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Mathematics LibreTexts

12: Functions of Several Variables


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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.