Computer Algebra and the Mathematics Curriculum: A Closer Look at Second Order Differential Equations

There is no longer any question about whether the availability of computer algebra packages will lead to changes in the mathematics curriculum. The question is now in what ways will the curriculum change. The question is of particular importance in higher education where many students, particularly those studying engineering, have traditionally been taught mathematical methods courses primarily from the point of view of techniques. The question is already being asked by many in the engineering community if, given the mathematical power now available at the push of a button, there is still a need for these kind of mathematics courses within engineering degrees. In this paper rather than discussing the whole of the mathematics curriculum for engineers we will focus on just one topic: second order differential equations. We shall examine a number of ways in which students could study this topic both with and without the aid of computer algebra. We shall identify advantages and disadvantages of the various approaches. We conclude that topics like this can be used to provide insight into over-arching mathematical themes such as linearity which are of enormous importance throughout the whole of engineering. This macroscopic picture is something which has often been missing from the traditional technique oriented approach.