swing, Stephen Wirkus and Richard Rand and Andy Ruina,
*College Mathematics Journal*, 29:4, 1998, 266-275. Article Summary - Applications of Fourier Series in Classical Guitar Technique, James R. Hughes,
*College Mathematics Journal*, 31:4, 2000, 300-303. Article Summary - Improving understanding in ordinary differential equations through writing in a dynamical environment, Samer Habre, Teaching Mathematics and Its Applications, 31:3, 2012, 153–166. Article Summary

## Software for differential equations and dynamical systems

- A Mathematics Software Database, R.S.Cunningham and David A. Smith,
*College Mathematics Journal*, 17:3, 1986, 255-266. Article - A Mathematics Software Database Update, R.S.Cunningham and David A. Smith,
*College Mathematics Journal*, 18:3, 1987, 242-247. Article Summary - The Compleat Mathematics Software Database, R.S.Cunningham and David A. Smith,
*College Mathematics Journal*, 19:3, 1988, 268-289. Article - Chaos and Fractal Software, Jonathan Choate,
*College Mathematics Journal*, 22:1, 1991, 65-69. Article Summary - Derive, A Mathematical Assistant, Jeanette R. Palmiter,
*College Mathematics Journal*, 23:2, 1992, 158-161. Article Summary - Theorist@, Francis Gulick,
*College Mathematics Journal*, 24:2, 1993, 178-182. Article Summary - MicroCalc Version 6, L. Carl Leinbach,
*College Mathematics Journal*, 24:3, 1993, 263-270. Article Summary - Maple@ V (software review), Eric R. Muller and K.J.Srivastava,
*College Mathematics Journal*, 25:1, 1994, 56-63. Article - Differential Systems 3.1, James P. Fink,
*College Mathematics Journal*, 25:4, 1994, 329-333. Article - ODE Solvers for the Classroom, Andrew Flint and Ron Wood,
*College Mathematics Journal*, 25:5, 1994, 458-461. Article Summary - Derive@, Version 3.0, reviewed by Lawrence G. Gilligan,
*College Mathematics Journal*, 26:3,1995, 238-243. Article - Forget Not the Lowly Spreadsheet, Michael G. Henle,
*College Mathematics Journal*, 26:4, 1995, 320-328. Article Summary - Dfield and Pplane, Alan T. Zehnder,
*College Mathematics Journal*, 27:2, 1996, 144-148. Article Summary - Interactive Differential Equations, James P. Fink,
*College Mathematics Journal*, 28:1, 1997, 63-66. Article Summary - VisualDSolve, Michael Frame,
*College Mathematics Journal*, 28:5, 1997, 398-405. Article Summary - IDEA: Internet Differential Equations Activities, Elly Claus-McGahan,
*College Mathematics Journal*, 29:5, 1998, 427-433. Article Summary