Math 4530-
Curves and Surfaces
Spring term, 2002

Homework Assignments

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Links:
Math 4530 maple page
Math 4530 home page
Professor Korevaar's home page
Department of Mathematics




Homework assignments (most recent first):


   Due Wednesday, May 8: HW #10 Problems related to the Gauss-Bonnet Theorem, from notes of Wednesday April 24. This assignment is optional if you are doing a project. If you are taking the final exam, it will graded as a take-home portion of the final, worth 30% of your score.

   Due Monday, April 22: HW #9 (but ask for an extension if you wish). Exercises 1,2 from Monday April 15 notes (compute Christoffel symbols for an orthogonal patch, and then use them to verify intrinsic formulas for Gauss curvature); Exercises 3,4 from Wednesday April 17 notes (compute lengths and areas for subdomains of the sphere and hyperbolic space, using stereographic maps and conformal metrics.
   Grading:  13 points possible, distributed as follows: 1 = 3 points, 2a = 2 points, 2b = 1 point, 3abc = 1 point each, 4abcd = 1 point each.

   Due Wednesday, April 10: HW #8 (our exam is on the 12th!)
   hwapril10.pdf
   The directory minimalsurfaces  contains minimal surface tools and information which may be helpful.
   Grading:  44 points possible, distributed as follows:
     1 = 2 points, 2 = 3 points, 3 = 2 points, 4, 5, 6, 7 = 3 points each;
     7.1.2, 1.3, 1.5, 1.6, 1.7 = 2 points each;
     7.3.5 = 3 points, 3.8 = 2 points, 3.10 = 4 points, 3.18, 3.19 = 2 points each;
     10 = 2 points.

   Due Monday, March 25: HW #6-7 (note the extension!) Add problem 4.2.5, plotting six minimal surfaces and computing their mean and Gauss curvature with Maple (You should get zero for the mean curvature!). The Helcat family of surfaces is a 1-parameter family of minimal surfaces joining the helicoid to the catenoid. You can use Maple to make a movie of this if you want, using the command "annimate3d". We will understand this example better after next week. Warning: Save frequently! Maple can't do some of these computations. After we study the minimal surface- complex analysis connection you will be able to do them by hand!
     Also, finish up:  hwmarch18.pdf

   Grading:  4.2.5 = 12 points, for drawing the surfaces and exploring which ones you could compute H and K for. The grading for "hwmarch18.pdf" is as follows: 29 points possible, distributed:
     Part I: 2.4 = 6 points, 2.19, 2.9 = 3 points each, Enneper = 2 points;
     Part II: 3.5, 3.7, 3.8, 3.10, 3.11 = 2 points each.
     Part III: a, b, d = 1 point, c = 2 points.

   Due Wednesday, March 6: HW #5
     HWI in Friday March 1 notes
     Chapter 2:   3.6, 4.3-4.5
     Chapter 3:   1.1, 1.4-1.8.
   Grading:  19 points, distributed as follows:
     2.3.6 = 3 points, 4.3, 4.4 = 2 points each;
     3.1.1= 1 point, 1.4 =2 point, 1.5 = 1 point, 1.6 = 2 points, 1.7 = 1 point, 1.8 = 2 points.

   Due Friday, March 1: HW #4
     Chapter 2:   2.1-2.6, 3.1-3.4, Plus class exercises I, II from Monday January 28 notes
   Grading: 24 points possible, 2 points each problem.     

   Due Monday, January 28: (Well, get it to me by Wednesday) HW #3 These are mostly Maple exercises. I have posted worksheets on our Maple page
which already contain many of the book procedures you will need. If you download these files and open them from Maple you will be well on your way.
     From Chapter 1: 6.2-6.6, 6.9-6.10; 6.9: kappa_3, kappa_4. 6.10: curve with kap3d1 and tau3d1.
     From Chapter 2: Look at 1.2-1.4. Hand in 1.6, 1.7, 5.1-5.5.

   Grading:  23 points, distributed as follows:
     Chapter 1: 6.2, 6.3 = 1 point each; 6.4, 6.5, 6.6, 6.9, 6.10 = 2 points each.
     Chapter 2: 1.6, 1.7 = 1 point each; 5.1-5.4 = 2 points each, 5.5 = 1 point.

   Solutions:
     hwsolsjan28a.pdf  chapter 1 portion
     hwsolsjan28b.pdf  chapter 2 portion


   Due Wednesday, January 23: HW #2
     From Chapter 1. Understand, but don't hand in 3.2-3.7. Do
     3.15-3.16, 3.21-3.22, 4.1-4.3, 5.10-5.13.
   Grading:  22 points, distributed as follows:
     3.15 = 1 point, 3.16, 3.21, 3.22, 4.1, 4.2 = 2 points each, 4.3 = 4 points, 5.10 = 2 points, 5.11 = 1 point, 5.12, 5.13 = 2 points each.

   Due Monday, January 14: HW #1
     Chapter 1:   1.1, 1.5-1.7, 1.9-1.13, 2.1-2.3;
     Handout questions on Pythagorean Theorem, (a)-(e).
   Grading:  26 points, distributed as follows:
     Chapter 1:   1.1 = 1 point, 1.5 = 2 points, 1.6, 1.7 = 3 points each, 1.9, 1.10, 1.11 = 2 points each, 1.12-1.13 = 1 point each, 2.1 = 2 points, 2.2, 2.3 = 1 point each.
     Handout:   a,b,c,d,e = 1 point each.