Lipsman, R. L., J. E. Osborn, and J. M. Rosenberg. 2008. The SCHOL Project at the University of Maryland: Using Mathematical Software in the Teaching of Sophomore Differential Equations. Journal of Numerical Analysis, Industrial and Applied Mathematics. 3(1-2): 81-103.
This is a publication of the European Society of Computational Methods in Sciences and Engineering
Abstract. At the University of Maryland, we have experimented over the last 16 years with the use of several problem-solving environments (PSEs) to enhance the teaching and enrich the syllabus of the sophomore-level basic differential equations course for science and engineering majors. We have developed educational materials for teaching this course in all of the “big three” PSEs: MATLAB (sometimes with Simulink also), Maple, and Mathematica, in formats varying from small computer labs to large lecture courses. In this paper we provide a brief history of our project and then discuss both the curricular and non-curricular issues that arose—some of which resulted in substantial improvements to the course materials we developed and some of which impeded the deployment of those materials. We also reveal what we have learned about realistic goals for a course at this level, in terms of the software and the mathematics, as well as for the faculty and the students. Finally we give some assessment of the relative advantages and disadvantages of the three PSEs for a sophomore-level differential equations course.
While this is an overview of the entire process and set of issues in using mathematical software there is a nice set of activities in pages 87-89 to include using series methods to solve a nonlinear differential equation, numerical methods, and effect of periodic external force on a pendulum.
Keywords: differential equations course, computer supplement, mathematical software, series, series solution, numerical methods, pendulum, external force
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