Chapter 3: Functions of Several Variables
Section 3.1: Functions and Their Graphs
Example 3.1.9
On the domain 0≤x,y,z≤3, graph the level surfaces w=5 and w=15 for the function w=lny+sinhxz+ycoshx+z.
Solution
Figure 3.1.9(a) shows the level surfaces w=5 in red, and w=15 in green.
The level curves on each of these level surfaces are included to provide some definition for surface.
The surfaces are drawn with Maple's implicitplot3d command, which assumes w=gx,y,z=c defines z=zx,y implicitly.
Table 3.1.9(a) contains the complete syntax for drawing Figure 3.1.9(a). (Select Evaluate in the Context Panel.)
use plots in module() local p,W; W:=ln(y+sinh(x*z))+y*cosh(x+z); p:=implicitplot3d([W=5,W=15],x=0..3,y=0..3,z=0..3,color=[red,green],style=surfacecontour,lightmodel=none,axes=frame,orientation=[130,70,0]): print(p); end module: end use:
Figure 3.1.9(a) Surfaces w=5,15 in red, green, respectively
W≔lny+sinhxz+ycoshx+z:plots:-implicitplot3dW=5,W=15, x=0..3,y=0..3,z=0..3,color=red,green,style=surfacecontour,lightmodel=none,axes=frame,orientation=130,70,0:
Table 3.1.9(a) Syntax for constructing Figure 3.1.9(a)
Of course, the graph of each surface could have been constructed interactively with the Plot Builder, and combined by copy/paste.
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