Abstract
This chapter presents the methods, software, and analysis to handle them in numerical computation. Derivatives and integrals are the basic tools of calculus and appear in many mathematical models. It is uncommon for the calculation of a derivative or integral to be the primary objective of a numerical computation, but they appear frequently as sub-problems, and the derivation of methods for more complex problems often involves evaluating them. Derivatives and integrals are also very useful as topics for teaching about numerical computation and analysis. They are easily understood, intuitive or pictorial motivations can be presented, the algebra is usually not too messy, and yet their calculation is not trivial.
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