Combining Engineering Problem Solving with Numerical Methods to Enhance Learning Effectiveness

ABSTRACT: A major challenge in teaching numerical methods to engineering students is to provide stimulating student motivation. The examples that are provided in most numerical methods textbooks typically do not establish the necessary content connections with the engineering student’s engineering major. In order to increase student motivation, they need to be shown practical examples from their particular fields that are best solved by using numerical methods. The dilemma here is that practical examples can be rather complex, and their coding and debugging may take too long, thus reducing the time available for learning the subject matter. In this paper we demonstrate, using two practical examples from the fluid mechanics field, the several benefits of the use of a number of software packages in teaching numerical methods. In the two examples the POLYMATH package, which is a user-friendly numerical problem-solving package, is used for the preparation, coding and debugging of the mathematical model. Once a correct, verified solution has been obtained for a particular model a different software package, more appropriate for coding the numerical solution algorithm can be used. In the first example Excel is used for programming the "successive substitution " method. In the second example MATLAB is used for programming Broyden's "quasi-Newton " algorithm. It is shown that the separation between the preparation and the debugging o