Chap14_Sec1

# Chap14_Sec1 - PARTIAL DERIVATIVES 14.1 Functions of Several...

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14.1 Functions of PARTIAL DERIVATIVES Several Variables In this section, we will learn about: Functions of two or more variables and how to produce their graphs.

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A function f of two variables is a rule that assigns to each ordered pair of real numbers ( x, y ) in a set D a unique real number denoted by f ( x, y ). s The set D is the domain of f. s Its range is the set of values that f takes on, that is, { f ( x , y ) | ( x , y ) D } We often write z = f ( x , y ) to make explicit the value taken on by f at the FUNCTION OF TWO VARIABLES general point ( x, y ). s The variables x and y are independent variables. s z is the dependent variable. One way of visualizing such a function is by means of an arrow diagram, where the domain D is represented as a subset of the xy -plane.
Another way of visualizing the behavior of a function of two variables is to consider its graph. If f is a function of two variables with domain D , then the graph of f is the set of all points ( x, y, z ) in R 3 such that

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Chap14_Sec1 - PARTIAL DERIVATIVES 14.1 Functions of Several...

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