Calculus

The Calculus package provides tools for working with the basic calculus operations of differentiation and integration. It can be used to produce approximate derivatives by several forms of finite differencing or to produce exact derivatives using symbolic differentiation (SD).

Differentiation

There are a few basic approaches to using the package, some of which we will examine in this section.

We use finite differencing to evaluate a derivative at a specific point and higher-order functions to create new functions that evaluate derivatives’ SD to produce exact derivatives for simple functions:

julia> using Calculus
julia> f(x)=sin(x)*cos(x);
julia> derivative(f,1.0) -0.4161468365471423
# Check since d(f) => cos*cos - sin*sin
julia> cos(1.0)^2 - sin(1.0)^2 -0.4161468365471423
# Possible to curry the function
julia> df = derivative(f)
julia> df(1.0)
-0.4161468365471423
# Also defined is the 2nd derivative
julia> d2f = second_derivative...