Kris Stewart

Computer games in the classroom, or, how to get perfect attendance, even at 8 AM

In this special session, we will compare and contrast several game engines that have been used in game development courses, and describe our experiences teaching such courses.

Undergraduate computational science and engineering programs and courses

This 90-minute panel session will discuss recent and future developments in incorporating Computational Science and Engineering into the undergraduate curriculum. There is a companion session devoted to tools and techniques and so the focus here is on programs and courses.The panelists will demonstrate a clear uniformity of purpose but a wide variety of approaches to increasing the CSE experience of undergraduates in different types of schools.The schools represented vary from large state universities to small private liberal arts colleges and a medium-sized school with a strong engineering bias.The approaches adopted also differ. There are complete programs built largely from existing courses, specific courses that are added to established programs to allow a student to follow an emphasis in CSE. The introduction of CSE into existing programs through faculty advice and education has also been successful.Yet other approaches represented among the panelists are the introduction of multi-disciplinary team-taught project-based courses as a springboard for growing an undergraduate CSE program including undergraduate research projects. The incremental use of small add-on courses to supplement conventional mathematics offerings with some CSE content has also been used successfully.Another approach represented on the panel is the use of a particular vehicle --- in this case graphics and visualization --- to introduce key ideas of CSE into regular parts of the curriculum.The unifying theme of the panel --- the desire to improve undergraduate CSE education will be evident throughout. By presenting a wide variety of approaches to achieve this end, it is hoped that any audience participants who wish to create a CSE thread in their own programs will find some ideas to help them. Some of the practical and political issues will also be discussed in the various contexts.The program for the panel would allow each panelist a maximum of 10 minutes to outline their programs and approaches. The remaining 30 (or more) minutes would then be reserved for general discussion and questions and contributions from the audience.

Avoiding stability-induced inefficiencies in BDF methods

Abstract Time-dependent partial differential equations are often treated by semidiscretization and the resulting problem solved using existing ordinary differential equation software restricted to low-order formulas. For certain classes of problems, the Backward Differentiation Formulas (BDF) are often dismissed due to their poor stability behavior near the imaginary axis for orders three and above. We explain why and for what problems this happens, what the appropriate tactic should be, and why this is not the tactic taken by most automatic codes. We present an idea that avoids this inefficiency in one automatic code.

Numerical experiments with a nonlinear evolution equation which exhibits blow-up

Abstract The results of numerical experiments which involve a nonlinear evolution equation exhibiting blow-up and the use of spectral and pseudospectral methods are examined. It is observed that in spite of the expected exponential-order accuracy of these methods in the case of smooth solutions, they do not perform well in the detection of blow-up.

The microcomputer as a tool in numerical analysis

The affordability of microcomputers makes them a practical tool for scientific computations and development of algorithms as well as a dramatic teaching aid. A package of mathematical software called SCRUNCH (1) is available to run in BASIC on moderate sized microcomputers (at least 8K and preferably 16K program space) to aid in the above tasks. SCRUNCH consists of translations of FORTRAN routines taken from three excellent sources:

A model for stability of the semi-implicit backward differentiation formulas

A model is presented for stability for an extension of linear multistep methods for stiff ordinary differential equations. The method is based on a prediction followed by a fixed number of corrections obtained by a Newton scheme with inexact Jacobian matrix. The impact on stability of error in the matrix over a broad range of linear, constant coefficient equations is modeled. The model provides practical guidance for implementation of software for stiff equations.