Numerical methods and the micro: Color graphics as an aid to comprehension

Most of us that teach in the numerical analysis/numerical methods area have been relying on large mainframes for years as a valuable tool in solving our problems of any size. Thus when the micros came along a few years back our natural inclination was to avoid them since they appeared to have nothing new to offer us. We perhaps thought “How could such a small machine compete with the real number crunchers we had become enamored with?” However, we only have to read the popular press to see the impact they are having all around us. Hence, it became imperative that we do look into the possibility that maybe they can make some valuable contributions. As Kelch and Hansen [1] implied in their article, there are many small colleges that can ill-afford the cost of a mainframe or even a mini but still they wish to teach meaningful courses. Aside from this perhaps there are concepts that can be illustrated in a more meaningful fashion even if a super-mini or mainframe is available. It was in this later vein that this project was undertaken. After viewing the rather amazing graphics that one could realize on an Apple II in a game-playing environment, the author decided that there must be some way that they could be used in a meaningful way in a classroom or course. The purpose of this report is to discuss the way that the Apple II graphics were used to display several popular numerical algorithms. It should be pointed out here that there is nothing special about the Apple II and the graphics did not have to be done in color to illustrate most of the important points. It was simply the case that the author used the type of machine that was most readily available to him. It was the author's feeling that beginning numerical methods students could more readily relate to many of the techniques if they had a visual image to relate to. The old adage “a picture is worth a thousand words” comes to mind. Although it is possible to give graphical illustrations in a textbook and in class, typically this is such a time-consuming task that one can only look at a few special cases. It was the plan of the author to allow the programs to accept a variety of functions for actual implementation by the user. The student will be able to alter various parameters as he runs an algorithm which will allow him to answer questions like “What if I do the following?”