Calculus With Julia

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The online Calculus with Julia notes list version 0.27, dated Aug. 31, 2026. The Quarto book uses Julia to teach graphical and numerical approaches to calculus, with symbolic methods added where useful, and is accompanied by a package of helper functions.

The online Calculus with Julia notes list a new release, version 0.27, dated Aug. 31, 2026, updating a teaching resource that uses the Julia programming language to explore calculus. The material combines graphical and numerical computation with algebraic work, giving students an alternative to courses centered mainly on symbolic computer algebra.

The notes describe themselves as a set of materials for learning calculus with Julia, an open-source programming language. Their stated aim is to use computation to make calculus concepts more accessible without making the lessons primarily about programming. The authors say the material focuses on a limited set of computational ideas, using functions and operators that can be composed to address common introductory calculus problems.

The site is organized as a Quarto book, with pages focused on individual concepts and try-it-yourself questions at the end of each page. Some questions have self-graded answers. The notes are paired with a Julia package called CalculusWithJulia, which supplies simple functions for common tasks and loads packages used throughout the lessons.

The preface says readers can consult separate material on getting started with Julia and on ways to interact with a Julia installation. It also invites contributions, including suggested topics, corrections and typo fixes. The site thanks contributors and specifically acknowledges @fangliu-tju for proofreading and identifying errors through a series of pull requests.

A Coding-Based Route Into Calculus

The release matters to students and instructors seeking computational approaches to introductory calculus. Instead of presenting a computer algebra system as the main means of producing symbolic answers, the notes describe Julia as a tool for exploring numerical and graphical aspects, while retaining algebraic reasoning as part of the learning process.

The preface says that learning by hand can help students understand symbolic methods, and that automated symbolic answers can make such exercises feel redundant. Its approach is to use technology to examine concepts while limiting the programming required. That may make the resource useful to learners who want to connect calculus with coding without first taking a broad programming course. The source describes the intended approach; it does not provide evidence that the notes improve learning outcomes or report adoption figures.

How the Notes Approach Calculus

The preface places the material within a teaching tradition that presents calculus from multiple perspectives. It refers to Harvard’s “rule of four,” which calls for graphical, numerical, algebraic and verbal explanations. The notes say Julia is used mainly for the graphical and numerical components, with algebraic treatment included at times.

The authors distinguish this design from approaches that center on computer algebra systems such as Mathematica, Maple or Sage. Those systems can produce symbolic results and support numerical illustration, while these notes put greater emphasis on computation with Julia and add symbolic work as appropriate. The resource credits a range of influences, including work by Gilbert Strang, Oliver Knill, Malcolm Schey and calculus textbook authors, as well as Wikipedia pages and other sources.

The site says it is possible to assemble a PDF using Quarto, but describes the result as large and less satisfactory than the online book. It points readers to Julia installation guidance and notes that Julia can be installed with the juliaup utility or by other methods.

“These notes use the programming language Julia to illustrate the graphical, numerical, and, at times, the algebraic aspects of calculus.”

— The Calculus with Julia notes’ preface

Release Details Still Unspecified

The supplied source identifies version 0.27 and its date, but does not give a change log or explain what was added or revised in this release. It is not clear from the report whether the version includes new topics, corrections, package changes or only other updates to the book.

The source also does not provide information on the number of readers, course adoptions, assessment results or plans for future releases. Its comments about the teaching approach are statements of intent, not reported findings from a study measuring student outcomes. Readers should consult the project’s release history or contributors for details beyond the version date and the general description of the resource.

Readers Can Explore and Contribute

Readers can use the online Quarto book, follow its Julia setup guidance and work through the try-it-yourself questions. The site also provides a route to suggest additions, report errors or correct typos through its “Edit this page” link. The source gives no announced schedule for version 0.28 or other next milestone, so further release timing is not known.

Key Questions

What is the latest version listed?

The source lists version 0.27, dated Aug. 31, 2026. It does not include a detailed list of changes in that release.

What does the resource teach?

It uses Julia to support learning calculus, with an emphasis on graphical and numerical exploration and some algebraic treatment. The notes say they aim to focus on calculus concepts rather than extensive programming instruction.

Do learners need to install Julia?

The notes include guidance for getting started with Julia and describe it as usable through a local installation. The source mentions juliaup as one installation option, but does not specify every setup requirement for every lesson.

Is there a companion package?

Yes. The CalculusWithJulia package provides simple helper functions for common tasks and loads packages used in the notes.

Is the book available as a PDF?

The authors say a PDF can be compiled from the Quarto book, but describe the resulting file as large and less satisfactory than the online version.

Source: hn