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Summer-Fall 1995

Three Activities from Exponential Growth and Decay Lab; Exploration of the Parachute Problem with Stella; How Long Does It Take a Harmonic Oscillator to Come to Rest?; Why Numerical Methods Don't Always Work; Rangeland Ecosystems Some Software for Teaching PDEs

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Item Three Activities from Exponential Growth and Decay Lab
By Edward Rosen; Bonnie Shulman; Bronislava Sokol
The authors emphasize qualitative analysis in these activities to show students how powerful geometric methods are in obtaining important information directly from differential equations without "solving" them explicitly. The application is intended to show the relevance of mathematics in predicting real world outcomes.

Item Exploration of the Parachute Problem with Stella
By Richard Melka; Donna Farrior
This parachute problem is open to a number of approaches and so is a good vehicle for the classroom. The authors engage students in looking at velocity and position in the context of the phase plane and in using STELLA to analyze the problem.

Item How Long Does It Take a Harmonic Oscillator to Come to Rest?
By Ben Pollina
"In a recent differential equations class I asked my students to determine how long it takes a damped linear oscillator like a mass on a spring to return to rest after it has been set in motion by some initial displacement. The answer we found surprised all of us..."

Item Why Numerical Methods Don't Always Work
By Glenn Ledder
It is tempting to assume that numerical methods work equally well for all initial value problems. This assumption is not true, however. Some problems are inherently difficult to solve by numerical methods, while others are inherently easy. The term "conditioning" is used by numerical analysts to describe the sensitivity of the solution of a problem to small perturbations in the problem data. If small changes in the data lead to large changes in the solution, the problem is said to be ill-conditioned; such problems pose difficulties for numerical solution.

Item Rangeland Ecosystems
By K.D. Cooper; Ray Huffaker; Thomas LoFaro
This project deals with one aspect of the problem of the effect of cattle on rangelands.

Item Some Software for Teaching PDEs
By Robert E. Terrell
The author describes some software to help students learn about the heat and wave equations.

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