Mathematics can still be taught without using a CAS and this is probably the case in most schools and universities. Although CAS and technology are often used by instructors to demonstrate or illustrate mathematical concepts, they are rarely used by students. When we consider our mathematics curriculum, “Differential Equations” is one course that we firmly believe can and should benefit from the use of CAS.  In this talk, we will report how our ODE course has evolved, as our engineering students have access to technology (Voyage 200 symbolic calculator) in the classroom at all times.  This talk will show examples of what students still do by hand and what CAS allows us to do now to enrich the learning experience.

Specific examples will focus on first order ODEs.  Students not only use analytical methods, but with the aid of technology they can also focus on subjects often neglected in ODES courses. They have to plot slope fields, and in some cases also use Picard approximations and compare them, if possible, with the Taylor series expansion of the exact solution. They also have to observe where the existence and uniqueness of solutions apply.  Moreover, a solution without its domain of existence can be considered incomplete.

The same approach can be applied to second order ODEs with constant coefficient and (non trivial) periodic input.  Usually, textbooks introduce Fourier series for PDEs but they are very rarely used to find the steady state solution of an ODE.  This is because these computations can be arduous when done manually and are more related to “applied” differential equations. With engineering students this should be part of the curriculum.  Using the Voyage 200, this can be more easily explored and students should be able to plot a partial sum of the steady state solution.