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Calculus: Concepts and Methods by Joan Davies, Ken Binmore

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Five

Vector functions

In this chapter we introduce the idea of a vector function and examine the instances in which it can be visualised. We have seen in Chapter 3 how partial derivatives are used to generalise the idea of the derivative of a real valued function of one real variable to that of a total derivative of a function of several variables. We extend this further to the idea of the total derivative of a vector function. This object is defined to be a matrix, and an understanding of the material covered in this chapter requires a good knowledge of the matrix algebra surveyed in Chapter 1. (Note especially §1.10.) Although it is quite demanding ...

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