A Mathematical Modeling Module with System Engineering Approach for Teaching Undergraduate Students to Conquer Complexity

This paper presents a mathematical modeling module for ODE courses. The module uses light-weight systems engineering approach to promote the competency of undergraduates to overcome the complexity in applied mathematics problems. The mathematics training of undergraduates in most colleges is limited to solving applications with a couple of variables in few steps of computations. Once faced with problems beyond that level of complexity, they are not only challenged to plan a scheme for finding solutions, but also to provide justification for their answers. This module combines an iterative modeling process with the compartmental analysis methodology to leverage these challenges. Verification and validation techniques are introduced for assuring the soundness of answers. The query-based process forces the students to trace critical mathematics equations to the corresponding phenomena of the problem under consideration. Examples within the module are arranged with incremental complexity. Stella is used as a modeling and simulation tool.