Advanced Calculus pp 18-33 | Cite as

# Partial Differentiation

## Abstract

Chapter 1 deals with functions of a single variable, written *f*(*x*). We now turn to functions of many variables, in general written *f*(*x*_{1}, *x*_{2},……, *x*_{ n }) where *x*_{1}, *x*_{2},……, *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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