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Chapter 3 Vector Derivatives

In this chapter we review important concepts relating to vector functions and their derivatives. As in introductory calculus, the derivative may be seen as giving the rate of change of a particular quantity. However, the move to higher dimensions involved with vector functions allows for multiple interpretations of the rate of change of a vector function, and therefore several different notions of the derivative. These interpretations are based on combining the following three concepts:
  • The gradient of a scalar-valued function.
  • The inner product (see Definition 2.3.1).
  • The cross product.
We will begin by examining the inner and cross products.