Calculus in Context: The Five College Calculus Project

Authors

• James Callahan, Smith CollegeFollow
• Kenneth Hoffman, Hampshire College
• David Cox, Amherst College
• Donal O'Shea, Mount Holyoke College
• Harriet Pollatsek, Mount Holyoke College
• Lester Senechal, Mount Holyoke College

Files

Description

Calculus in Context: The Five College Calculus Project is a thorough reframing of what it means to learn calculus. It starts with a “clean slate;” there is no presumptive commitment to any aspect of the traditional course. Instead, the curriculum is guided by the following principles:

• Calculus is fundamentally a way of dealing with functional relationships that occur in scientific and mathematical contexts. The techniques of calculus must be subordinate to an overall view of the underlying questions.
• Technology radically enlarges the range of questions we can explore and the ways we can answer them. Computers can be engaged as much more than tools for teaching the traditional calculus course.
• The concept of a dynamical system is central to science. Therefore, differential equations belong at the center of calculus, and technology makes this possible at the introductory level.
• The process of successive approximations is a key tool of calculus, even when the outcome of the process—the limit—cannot be explicitly given in closed form.

These principles are implemented from the outset. The very first chapter begins with questions about describing and analyzing the spread of a contagious disease. A model is built, a model that is a system of non-linear differential equations. Then a numerical assault is begun on those equations, and the door is opened to a solution by successive approximations.

In the following chapters, successive approximations and computational tools continue to assert their central role. For example, the concepts of local linearity and the derivative emerge from ever-more-enlarged computer “microscope” views of a function’s graph. This conceptual focus leads to a further study of differential equations and dynamical systems that concentrates on their scientific contexts and the structural and computational issues they present. The computational basis of integration is fully developed along the same lines and in a way that leads naturally to the fundamental theorem. Computer graphics provide dramatic visual evidence for the “big Oh” notation used to describe how Taylor polynomials give successively better approximations to a function. Even these few instances begin to illustrate how the principles cited above can be implemented and how that implementation can alter what it means to learn calculus.

Publication Date

2026

Publisher

W.H. Freeman (1995), The Five College Calculus Project (2008, 2026)

Disciplines

Physical Sciences and Mathematics

Creative Commons License

This work is licensed under a Creative Commons Attribution-Share Alike 4.0 International License.

Comments

The Archive

The downloadable files in this archive are of several sorts and are meant to serve two distinct audiences: first, users who are interested in studying and teaching calculus; second, developers who wish to create their own calculus materials that are based in some way on Calculus in Context: The Five College Calculus Project.

The first nineteen downloads are intended for users:

• Download Full Text is a PDF of the book with red hypertext links for all internal cross-references, suitable for viewing online.

• Full Text Print Version is a PDF of the book suitable for printing; links are printed in black, but the two full text versions are otherwise identical.

• Fourteen PDF files that give the frontmatter, twelve individual chapters, and backmatter of the book.

• Three Supplements: a PDF of the Handbook for instructors, a PDF of the Solution manual, and a ZIP file containing the QBASIC computer programs used in the book.

The last three downloads are intended for developers:

• A ZIP file containing all LaTeX and EPS image files for the full book.

• A ZIP file containing all LaTeX and EPS image files for the Solution manual.

• A plain-text README file that gives more information about using the source ZIP files.

The Five College Calculus Project

The Five College Calculus Project began in the late 1980s as a response to a National Science Foundation calculus initiative. Under the auspices of Five Colleges, Inc., a group of Five College faculty sought an NSF grant to develop a new calculus course based on a highly innovative one already being taught at one of the five, Hampshire College. The proposal, titled Calculus in Context, was successful; the project received the only multi-year grant awarded in the initiative’s first year.

In 1995, the project produced the first version of the text, Calculus in Context. It was published by W.H. Freeman and remained in print for about a decade. At that point, Five Colleges, Inc. recovered the copyright, and the project began distributing a free online version of the text in 2008 at the site

https://www.science.smith.edu/~callahan/intromine.html

The online version attracted students and faculty, as well as other faculty interested in developing the ideas of Calculus in Context for their own purposes. To address both needs, the authors decided to create a definitive, comprehensive, and final version in this 2026 distribution.

The new version, Calculus in Context: The Five College Calculus Project, has been corrected and updated in 2026 from the original 1995 version. Technological advances in the intervening time have also been incorporated. The full text is now available in two versions with identical content. One, intended for online use, has red hyperlinks for all cross-references. The other is suitable for printing and binding as a book, with links printed in black. In addition, images created initially in PostScript have been converted to Encapsulated PostScript so that developers can alter and compile the source files using pdflatex as well as latex. These enhancements to the archive were carried out by David Cox.

The subtitle of the new version, The Five College Calculus Project, is included here to emphasize the collaborative nature of the project and to honor Kenneth Hoffman and Hampshire College for the crucial contribution each made. There is further information about the Five College Calculus Project in the Preface and the Afterword of the text itself.

Recommended Citation

Callahan, James; Hoffman, Kenneth; Cox, David; O'Shea, Donal; Pollatsek, Harriet; and Senechal, Lester, "Calculus in Context: The Five College Calculus Project" (2026). Open Educational Resources: Textbooks, Smith College, Northampton, MA.
https://scholarworks.smith.edu/textbooks/11

Rights

Copyright © 2026 by James Callahan and Kenneth Hoffman