ABSTRACT
This chapter reflects on the ordering of the previous three chapters: limits, differentiation and integration. The problem for limit-first approaches to calculus is that there is not a lot of opportunity in many pre-calculus curricula for limit ideas to be discussed and limit-related problems attacked. It provides an introduction to infinitesimal calculus. The chapter shows that infinitesimals were important in the early development of the calculus following Leibniz’s approach. Differentiation comes before integration in almost all calculus courses, but this need not be the case; Henle and Kleinberg, for instance, is a calculus textbook where integration is covered before differentiation. Nevertheless, it is possible to develop a modified (spiral curriculum) form of that does not explicitly refer to supremum and infimum.
