Chapter 1 deals with functions of a single variable, written f(x). We now turn to functions of many variables, in general written f(x1, x2,……, x n ) where x1, x2,……, x n are n independent variables, but most attention will be focused on the special (and simplest) case, n = 2, where the function is written f(x, y). This two-variable calculus has the most applications to the real world and has the merit of being applied to problems that can be visualised in three-dimensional space. The general scheme is therefore to state results in general, but to use two dimensions when doing examples, except in rare circumstances.
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