Math-203, Multivariate Calculus
Section 12.6 — Cylinders & Quadric Surfaces

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—

  1. In the left menu, click the link labeled M12.6A Traces of Surfaces.
    1. Play with different traces in different planes.
    2. Play with different surfaces by changing the formula in the "Traces of" drop-down menu.
    3. 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.

  2. In the same page, click the link labeled M12.6B Quadric Surfaces.
    1. See how a suface changes by changing the values of a, b, and c in the slider bars.
    2. Play with different surfaces by changing the formula in the drop-down menu.
    3. Do the exercises by clicking the "Exercises" tab below the plot window.

  3. To easily create your own 3-D surface plots and animations in Maple, start Maple and click through the sequence:
    1. Tools (in the top menu)
    2.    > Tutors
    3.      > Calculus–Multivariate
    4.         > Cross Sections
    5. 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 .. by = a .. b,  or  z = a .. b.



Page 832, problems:

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