November 1996  ICTCM IX (Reno)  9-1

\underline{General Comments}:

• problem is not constant coefficients – it’s piecewise constant coefficients

• explicit solution can be found (need to continuously match solutions)

• system, but decoupled: v equation can be solved as 1st-order linear IVP; x equation can be solved by direct integration

• show explicit solution? Maple code for computation? YES!!

• nondimensionalization would make problem appear even simpler

• same methods work with Release 4; piecewise is nice, but dsolve does not appear to be able to solve the general prob-

  lem, e.g., K[pw_const] := piecewise( t<td, k1, k2 );

\underline{Pedagogy}:

• how many students could solve this problem?

• how long? how many tries?

• how would the solution be used?

• how many could understand the basic idea? (piecewise)

• what is really important?

• CLAIM:

– working with mathematical models

– structure of the problem and the solution

– interpreting solutions; limitations of applicability – confirm/verify results

– explain model; revise/extend as necessary