Below are short summaries of recent differential equations articles which have appeared in the College Mathematics Journal. 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, Chris Leary, or Mike Breen.  This project was begun as a part of the Undergraduate Faculty Program at the 2001 IAS/Park City Mathematics Institute. 

• First order equations
• Higher order linear equations and linear systems
• Difference equations,  discrete dynamical systems, and fractals
• Nonlinear differential equations
• Numerical methods for differential equations
• Other topics in differential equations
• Software for differential equations and dynamical systems

First order equations

• Some Socially Relevant Applications of Elementary Calculus, Colin Clark, College Mathematics Journal, 4:2, 1973, 1-15.
• The Homicide Problem Revisited, David A. Smith, College Mathematics Journal, 9:3, 1978, 141-145.
• Creative Teaching by Mistakes, Andrejs Dunkels and Lars-Erik Persson, College Mathematics Journal, 11:5, 1980, 296-300.
• Differential Equations and the Battle of Trafalgar, David H. Nash, College Mathematics Journal, 16:2, 1985, 98-102.
• Both a Borrower and a Lender Be, William Miller, College Mathematics Journal, 16:4, 1985, 284.
• The Problem of Managing a Strategic Reserve, David Cole and Loren Haarsma and Jack Snoeyink, College Mathematics Journal, 17:1, 1986, 48-60.
• A Linear Diet Model, Arthur C. Segal, College Mathematics Journal,18:1, 1987, 44-45.
• The Snowplow Problem Revisited, Xiao-peng Xu, College Mathematics Journal, 22:2, 1991, 139.
• Four Crotchets on Elementary Integration, Leroy F. Meyers, College Mathematics Journal, 22:5, 1991, 410-413.
• Physical Demonstrations in the Calculus Classroom, Tom Farmer and Fred Gass, College Mathematics Journal, 23:2, 1992, 146-148.
• What It Means to Understand A Differential Equation, John H. Hubbard, College Mathematics Journal, 25:5, 1994, 372-384.
• Teaching Differential Equations with a Dynamical Systems Viewpoint, Paul Blanchard, College Mathematics Journal, 25:5, 1994, 385-393.
• Asking Good Questions about Differential Equations, Paul Davis, College Mathematics Journal, 25:5, 1994, 394-400.
• A Balloon Experiment in the Classroom, Thomas Gruszka, College Mathematics Journal, 25:5, 1994, 442-444.
• Designing a Rose Cutter, J. S. Hartzler, College Mathematics Journal, 26:1, 1995, 41-43.
• Minimal Time of Descent, Jack Drucker, College Mathematics Journal, 26:3, 1995, 232-235.
• Discovering Differential Equations in Optics, William Mueller and Richard Thompson, College Mathematics Journal, 28:3, 1997, 217-223.
• Spirals and Conchospirals in the Flight of Insects, Khristo N. Boyadzhiev, College Mathematics Journal, 30:1, 1999, 23-31.
• FFF #142.  Calculating the Average Speed, Bill Simpson, College Mathematics Journal, 30:3, 1999, 209.
• Things I Have Learned at the AP Reading, Dan Kennedy, College Mathematics Journal, 30:5, 1999, 346-355.

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.
• Talking About Particular Solutions, Sidney H. L. Kung, College Mathematics Journal, 3:1, 1972, 67-71.
• On Particular Solutions of Pn(D)Y=0, H. L. Kung, College Mathematics Journal, 4:1, 1973, 14-25.
• Solving Systems of Linear Differential Equations, Michael Olinick, College Mathematics Journal, 4:1, 1973, 26-30.
• 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.
• Another Approach to a Standard Differential Equation, R.S.Luthar, College Mathematics Journal, 10:3, 1979, 200-201.
• Differential Operators Applied to Integration, Kong-Ming Chong, College Mathematics Journal, 13:2, 1982, 155-157.
• Differential Equations and the Battle of Trafalgar, David H. Nash, College Mathematics Journal, 16:2, 1985, 98-102.
• 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.
• Predator-Prey Model, David P. Kraines and Vivian Y. Kraines and David A. Smith, College Mathematics Journal, 22:2, 1991, 160-162.
• Systems of Linear Differential Equations by Laplace Transform, H. Guggenheimer, College Mathematics Journal, 23:3, 1992, 196-202.
• Fireworks, J.M.A.Danby, College Mathematics Journal, 23:3, 1992, 237-240.
• Timing Is Everything, J. Thoo, College Mathematics Journal, 23:4, 1992, 308-309.
• Teaching the Laplace Transform Using Diagrams, V. Ngo and S. Ouzomgi, College Mathematics Journal, 23:4, 1992, 309-312.
• FFF #63. An Euler Equation, Ed Barbeau, College Mathematics Journal, 24:4, 1993, 343-344.
• New Directions in Elementary Differential Equations, William E. Boyce, College Mathematics Journal, 25:5, 1994, 364-371.
• What It Means to Understand A Differential Equation, John H. Hubbard, College Mathematics Journal, 25:5, 1994, 372-384.
• Teaching Differential Equations with a Dynamical Systems Viewpoint, Paul Blanchard, College Mathematics Journal, 25:5, 1994, 385-393.
• Computers, Lies, and the Fishing Season, Robert L. Borrelli and Courtney S. Coleman, College Mathematics Journal, 25:5, 1994, 401-412.
• 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.
• FFF #78. Solving a Second-order Differential Equation, Ed Barbeau, College Mathematics Journal, 25:5, 1994, 432-433.
• A Progression of Projectiles: Examples from Sports, Roland Minton, College Mathematics Journal, 25:5, 1994, 436-442.
• Matrix Patterns and Undertermined Coefficients, Herman Gollwitzer, College Mathematics Journal, 25:5, 1994, 444-448.
• The Lighter Side of Differential Equations, J. M. McDill and Bjorn Felsager, College Mathematics Journal, 25:5, 1994, 448-452.
• Experiments with Probes in the Differential Equations Classroom, David O. Lomen, College Mathematics Journal, 25:5, 1994, 453-457.
• Sonnet from the Bard of Peirce-upon-Charles (poem), Ezra Hausman, College Mathematics Journal, 25:5, 1994, 457.
• Distinguised Oscillations of a Forced Harmonic Oscillator, T. G. Proctor, College Mathematics Journal, 26:2, 1995, 111-117.
• 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.
• Projectile Motion with Arbitrary Resistance, Tilak de Alwis, College Mathematics Journal, 26:5, 1995, 361-367.
• The Falling Ladder Paradox, Paul Scholten and Andrew Simoson, College Mathematics Journal, 27:1, 1996, 49-54.
• Solving Linear Differential Equations by Operator Factorization, A. B. Urdaletova and S. K. Kydyraliev, College Mathematics Journal, 27:3, 1996, 199-203.
• A Home Heating Model for Calculus Students, Prashant S. Sansgiry and Constance C. Edwards, College Mathematics Journal, 27:5, 1996, 394-397.
• Harmonic Oscillators with Periodic Forcing, Temple H. Fay, College Mathematics Journal, 28:2, 1997, 98-105.
• Who Cares if X2 + 1 = 0 Has a Solution?, Viet Ngo and Saleem Watson, College Mathematics Journal, 29:2, 1998, 141-144.
• The Effects of a Stiffening Spring, Sharon Hill and Karen Clark, College Mathematics Journal, 30:5, 1999, 379-382.

Difference equations, discrete dynamical systems, and fractals

• Vectors Point Toward Pisa, Richard A. Dean, College Mathematics Journal, 2:2, 1971, 28-39.
• A General Formula for the Nth Term of a Sequence, Etta Mae Whitton, College Mathematics Journal, 2:2, 1971, 96-98.
• Telescoping Sums and the Summation of Sequences, G. Baley Price, College Mathematics Journal, 4:2, 1973, 16-29.
• Stirling's Triangle of the First Kind Absolute Value Style, Hugh Ouellette and Gordon Bennett, College Mathematics Journal, 8:4, 1977, 195-202.
• Stirling's Numbers of the Second Kind Programming Pascal's and Stirling's Triangles, Satish K. Janardan and Konanur G. Janardan, College Mathematics Journal, 9:4, 1978, 243-248.
• Binary Grids and a Related Counting Problem, Nathan Hoffman, College Mathematics Journal, 9:4, 1978, 267-272.
• Summation of Finite SeriesA Unified Approach, Shlomo Libeskind, College Mathematics Journal, 12:1, 1981, 41-50.
• Sequences, Series, and Pascal's Triangle, Lenny K. Jones, College Mathematics Journal, 14:3, 1983, 253-256.
• Pascal's Triangle, Difference Tables and Arithmetic Sequences of Order N, Calvin Long, College Mathematics Journal, 15:4, 1984, 290-298.
• The Factorial Triangle and Polynomial Sequences, Steven Schwartzman, College Mathematics Journal, 15:5, 1984, 424-426.
• A Discrete Look at 1 + 2 + ... + n, Loren C. Larson, College Mathematics Journal, 16:5, 1985, 369-382.
• The Pascal Polytope: An Extension of Pascal's Triangle to N Dimensions, John F. Putz, College Mathematics Journal, 17:2, 1986, 144-155.
• Generating Functions, William Watkins, College Mathematics Journal, 18:3, 1987, 195-211.
• Fibonacci Numbers and Computer Algorithms, John Atkins and Robert Geist, College Mathematics Journal, 18:4, 1987, 328-336.
• Two Simple Recursive Formulas for Summing 1^k + 2^k + ... + n^k, Michael Carchidi, College Mathematics Journal, 18:5, 1987, 406-409.
• Powers and Roots by Recursion, Joseph F. Aieta, College Mathematics Journal, 18:5, 1987, 411-416.
• Elementary Transcendental Functions, Harley Flanders and J. Sutherland Frame, College Mathematics Journal, 18:5, 1987, 417-421.
• Pseudorandom Number Generators and a Four-Bit Computer System, James C. Reber, College Mathematics Journal, 20:1, 189, 54-55.
• Spreadsheets, Power Series, Generating Functions, and Integers, Donald R. Snow, College Mathematics Journal, 20:2, 1989, 143-152.
• The Eternal Trianglea History of a Counting Problem, Mogens Esrom Larsen, College Mathematics Journal, 20:5, 1989, 370-384.
• A Hidden Case of Negative Amortization, Bert K. Waits and Franklin Demana, College Mathematics Journal, 21:2, 1990, 121-126.
• A Chaotic Search for i, Gilbert Strang, College Mathematics Journal, 22:1, 1991, 3-12.
• Discrete Dynamical Modeling, James T. Sandefur, College Mathematics Journal, 22:1, 1991, 13-22.
• The Orbit Diagram and the Mandelbrot Set, Robert L. Devaney, College Mathematics Journal, 22:1, 1991, 23-38.
• Theory vs. Computation in Some Very Simple Dynamical Systems, Larry Blaine, College Mathematics Journal, 22:1, 1991, 42-44.
• Chaiotic Mappings and Probability Distributions, Paul C. Matthews and Steven H. Strogatz, College Mathematics Journal, 22:1, 1991, 45-47.
• The Root-Finding Route to Chaos, Richard Parris, College Mathematics Journal, 22:1, 1991, 48-55.
• Software Review: Chaos and Fractal Software, Jonathan Choate, College Mathematics Journal, 22:1, 1991, 65-69.
• Commutativity of Polynomials, Shmuel Avital and Edward Barbeau, College Mathematics Journal, 23:5, 1992, 386-395.
• Fibonacci Numbers, Recursion, Complexity, and Induction Proofs, Elmer K. Hayashi, College Mathematics Journal, 23:5, 1992, 407-410.
• Investigation of a Recurrence Relation: Student Research Project, Dmitri Thoro and Linda Valdes, College Mathematics Journal, 25:4, 1994, 322-324.
• The Dynamics of Newton's Method for Cubic Polynomials, James A. Walsh, College Mathematics Journal, 26:1, 1995, 22-28.
• Can We See the Mandelbrot Set?, John Ewing, College Mathematics Journal, 26:2, 1995, 90-99.
• A Geometric Approach to Linear Functions, Jack E. Graver, College Mathematics Journal, 26:5, 1995, 389-394.
• Bargaining Theory, or Zeno's Used Cars, James C. Kirby, College Mathematics Journal, 27:4, 1996, 285-286.
• A Recurrence Relation in the Spinout Puzzle, Robert C. Lamphere, College Mathematics Journal, 27:4, 1996, 286-289.
• Fractals in Linear Algebra, James A. Walsh, College Mathematics Journal, 27:4, 1996, 298-304.
• Basins of Attraction, Nusse, Helena E. and Yorke, James A., Science,  Vol. 271, 8 March 1996, pp. 1376–1380.
• How Chaotic Things Work, William C. Mercier, College Mathematics Journal, 28:2, 1997, 110-118.
• Fibonacci Powers and a Fascinating Triangle, Dale K. Hathaway and Stephen L. Brown, College Mathematics Journal, 28:2, 1997, 124-128.
• A Continuous Version of Newton's Method, Steven M. Hetzler, College Mathematics Journal, 28:5, 1997, 348-351.
• Studying the Cantor Dust at the Edge of Feigenbaum Diagrams, Aaron Klebanoff and John Rickert, College Mathematics Journal, 29:3, 1998, 189-198.
• A Simple Decision Rule for a Guessing Game, Luiz Felipe Martins, College Mathematics Journal, 29:5, 1998, 371-375.
• Candies and Dollars, Saad M. Adnan, College Mathematics Journal, 29:5, 1998, 414-415.
• Will the Real Bifurcation Diagram Please Stand Up!, Chip Ross and Jody Sorensen, College Mathematics Journal, 31:1, 2000, 2-14.

Nonlinear differential equations

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

College Mathematics Journal, 31:5, 2000, 338-346.

Numerical methods for differential equations

• A Rich Differential Equation for Computer Demonstrations, Bernard W. Banks, College Mathematics Journal, 21:1, 1990, 45-50.
• Newton's Principia and Inverse-Square Orbits, N. Nauenberg, College Mathematics Journal, 25:3, 1994, 212-221.
• Computers, Lies, and the Fishing Season, Robert L. Borrelli and Courtney S. Coleman, College Mathematics Journal, 25:5, 1994, 401-412.

Other topics in differential equations

• An Alternative Approach to the Vibrating String Problem, James Chew, College Mathematics Journal, 12:2, 1981, 147-149.
• Computer Graphics for the Vibrating String, Howard Lewis Penn, College Mathematics Journal, 17:1, 1986, 79-89.
• How Should We Introduce Integration? David M. Bressoud, College Mathematics Journal, 23:4, 1992, 296-298.
• 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.
• Distinguised Oscillations of a Forced Harmonic Oscillator, T. G. Proctor, College Mathematics Journal, 26:2, 1995, 111-117.
• Zeroing In on the Delta Function, Joan R. Hundhausen, College Mathematics Journal, 29:1, 1998, 27-32.
• How to Pump a Swing, Stephen Wirkus and Richard Rand and Andy Ruina, College Mathematics Journal, 29:4, 1998, 266-275.
• Applications of Fourier Series in Classical Guitar Technique, James R. Hughes, College Mathematics Journal, 31:4, 2000, 300-303.

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