The Mathlet Toolkit: Creating Dynamic Applets for Differential Equations and Dynamical Systems

摘要

Dynamic/interactive graphing applets can be used to supplement standard computer algebra systems such as Maple, Mathematica, Derive, or TI calculators, in courses such as Calculus, Differential Equations, and Dynamical Systems. The addition of this type of software can lead to discovery learning, with students developing their own conjectures, and possibly proofs (as has happened when students explore geometry with interactive software). The author has both developed and used such applets in the teaching of various mathematics courses. Furthermore, in collaboration with several students, tools for easily creating new applets have been developed (the Mathlet Toolkit), so that mathematics educators can customize applets to their courses without having to become Java programming experts. In this paper we describe some guided investigations in differential equations and dynamical systems which can be used with students, and show how applets for such investigations can be created with minimal effort or programming knowledge.