Math 243 material, Fall 2005


Course information sheet (PDF format)

Homework assignments

  1. Homework #1 (practice) : 11.1 # 7,11,19,23,27,31,35,45; 11.2 # 5,17,23,33,39,43,53,67; 11.3 # 1,7,13,15,17,21.
    Homework #1 due Thursday, Sept. 1 : 11.1 # 46,48; 11.2 # 36, 44, 68; 11.3 # 18,29

  2. Homework #2 (practice) : 11.4 # 3, 7, 13, 15, 23, 29, 31, 35, 39; 11.5 # 3, 9, 20, 23, 33
    Homework #2 due Thursday, Sept. 8 : 11.4 # 44, 48, 51; 11.5 # 34, 40*, 58*. Notes: The phrases "Show that" and "Prove that" mean that you must explain why the given statement is true. For #40, there is a hint in the back for #55, which is the same problem.

  3. Homework #3 (practice) : 11.6 # 5, 11, 13, 19, 25, 35; 11.7 # 5, 7, 9, 13, 21, 23, 25, 27, 31, 33, 41, 43; 11.8 # 5, 9, 15, 19, 23, 25, 27, 33, 35, 37, 41, 43, 55.
    Homework #3 due Thursday, Sept. 15 : (1) 11.6 # 40. (2) Given lines L and M with parametric equations (1,0,0)+<0,1,1>t and (1,0,0)+<0,1,-1>u, respectively, find a hyperboloid that contains both L and M. (3) Sketch and describe each of the following surfaces in spherical coordinates: (a) &rho=&phi, 0 &le &phi &le &pi. (b) &rho=&theta, 0 &le &theta &le 2&pi. (c) &phi=&theta, 0 &le &theta &le &pi/2.

  4. Homework #4 (practice) : 12.2 # 5, 7, 11, 15, 23, 27, 29, 33, 37, 39, 53-58; 12.3 # 1, 3, 7, 11, 19, 25, 27, 29, 31, 33, 39, 41, 43, 45, 53; 12.4 # 3, 9, 15, 19, 23, 31, 33, 35, 39, 43, 53
    Homework #4 due Thursday, Sept. 22 : 12.2 # 42; 12.3 # 44; 12.4 # 40, 63; Find lim (x,y)->(0,0) x4y4 / (x6 + y6) or prove that is doesn't exist.

  5. Homework #5 (practice) : 12.5 # 9, 13, 15, 19, 25, 27, 29, 33, 39, 45, 51, 53, 63
    Homework #5 due Thursday, Sept. 29 : 12.5 # 46, 54, 59

  6. Homework #6 (practice) : 12.6 # 7, 9, 13, 17, 23, 25, 31, 33, 43; 12.7 # 3, 7, 9, 15, 17, 21, 23, 27, 31, 33, 35, 39, 43, 51; 12.10 # 3, 7, 9, 11, 13, 17, 21, 25, 27, 29
    Homework #6 due Thursday, Oct. 6 : 12.6 # 32, 44; 12.7 # 24, 42; 12.10 #20.
    BONUS Problem (alse due Oct. 6. Turn in separately): (a) Sketch the level sets of a function f(x,y) such that along every straight line through (0,0), f has a local minimum at (0,0), BUT f(x,y) does not have a local minimum at (0,0). (b) Find a polynomial f(x,y) satisfying (a).

  7. Homework #7 (practice) : 12.8 # 3, 7, 13, 17, 23, 27, 31, 33, 35-37, 47, 53, 61; 12.9 # 3, 9, 11, 13, 15, 17, 19, 21, 25, 29, 39, 41; 13.1 # 3, 11, 15, 19, 27, 29, 35; 13.2 # 3, 9, 11, 17, 19, 23, 25, 29, 33, 43
    Homework #7 due Thursday, Oct. 13 : 12.8 # 34, 50; 12.9 # 38, 62; 13.1 # 24; 13.2 # 34

  8. Homework #8 (practice) : 13.3 # 9, 13, 17, 25, 27, 29, 35, 37, 41, 45; 13.4 # 7, 11, 13, 17, 21, 27, 29, 33, 37, 39; 13.5 # 5, 9, 15, 23, 29, 31, 35, 43, 44, 45, 53, 57
    Homework #8 due Thursday, Oct. 20 : 13.4 # 34, 41 (the answer in the back of the book is wrong); 13.5 # 26; (A) Find the volume of intersection of the spheres x2+ y2 + z2=4 and x2+ y2 + z2 -8x+7=0; (B) A lamina of constant density, in the xy-plane, has mass 2, centroid (3,4) and moment of inertia about the x-axis equal to 50. Find the moment of inertial about the line y=-1.

  9. Homework #9 (practice) : 13.6 # 3, 5, 9, 13, 15, 19, 25, 39, 41, 43; 13.8 # 3, 7, 9, 13, 15, 21, 23
    Homework #9 due Thursday, Oct. 27 : 13.6 # 12, 26; 13.8 # 16

  10. Homework #10 (practice) : 13.7 # 3, 5, 7, 11, 15, 19, 23, 31, 35, 37; 13.9 # 1, 3, 5, 7, 9, 11, 13, 15, 17, 19
    Homework #10 due Thursday, Nov. 3 : 13.7 # 20; 13.9 # 10, 20; (A) Find the volume inside the surface z=(x2+y2+z2)2; (B) Find the area inside the astroid x2/3+y2/3 =a2/3. Hint: use x=u cos3t, y = ?
    BONUS PROBLEMS (DUE NOV. 10): 13.9 # 28, 29

  11. Homework #11 (practice) : 14.1 # 1, 5, 9, 11, 13, 15, 19, 23, 29, 31, 33; 14.2 # 1, 3, 7, 9, 13, 15, 19, 23, 27, 31, 33, 35, 39; 14.3 # 1, 5, 7, 11, 13, 19, 23, 29
    Homework #11 due Thursday, Nov. 10 : 14.1 # 20, 38; 14.2 # 24, 34; 14.3 # 10, 30

  12. Homework #12 (practice) : 14.4 # 1, 3, 7, 9, 11, 15, 17, 21, 23, 29, 31, 33; 14.5 # 3, 5, 7, 9, 11, 13, 17, 19, 23, 27
    Homework #12 due Thursday, Nov. 17 : 14.4 # 20, 24, 34; 14.5 # 16, 22

  13. Homework #13 (practice) : 14.6 # 1, 5, 7, 9, 11, 13, 16, 24; 14.7 # 1, 3, 5, 7, 9, 11, 13, 15, 17
    Homework #13 due WEDNESDAY, Dec. 7 : 14.6 # 12, 25; 14.7 # 6, 10


Exam #1.

Tuesday, September 27. Covers Chapter 11, plus sections 12.2-12.3.

Exam #2.

Tuesday, October 25. Covers sections 12.4--12.10 and 13.1--13.5.

Exam #3.

Wednesday, November 30. Covers sections 13.6-13.9, 14.1-14.5.

Final Exam.

Friday, December 16, 1:30-4:30. Comprehensive.

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