Introduction

1 A field is a function defined over a continuous region. This includes, Scalar Field g(x), Vector Field v(x), Fig. 3.1 or Tensor Field T(x).

2 We first introduce the differential vector operator "Nabla" denoted by V

3 We also note that there are as many ways to differentiate a vector field as there are ways of multiplying vectors, the analogy being given by Table 3.1.

Multiplication

Differentiation

Tensor Order

u-v dot u X v cross u ® v tensor

V-v divergence Vxv curl Vv gradient

\ t

Table 3.1: Similarities Between Multiplication and Differentiation Operators

Table 3.1: Similarities Between Multiplication and Differentiation Operators

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