The Terminator and Other Geographical Curves (UMAP)

This module seeks to: 1) strengthen students' intuition in multidimensional geometry; 2) consolidate their command of differentials; 3) provide exercises, at a level between mechanical and theoretical, that do not require any background on applications; and 4) show important applications that rarely appear in calculus texts. It shows how to use differentials of vector-valued functions to determine the angle between two routes, or the azimuth (direction) for the shortest route from one point to another, on the surface of the earth. Real examples accompany the theory. The exercises are at a level intermediate between mechanical problems and abstract proofs and fit in any multivaraible calculus course.

Table of Contents:

INTRODUCTION

REVIEW OF DIFFERENTIALS
Differentials With One Variable
The Differential of Planar Curves
The Differntial of Spatial Curves
Great Circles
Angles Between Curves in Euclidean Spaces

DIFFERENTIALS OF FUNCTIONS OF SEVERAL VARIABLES
Differentials of Real-Valued Functions of Several Variables
Level Sets of Functions of Several Variables

SAMPLE EXAMINATION PROBLEMS

SOLUTIONS TO THE ODD-NUMBERED EXERCISES

SOLUTION TO THE SAMPLE EXAM PROBLEMS

REFERENCES

ACKNOWLEDGMENTS

ABOUT THE AUTHOR