Elementary calculus

Abstract

This chapter deals with calculating derivatives, antiderivatives (or primitive functions, indefinite integrals) and definite integrals, as well as calculating sums and products. Although Maple is very powerful in calculating antiderivatives, sometimes it can be useful to help it a little bit; this chapter pays attention to several ways to do so, demonstrated by simple examples. Moreover, reliability and methods for checking are discussed.

Calculus is based on the concept of functions. It is often more convenient to use functions than expressions in calculations. In Chapter 6, Creating and using mathematical functions, the use of functions is discussed, especially in connection with calculus.

Applying series approximations, for instance for antiderivatives, is shown in chapter 8, Taylor or Laurent expansions and limits. In that chapter limits are dealt with too.