In past two decades, undergraduate courses in differential equations and their applications have undergone revolutionary changes by embracing numerical simulations and scientific visualization. Several notable commercial software products, including Phaser, the winner of EDUCOM/NCRIPTAL "Best Mathematics Software in Higher Education" award in 1989, have made this revolution possible. The original Phaser has been completely rewritten in Java, a platform-neutral language with excellent Internet support. Many new visualization features have been added, notably a Gallery for viewing and organizing multiple simulations.
This project is supporting three full-scale development activities for Phaser: (a) Developing and distributing freely a browser version of Phaser, akin to AcrobatReader by Adobe; and facilitating wide distribution of dynamic Phaser Projects and Galleries over the Internet. (b) Creating a portal of multidisciplinary differential and difference equations projects in collaboration with mathematicians, scientists, and engineers, posting these projects on www.phaser.com, and creating Galleries for dynamical systems and their applications suitable for beginning and advanced undergraduate students. (c) Testing and evaluating the use of Phaser with students and faculty at diverse institutions.
In addition, development continues on the Phaser numerical engine. Methods are being developed and tested for validating numerical simulations of chaotic systems using the concept of shadowing.
