13 Functions of Several Variables

Chapter Introduction

A function of the form y=f(x) is a function of a single variable; given a value of x, we can find a value y. Even the vector-valued functions of Chapter 12 are single-variable functions; the input is a single variable though the output is a vector.

There are many situations where a desired quantity is a function of two or more variables. For instance, wind chill is measured by knowing the temperature and wind speed; the volume of a gas can be computed knowing the pressure and temperature of the gas; to compute a baseball player’s batting average, one needs to know the number of hits and the number of at-bats.

This chapter studies multivariable functions, that is, functions with more than one input.

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