Vector calculus

18.1 Introduction

In the previous chapter, we looked at functions of more than one variable. For a function of two variables (x, y) we define a function u = f (x, y) which can be represented by a surface. For each pair of values (x, y) we can find a single value for u, showing that u is a scalar quantity. For this reason, a function of spatial coordinates is called a scalar field. We also saw how to calculate a gradient of a function of two variables and that the gradient depends on the direction of the path that we choose across the surface. This means that the gradient must be described by both a magnitude and a direction. From Chapter 9, we know that vectors are used to represent quantities that have both magnitude and direction ...

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