Problem Centered Course in Numerical Methods

NOTE: The first page of text has been automatically extracted and included below in lieu of an abstract Session 3513 Problem-centered Course in Numerical Methods Bruce A. Finlayson University of Washington Introduction. The following educational elements were all included in one course: oral and written - communication, design, generation of multimedia lessons, use of sophisticated computer software, group learning, and learning by objective. An undergraduate elective course on numerical methods and modeling has been reorganized to focus on the problem of reducing automobile pollution. The course has essentially been turned upside down. In the past, each problem was posed, and the need for its solution explained. Then the general equations were reduced to the point that a viable model was achieved. Several such problems were treated in each quarter. In the revised course, one societal problem is posed, namely automobile pollution, and a catalytic converter is chosen as one solution. The first models are very simple, but are within the reach of the students at the start of the course. Then these models are used to show the need for including additional phenomena, which necessitates more complicated numerical methods. In this way the students practiced ‘just in time learning’. Their motivation was increased, and their success at solving difficult problems was higher. Overview. The course began with an assignment of an essay on the scope of the automobile pollution problem, thereby giving them experience in written communication. One side benefit for the professor is the large number of unusual sources of information the students find. This was the first time in this professor’s experience that material on a CD-ROM encyclopedia was used as a reference in an assignment. The course went through the same topics as in the past: methods to solve algebraic equations, initial value problems, boundary value problems, and partial differential equations. However, each type of equation arose in some manner in the catalytic converter for an automobile. The programs MATLAB and EXCEL were used to solve the various numerical models. The models were improved week by week, and after seven weeks the models were much more sophisticated and powerful than had been achieved in prior courses. Then a design problem was posed. Solution of the design problem involved using the model, working in groups, and presenting the design in written and oral format. At one point in the course the class considered doing experiments to test various catalysts, but this was abandoned as too time consuming. Mathematical Models. In order to make the course manageable the problem was simplified somewhat. The class treated only carbon monoxide (CO), since the details to treat propylene, methane and other components just add complicated bookkeeping that doesn’t improve understanding. The CO kinetics were from Oh and Cavendishl. A variety of models were used, as listed here. The approach was to assign homework problems for each model that invoked some numerical procedure. The models are organized so that by the end of the course all . ..,, ?@Ai~ 1996 ASEE Annual Conference Proceedings ‘..+,yyy’,: