In this chapter, we will discuss various topics related to calculus. Calculus is the branch of mathematics that concerns the processes of differentiation and integration. Geometrically, the derivative of a function represents the gradient of the curve of the function, and the integral of a function represents the area below the curve of the function. Of course, these characterizations only hold in certain circumstances, but they provide a reasonable foundation for this chapter.

We start by looking at calculus for a simple class of functions: the polynomials. In the first recipe, we create a class that represents a polynomial and define methods that differentiate and integrate the polynomial. Polynomials are convenient because the derivative or integral of a polynomial is again a polynomial. Then, we use the SymPy package to perform symbolic differentiation and integration on more general...