Section 13.1
Introduction to Functions of
Several Variables
Examples:
f ( x, y )  4  x  4 y
2
V ( r , h)   r h
2
f ( x, y )  ln( xy  6)
2
The graph of a function of two
variables is the set of all points
(x,y,z) for which z=f(x,y) and (x,y)
is in the domain of f.
Geometrically, this can be
interpreted as a surface in space.
You can also visualize functions of two
variables in the plane by considering level
curves (or contour lines) along which the
value of f(x,y) is constant. This method is
often used in weather maps and in
representing electric potential fields.
Figure 13.7 and Figure 13.8
Alfred B. Thomas/Earth Scenes
USGS