A Kinematic Approach to the Fundamental Theorem of Calculus (UMAP)

As part of a project to revise and update the engineering program at Union College, the author, along with mathematician colleague Karl Zimmermann and physicist colleague Gary Reich, developed an Integrated math/physics course. The course covers most of what is usually covered in the first three terms of a standard calculus sequence and the first term of a standard physics sequence. Although the course is self-contained, its rapid pace presumes that all students have had some previous exposure to calculus.

Table of Contents:

INTRODUCTION

THE AREA APPROACH

THE KINEMATIC APPROACH
The Easy Method
The Hard Method
Equating the Answers

COMAPARING THE PROOFS

MAKING THE PROOFS RIGOROUS

A CLOSING COMMENT ON HOW THE TWO PROOFS COMPARE

REFERENCES

ACKNOWLEDGMENTS

ABOUT THE AUTHOR