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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.

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Michelle Mills Strout
2002-06-28