Calculus with Julia

Calculus with Julia is a structured set of instructional notes that teach introductory and multivariable calculus through the Julia programming language. It emphasizes a computational, numerical approach while retaining symbolic reasoning where helpful, following a multi-perspective pedagogy (graphical, numerical, algebraic, verbal). The material is organized into focused pages with worked examples and self-graded exercises, and comes with a companion CalculusWithJulia package plus guidance on installing and interacting with Julia. The author limits the programming scope to what is needed for calculus so learners can focus on concepts rather than general software mechanics.

The content spans foundational topics (numbers, functions, graphs), precalculus, limits and continuity, differentiation (including symbolic derivatives, optimization, Newton’s method, related rates, Taylor series), integration (FTC, numerical quadrature, substitution, integration by parts, improper integrals, arc length, volumes, orthogonal polynomials), ODEs (Euler’s method, DifferentialEquations.jl), and vector calculus (line/surface integrals, grad/div/curl, Green/Stokes/divergence theorems). Appendices cover Julia setup, interfaces, alternative packages (Symbolics.jl, SciML, Makie), plotting, and a quick-start guide. The notes are presented as a Quarto book, encourage contributions, and are intended for learners who want hands-on, computation-driven calculus with modern Julia tooling.