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Reviews - Articles on Differential Equations

Below is a list of recent differential equations articles most of which have appeared in the College Mathematics Journal. Some of these have short summaries attached. We envision this as a growing body of reviews and invite you to submit reviews and references to this page. See the tab "Submit Manuscript" for instructions on how to submit a review.

This page lists recent differential equations articles that have appeared in the College Mathematics Journal. Individual articles are available through JSTOR by clicking on the "Article" link.  Some of the articles have short summaries attached. Tom Judson, Chris Leary and Mike Breen wrote most of the summaries. Some summaries appeared in ERIC or 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.

We envision this as a growing body of reviews and invite you to submit reviews and references to this page.

Questions, comments, and future reviews should be sent to Tom Judson.  

Topics Index Author Index

First order equations

  • 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   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
  • 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   Summary
  • 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


Higher order linear equations and linear systems

  • 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   Summary
  • On Particular Solutions of Pn(D)Y=0, H. L. Kung, College Mathematics Journal, 4:1, 1973, 14-25.  Article   Summary
  • Solving Systems of Linear Differential Equations, Michael Olinick, College Mathematics Journal, 4:1, 1973, 26-30.  Article   Summary
  • Factorization of Operators of Second Order Linear Homogeneous Ordinary Differential Equations, Donn C. Sandell and F. Max Stein, College Mathematics Journal, 8:3, 1977, 132-141.  Article   Summary
  • Another Approach to a Standard Differential Equation, R.S.Luthar, College Mathematics Journal, 10:3, 1979, 200-201.  Article   Summary
  • Differential Operators Applied to Integration, Kong-Ming Chong, 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   Summary
  • 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   Summary
  • 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   Summary
  • 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   Summary
  • Projectile Motion with Arbitrary Resistance, Tilak de Alwis, College Mathematics Journal, 26:5, 1995, 361-367.  Article   Summary
  • The Falling Ladder Paradox, Paul Scholten and Andrew Simoson, College Mathematics Journal, 27:1, 1996, 49-54.  Article   Summary
  • Solving Linear Differential Equations by Operator Factorization, A. B. Urdaletova and S. K. Kydyraliev, College Mathematics Journal, 27:3, 1996, 199-203.  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

 

Nonlinear differential equations

  • 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  Summary
  • 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   Summary
  • 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


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


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   Summary
  • 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
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   Summary
  • 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   Summary
  • 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   Summary
  • Differential Systems 3.1, James P. Fink, College Mathematics Journal, 25:4, 1994, 329-333.  Article   Summary
  • 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   Summary
  • 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
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