Course Materials

Don’t just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?

Free Calculus Textbooks

Below is a list of free calculus texts that you may use as an additional resource. If you find one of these more helpful than another or if you know of additional resources, please let me know. Also, let me know if you encounter a broken link.

  • Calculus for Team-Based Inquiry Learning by TBIL Institute Fellows. Activities and exercises for easily implementing Team-Based Inquiry Learning in a single-variable calculus classroom. PDF and HTML versions.
  • CLP Calculus Textbooks by Joel Feldman, Andrew Rechnitzer, and Elyse Yeager were written for standard university calculus courses at the University of British Colombia. Free PDF and web-based textbooks.
  • APEX Calculus is an open-source textbook by a group of faculty from Virginia Military Institute. It has the look and feel of a traditional calculus (e.g., Stewart’s Calculus). Includes interactive 3D graphics.
  • Open Source Calculus and Analysis by a group of faculty at Ghent University. This book substantially builds on APEX Calculus. As compared to the APEX Calculus, it comes with precalculus, more formalism, proofs of most theorems (and more theorems), differential equations, computer laboratories, review exercises, built-in code for symbolic computation, and many other things. It’s tailored to students in engineering programs. Multiple free PDFs available for download.
  • MOOCulus Textbook is a free textbook from the Ximera folks at Ohio State University. This text is mostly an adaptation of the Community Calculus text listed below.
  • Community Calculus by David Guichard (Whitman College). This one is also available as a free PDF. You can also purchase a very inexpensive hardcopy from Lulu.
  • Active Calculus by Matt Boelkins (Grand Valley State College). This is one of the newer additions to the list of free calculus texts.
  • Coordinated Calculus by Nathan Wakefield (University of Nebraska) et al. This is the calculus textbook used at the Univerisity of Nebraska. Based upon Active Calculus by Matthew Boelkins (see above).
  • Calculus by Gilbert Strang (MIT). This book is available as a free PDF from the MIT Open Courseware Project. There are also some corresponding videos, which can be found here.
  • Calculus Refresher by Paul Garrett (University of Minnesota). Another free PDF. This short book seems designed for students who have had some experience with calculus and need some review.
  • Funny Little Calculus Text by Robert Ghrist (University of Pennsylvania). Currently only first semester calculus, very short, and no exercises, but a free PDF.
  • Paul’s Online Math Notes by Paul Dawkins (Lamar University). Paul’s notes cover Calculus 1-3, Linear Algebra, and more. The notes are available as free HTML-based material. These notes seem to be popular with students.
  • Differential Calculus with Sage by David Joyner (United States Naval Academy, retired) and William Granville. This free book is based on Granville’s classic text book Elements of the Differential and Integral Calculus, which fell into the public domain. The book covers first semester calculus and incorporates Sage, which is an open-source mathematics software package.
  • Integral Calculus with Sage by Dale Hoffman (Bellevue Community College), William Stein (SageMath), and David Joyner (United States Naval Academy, retired). The book picks up where the previous book left off.
  • Contemporary Calculus by Dale Hoffman (Bellevue Community College). A free online calculus text that is being developed for the Open Course Library Project of the Washington State Colleges. This book is part of the foundation for the previous book. It covers three semesters of calculus and seems to do a thorough job of it, but the formatting is awful.

Additional Videos, Applets, & Problems

Below is a partial list of applet and video repositories related to calculus. There are lots more out there. If you know of a good resource that’s not listed below, please let me know.


Dana C. Ernst

Mathematics & Teaching

  Northern Arizona University
  Flagstaff, AZ
  Google Scholar
  Impact Story

Current Courses

  MAT 226: Discrete Math
  MAT 320: Foundations
  MAT 431: Analysis

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  Flagstaff and NAU sit at the base of the San Francisco Peaks, on homelands sacred to Native Americans throughout the region. The Peaks, which includes Humphreys Peak (12,633 feet), the highest point in Arizona, have religious significance to several Native American tribes. In particular, the Peaks form the Diné (Navajo) sacred mountain of the west, called Dook'o'oosłííd, which means "the summit that never melts". The Hopi name for the Peaks is Nuva'tukya'ovi, which translates to "place-of-snow-on-the-very-top". The land in the area surrounding Flagstaff is the ancestral homeland of the Hopi, Ndee/Nnēē (Western Apache), Yavapai, A:shiwi (Zuni Pueblo), and Diné (Navajo). We honor their past, present, and future generations, who have lived here for millennia and will forever call this place home.