Touchstone Problems

Since students assimilate new knowledge based on existing mental models [11], it is important to help students develop mental models which they can then use to assimilate new information. Touchstone problems are those which exhibit many of the issues relevant to a field of study like numerical analysis and can be covered many times from different perspectives. In this course there will be the touchstone problems which are covered in depth during lecture, and each student will develop their own touchstone problem as part of the course project. A well understood touchstone problem will provide an analogy to engineering problems they find in practice. Understanding how numerical techniques apply to the touchstone problem will allow the students to apply the same techniques to real problems.

Some typical touchstone problems in ordinary differential equations (ODEs) and partial differential equations (PDEs) are the temperature of coffee over time and the temperature of a discretized bar over time. For this course, we will use ODE and PDE touchstone problems which model software engineering concepts, video game functionality, and electric circuits. These are all areas which computer science students have some previous experience and/or interest.