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

The Text

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. The twelve chapter titles indicate the scope and organization of the book:

1. A context for calculus

2. Successive approximations

3. The derivative

4. Differential equations

5. Techniques of differentiation

6. The integral

7. Periodicity

8. Dynamical systems

9. Functions of several variables

10. Series and approximations

11. Techniques of integration

12. Case studies

Publication Date

2026

Creative Commons License

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

Comments

The Five College Calculus Project was funded by a number of sources, including multi-year grants from the National Science Foundation in 1988 and 1991. The Calculus in Context text found in this archive has been corrected and updated in 2026 from the original edition published in 1995. In particular, all the embedded image files that had been written in the PostScript language have been converted by David Cox into Encapsulated PostScript to allow compilation of the sources by pdflatex as well as the original program latex. David Cox has also created hypertext links for all cross-references in the book. This leads to two different PDF forms of the book: a “print” version and an “online” version. Only one set of sources is involved, however, because the creation of the hyperlinks is simply toggled off or on in the master file that controls compilation. The authors intend the 2026 text to be the final version of their work and wish it to be freely available to all through download from this archive.

The Archive

This archive has three sections. The first, Documents, has all the downloadable PDF files and QBasic programs intended for students and instructors who want to learn or to teach calculus using Calculus in Context. Note that the full text is available in both an “online” version with hyperlinked cross-references and a standard “print’ version. The second, Sources, has the downloadable zip files that contain the LaTeX and Encapsulated PostScript source files needed by those who want to develop new calculus materials based in some way on Calculus in Context. There is also a README file that gives further information about the zip files. The third, Comments, provides further information about the development of Calculus in Context between 1988 and 2026.

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