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 11 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.
Gregory Hartman (Virginia Military Institute). Contributions were made by Troy Siemers and Dimplekumar Chalishajar of VMI and Brian Heinold of Mount Saint Mary's University. This content is copyrighted by a Creative Commons Attribution - Noncommercial (BY-NC) License. http://www.apexcalculus.com/