The Gradient and Some of its Applications (UMAP)

This module considers some relationships between curves and surfaces: How is the rate of climb in the vertical direction on a surface related to the equation of the surface? Is it possible to find a path on a surface for which the rate of climb is optimized? Students compute gradients and use them to solve practical problems involving steepest ascent.

Table of Contents:

1. INTRODUCTION

2. PRELIMINARIES

3. DEFINITION OF THE GRADIENT

4. FINDING THE TEANGENT VECTOR TO A CURVE ON A SURFACE USING THE GRADIENT

5. SUMMARY

6. APPLICATION OF THE GRADIENT TO FINDING CURVES OF STEEPEST ASCENT (DESCENT)

7. MODEL EXAM

8. ANSWERS TO EXERCISES AND MODEL EXAM