Dr. K. G. TeBeest
NOTE: You will NOT be responsible for knowing hyperboloids of TWO sheets.NOTE: Study and be familiar with the formulas and corresponding surfaces in Table 1 (except hyperboloids of TWO sheets).
You DEFINITELY want to do this!
Click >>THIS LINK<< . This will open a new page that lets you play with animations of various surfaces in 3-D.
Here are the instructions to use the above demonstration—
- In the left menu, click the link labeled M12.6A Traces of Surfaces.
- Play with different traces in different planes.
- Play with different surfaces by changing the formula in the "Traces of" drop-down menu.
- Do the exercises by clicking the "Exercises" tab below the plot window.
In most of these demonstrations, click and hold the left mouse button and drag to rotate the image.
- In the same page, click the link labeled M12.6B Quadric Surfaces.
- See how a suface changes by changing the values of a, b, and c in the slider bars.
- Play with different surfaces by changing the formula in the drop-down menu.
- Do the exercises by clicking the "Exercises" tab below the plot window.
- To easily create your own 3-D surface plots and animations in Maple, start Maple and click through the sequence:
- Tools (in the top menu)
- > Tutors
- > CalculusMultivariate
- > Cross Sections
- A small window will pop up.
Play with the surface that's given.
You may also change the "Expression" to enter a different formula to study a different surface.
Enter different slicing planes. You may use planes of the form
x = a .. b, y = a .. b, or z = a .. b.
Page 832, problems:
- 1 7 odd,
- 9(a,b),
- 11, 13, 17, 19,
- 21 28 all except 24,
- 21 28 all,
- 29, 31,
- 47
- Read and do these examples of using Maple to plot surfaces in 3-D.
Use Maple to check your work on any of the problems.