Teaching Numerical Methods in ODE Courses

Nowadays, numerical methods play an important role in courses on ordinary diierential equations (ODEs). We believe that popular texts place far too much emphasis on the derivation and study of numerical methods per se. Because the aim is to teach students about ODEs, the emphasis should be placed on teaching what they need to know so as to use quality software to gain insight about solutions and their behavior. Here we present brieey the fundamentals of numerical methods from this perspective. The approach implies that certain topics in the theory of ODEs ought to be discussed even in a rst course. We describe brieey quality software for initial value problems available in several distinct areas of application. In this we comment about how the area can innuence the techniques used. Pointers are also provided to software for boundary value problems.