IntroductiontoFunctionsofSeveralVariables-Tidewater.pptVIP

* Chapter 8: Functions of Several Variables Section 8.1 Introduction to Functions of Several Variables Written by Karen Overman Instructor of Mathematics Tidewater Community College, Virginia Beach Campus Virginia Beach, VA With Assistance from a VCCS LearningWare Grant In this lesson we will discuss: Notation of functions of several variables Domain of functions of several variables Graphs of functions of several variables Level curves for functions of several variables Notation for Functions of Several Variables Previously we have studied functions of one variable, y = f(x) in which x was the independent variable and y was the dependent variable. We are going to expand the idea of functions to include functions with more than one independent variable. For example, consider the functions below: The function z = f(x, y) is a function of two variables. It has independent variables x and y, and the dependent variable z. Likewise, the function w = g(x, y, z) is a function of three variables. The variables x, y and z are independent variables and w is the dependent variable. The function h is similar except there are four independent variables. Hopefully you can see the notation for functions of several variables is similar to the notation you’ve used with single variable functions. When finding values of the several variable functions instead of just substituting in an x-value, we will substitute in values for each of the independent variables: For example, using the function f on the previous slide, we will evaluate the function f(x, y) for (2, 3) , (4, -3) and (5, y). A Function of Two Variables: A function f of two variables x and y is a rule that assigns to each ordered pair (x, y) in a given set D, called the domain, a unique value of f. Functions of more variables can be defined similarly. The operations we performed with one-variable functions can also be performed with functions of several variables. For example, for the two-variable funct