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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largely unmotivated, and many of the applications seem out of date and out of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
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