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

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## 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