Functions of two variables Graphical Numerical and Analytical

Functions of two variables Graphical, Numerical and Analytical Points of view

Functions of One variable n In first and second semester calculus, you studied functions of one variable. That is, one quantity depends on another quantity. ¨ For instance, the area of a circle depends only upon its radius. ¨ The position of a moving object varies with time. n You have seen several ways of representing these relationships.

Functions of One Variable Analytical representation x 1 2 3 4 5 y=f(x). 841 1. 82. 423 -3. 03 -4. 80 Numerical Representation Graphical Representation

Dependance on more than one quantity n Most quantities in life depend on a number of different factors. ¨ Volume of a right circular cone depends on its height and the radius of its base ¨ The pressure of an ideal gas depends on the number of moles of the gas, the volume of the gas, the absolute temperature of the gas.

Graphing Functions of Two Variables

When we do this with many points… We get a surface instead of a curve!

In Calculus C. . . n We will study the calculus of functions of several variables. ¨ We will see how to picture these functions and extract information from the graphs. ¨ We will analyze their rates of change (differentiation) ¨ We will look at integration for these functions, as well.