Calculus Resources

This section of the site provides links to some of our favourite open Calculus textbook resources.


APEX Calculus is a free, open calculus textbook created by Greg Hartman of the Virginia Military Institute. University of Lethbridge has used APEX Calculus since 2015. Traditionally we used PDF textbooks edited by Sean Fitzpatrick to align with the U of L calculus courses.

The PDF books look great, and they're a good choice if you want to print a coursepack. But the PDF does not meet basic accessibility requirements, and it does not scale well for students wanting to access the book on a phone.

Since 2019, Sean Fitzpatrick has been working with Greg Hartman and a team of editors to convert the book to a new format, called PreTeXt. PreTeXt allows us to output to both PDF and HTML, and the HTML supports a lot of nice features, like optimization for small screens, embedded videos, and interactive exercises.

We host several versions of APEX Calculus here, depending on your needs. There is one "pure" version with no modifications specific to U of L.

Next is the same book as above, but with videos included.

The next version is divided into parts to reflect the standard four-semester calculus sequence at U of L. This version also contains embedded videos recorded by Sean Fitzpatrick to match the content of the book. Videos are currently available for all chapters except for the chapters on vectors, and vector-valued functions. The PDF version has exactly the same content as the HTML. Videos are replaced by a thumbnail and a QR code the reader can use to access the video on a mobile device.

There is a second version of the APEX textbook, with content rearranged to fit our Accelerated Calculus stream:

There are several PDF versions of these textbooks available. For each course, we provide both the original and PreTeXt-based versions of the book, in both colour and print formats. For details, see our home page.

There are many other excellent calculus resources. We have chosen to link to books written in PreTeXt, since these are available in HTML, and they often have useful features for self-study, such as interactive exercises.

Active Calculus (Single variable), by Matt Boelkins

Active Calculus (Multivariable), by Matt Boelkins

Page maintained by Sean Fitzpatrick. .