Calculus occupies a pivotal position in math and science education. Typically, it is the first exposure our students have to higher mathematics, it is the first encounter with modern concepts of rigor and proof, it is the foundation for much of the mathematics used engineering courses, and it is the mathematical language that will be used by scientists to express many of the most important ideas in science.
We are of the opinion that calculus textbooks are not presenting calculus as the foundation of modern mathematics, engineering, science, and technology. The needs of modern scientists seem to have little influence on the calculus course, the "rigor" in calculus is uneven and largely unmotivated, and many of the applications seem out of date and out of touch.
We wrote this book as a first step in addressing the foundational role of calculus. However, it soon became apparent that "modernizing" the calculus course would also require an examination of pedagogical issues as well. In fact, we decided that to be truly effective, a calculus textbook would have to address 3 issues in particular:
- How students learn mathematics and in particular, calculus
- How calculus is used in modern mathematical, engineering, and scientific applications
- How best to use technology, reform, and traditional techniques to address the first two issues
Over the next few years, we researched these issues until we had addressed them to our satisfaction. We also worked with students to ascertain their preferences between different topics, definitions, and applications. These efforts resulted in a detailed plan for writing the textbook, and the implementation of that plan has now culminated in the textbook itself. <Back to home page>