Computer modules for a mathematical modelling course

Abstract

I . Introduction Mathematical modelling has become recognized as an important component in applied mathematics curricula during the past ten years. Evidence of this fact is the existence of several textbooks in modelling published in recent years. The need for such a course stems from the neglect of modelling concepts in most undergraduate courses in which time constraints usually do not allow the inclusion of modelling with the theory and techniques. At Florida State University, the course Mathematical Modelling of Scientif ic Problems, a junior level course (with prerequisites of calculus, including some ordinary d i f f erential equations), has been introduced to f i l l this void. The computer can play a v i ta l role in a modelling course without downgrading the role of qualitative analysis. As a calculation and graphing device the computer can free time for concentration on modelling concepts such as formulation, result analyses and modification. The results of computer runs often suggest the form of an analysis that can generalize and render understandable the specific results of a few "model runs;" see Greenspan (1971). The computer can indicate the degree to which approximations made in an analysis are in fact realized. The computer could indicate that a part icular model is absurd and this save the modeller the effort of considering the model at a l l . As part of the CAUSE project at FSU, a package of mathematical modelling modules have been developed during the past 3 years. They consist of FORTRAN programs which produce digital and graphical output with l i t t l e computer experience required by the user. The modules play a variety of roles in the course. The instructor can use them to generate examples of material discussed in class. The students can use them to answer their own questions such as "What would happen i f our