Ordinary Differential Equations at Mudd

Contemporary courses in ordinary differential equations (ODEs) introduce modeling and the use of interactive computer experiments as a supplement to ODE courses. These experiments use software solvers in an open-ended and exploratory fashion. Experiments often involve mathematical modeling in application areas encountered by undergraduate science and engineering students. The completion of an experiment requires the student to communicate the results in a laboratory report which can be collected and graded. Many ODE textbooks have experiments which are usually labeled as “labs”.

This site will focus on the work of C*ODE*E (the Consortium for ODE Experiments) in designing interactive computer experiments involving ODEs, real-world models and related areas of mathematics. The Consortium includes mathematics faculty and institutions with commitments to this approach to teaching and learning of ODEs.

ODEs form a natural setting for interactive computer experiments because

  • There is a wealth of applications to draw from in a wide variety of modeling areas
  • The attractive feature of interactive computer experiments in ODEs is that they provide a powerful “hands-on” experience in graphically visualizing the behavior of solutions of ODEs and the systems they model.
  • ODEs is a required course for students in most physical and biological sciences, for engineers and for mathematicians.

Since solutions of ODEs define curves, much can be learned about their behavior by graphing them. These graphs, generated with easy-to-use interactive solver packages, provide compelling visual evidence of theoretical deductions and a clear understanding of the qualitative properties of solutions. Interactive computer experiments are currently an integral part of most ODE courses and this site provides support for this activity.