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Active Problem Solving in a Graduate Course on Modeling and Numerical Methods

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Chemical Engineering 5743, “Chemical Engineering Modeling,” traditionally has been taught in the lecture format at Oklahoma State University. Dr. High (the instructor) has taught the course as such for seven years. In the fall of 2005, Dr. Maase (co-instructor) developed EXCEL/VBA demonstrations, activities, and homework, and Dr. High did the same with MATLAB. These computer tools were used by the students to solve algebraic, ordinary differential equations (initial value and boundary value) and partial differential equations (parabolic and elliptic). Traditional courses focus on numerical and mathematical methods as necessary skills. In the fall of 2006, the authors decided to introduce components to the course that expose students to case studies, active problem solving, team work, and experimentation with the overall aim of promoting creative and critical thinking as students identify and practice the art of modeling.

The 13 graduate students in the fall 2006 course were tasked with a semester project to “Design an encapsulated drug (of your group’s choice) that effectively delivers an appropriate dose for an appropriate number of hours. Select the most cost effective method.” The graduate students were introduced to the problem with a case study described in “User’s Guide to Engineering” by Jensen1, a freshman introductory engineering text. This “Dissolution Case Study” has been developed based on a series of several Chemical Engineering Education articles. In the case study, a lollipop simulates the coating of a new pharmaceutical. A simple first order ODE describes the rate of change of the lollipop radius with respect to time. This rate is dependent on the mass transfer coefficient, the concentration gradient, and the molar density of the lollipop. Students are asked to develop experimental procedures to test the proposed model. This was the case study that the graduate students used as a starting point for their projects.

For the graduate course, the students were put in heterogeneous groups by considering their country of origin, the degree they are pursuing (M.S., Ph.D.), and their background experience in computer applications / programming, experimentation / lab work, and numerical method experience. The students began by creating an initial experimental protocol for their physical model (equipment/supplies needed, data collection procedure), their initial computer modeling/numerical methods appropriate for solving the mathematical model, necessary simplifications made to begin the research, and expectations of future considerations that more appropriately model the real system. Throughout the semester the students improved their physical and mathematical modeling complexity to give them appropriate tools to reach the goal of successfully designing encapsulated drugs. Teams gave final presentations of the results of their efforts. Assessments are presented examining the effectiveness of our team-based, active learning experience. Modeling, experimental design, experimental procedure and competence, and proficiency in applied numerical methods and computer programming are evaluated.

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High, K., & Maase, E. (2007, June), Active Problem Solving In A Graduate Course On Modeling And Numerical Methods Paper presented at 2007 Annual Conference & Exposition, Honolulu, Hawaii. 10.18260/1-2--2271