Short Writing Assignments For Gaining Understanding In Differential Equations

 

Michael A. Brilleslyper, United States Air Force Academy

 

Modern differential equations courses focus extensively on mathematical models and their qualitative analysis.  In this paradigm, a large variety of technological tools are utilized to view slope fields, phase portraits, and trajectories of solutions.  Far less time is spent on the classification of differential equations and the various analytic techniques for solving them. In this type of curriculum, assessment must necessarily focus more on interpretation of results and on the process of model building.  Short writing assignments offer an ideal mechanism for assessing student understanding of key concepts in the subject.  In particular, writing requires students to synthesis important ideas and to articulate the essential features and underlying assumptions in mathematical models. In this talk we will present five short writing assignments that cover the main points of a standard first course in differential equations.  The assignments emphasize making clear connections between mathematical models and the physical systems that they supposedly represent.