ABSTRACT
In this chapter, the author consider some possible directions that a first course in calculus may take a student. This includes calculus immediately beyond what was covered in earlier chapters, the transition to university analysis, calculus in disciplines other than mathematics and the preparation of future school calculus teachers. Students may wonder why the topic of convergence is covered in a calculus context. The study of functions of a single (independent) variable leads into a study of functions of two or more variables, and while there are clear similarities there are also some differences. While the Riemann integral works well for many functions some fields require other kinds of integration. Many fields use mathematics, and they often require particular parts of calculus, some of which are quite specialised/advanced. In electrical engineering, the fourier transform is used to analyse varying voltages and currents.
