Calculus with Julia is a set of lecture notes designed to teach introductory calculus through hands‑on programming in the Julia language. The notes follow the Harvard ‘rule of four’ by using Julia to illustrate the graphical, numerical, and, when helpful, the algebraic aspects of calculus, while leaving the verbal component to exposition. As the author states, the real goal is to use technology to reach the underlying concepts without getting bogged down in the mechanics of the computer language.
To reduce mechanical overhead, the notes are paired with the Julia package CalculusWithJulia, which supplies a small collection of composable actions that turn many calculus problems into simple function calls of the form action(function, arguments...). This package loads useful dependencies and provides streamlined helpers, letting students concentrate on understanding the mathematical ideas rather than on low‑level coding details.
The support section on Newton’s method demonstrates the package’s utility: it loads CalculusWithJulia together with Plots, SymPy and Roots, then uses automatic derivatives to iterate the update x_{i+1}=x_i-f(x_i)/f'(x_i) for f(x)=x^3-2x-5, converging to a root in just a few steps. This example shows how the package’s symbolic capabilities can be combined with numeric iteration to solve problems efficiently.