Chapter 3: Functions of Several Variables
Section 3.1: Functions and Their Graphs
Obtain a contour map for the function zx,y defined implicitly by the equation x⁢y+z⁢coshz−1=1.
Draw the surface as per Example 3.1.4. Set the style to contour, and rotate the graph so the viewpoint is from directly above. The figure drawn below has been made with the Plot Builder. Click on the graph to see in the Plot Builder all the settings that were used.
Alternatively, the implicitplot3d command in Maple graphs the surface zx,y defined implicitly by an equation of the form fx,y,z=0. There is no command designed to produce a contour map for zx,y if it is defined implicitly.
The implicitplot3d command, however, will draw contours on the surface, as seen in Figure 3.1.4(b), reproduced here as Figure 3.1.5(a). (Recall that Figure 3.1.4(b) was produced in the Plot Builder.) If the rendering of the surface is suppressed so that just its contours show, the graph can be rotated so it looks like all the contours lie in the xy-plane. This is how Figure 3.1.5(b) was obtained from the Plot Builder.
Figure 3.1.5(c) is obtained with the implicitplot3d command itself, implemented as shown below. (Select Evaluate in the Context Panel.)
The astute reader will note the subtle difference between Figures 3.1.5(b) and 3.1.5(c). In the former, the axis label z survives the rotation, and can be seen to the left of the negative x-axis; in the latter, the label on the z-axis is suppressed by invoking the label option.
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