MATH 550
Professor Girardi
Quiz 7
Due the week of 2 April 2000.

  1. Problem 14 from Section 7.1 (pg 402).
  2. Problem 2b from Section 7.2 (pg 418).
  3. Problem 6 from Section 7.2 (pg 418).
  4. Problem 8 from Section 7.3 (pg 428). Since we have not answered questions on Section 7.3, here are some hints.
    First to identify the surface (i.e. make a rough sketch of it - just sketch it, you do not need to know the name of it). Think of fixing a u0 and letting v vary from 0 to 2pi ... what do you get ... well, in this case,
    Phi(u0 , v ) = ( (2-cosv ) cos u0 , (2-cosv ) sinu0 , sin v )
    ... now we can rewrite this as
    Phi(u0 , v ) = ( 2 cos u0 , 2 sinu0 , 0 ) + cos v ( - cos u0 , - sinu0 , 0) + sin v ( 0 , 0 , 1)
    ... which we can rewrite as
    Phi(u0 , v ) = R0 + cos v e1 + sin v e2
    ... which we know is a circle (IS 1.6), carefully draw it in ... noting that e1 = - 1/2 of R0 . Now that you have done this, let u vary from 0 to 2pi to see what you get. Now for the rest of the problem, see IS 7.d.2.

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