# Chapter 9: Derivatives of Vector Fields and the Gradient in Polar Coordinates

##

## Introduction

The divergence and curl of vector fields are defined, the problem of providing visual representation of fields is discussed, and the gradient of a scalar field is discussed in some detail. In particular we consider how to express it in an arbitrary orthogonal coordinate system, in three different ways.

## Topics

9.1 Derivatives of Vector Functions; the Divergence

9.2 The Curl

9.3 Visualizing Functions of Two Variables

9.4 The Gradient in Polar Coodinates and other Orthogonal Coordinate Systems