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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