Math 2210-4
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Professor Korevaar
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Homework is due at the start of class, on Fridays, unless otherwise noted. Homework solutions will be posted by the following Monday.
Homework assignments (most recent first):
Circled or underlined problems are to be handed in, others are only recommended.
Due Wednesday, April 27:
17.4 9, 14.
17.5 1, 3, 9, 11.
17.6 1, 5, 15.
17.7 3, 9, 19.
sols14.pdf solutions
Grading: 27 points, distributed as follows: (Note: If the main point of an integral is to do the computation, do it by hand. If the main point is setting up the integral, then feel free to use technology (graphing calculator, MAPLE, etc) to get the answer from the correctly set-up integral.
17.4 14 = 2 points.
17.5 3, 9, 11 = 3 points each.
17.6 1 = 2 points, 5 = 3 points, 15a,c,e = 2 points each.
17.7 5 = 3 points, 19 = 2 points.
Due Friday, April 22:
17.3 1, 7, 9, 11, 13, 21, 22. In 13, do the computations both ways - via a path integral and with a potential function.
17.4 1, 6, 7, 9, 14, 16, 19. postpone the flux integral part of 9 (but do the line integral), and postpone all of 14 until next week.
sols13.pdf solutions
Grading: 21 points, distributed as follows: (Note: If the main point of an integral is to do the computation, do it by hand. If the main point is setting up the integral, then feel free to use technology (graphing calculator, MAPLE, etc) to get the answer from the correctly set-up integral.
17.3 1, 9 = 2 points each; 13 = 4 points (2 points each way); 21 = 2 points.
17.4 1, 6, 7 = 3 points each; 16 = 2 points.
Due Friday, April 15:
16.8 3, 5, 7, 12, 15, 22, 23.
17.1 1, 2, 10, 11, 15, 17, 20abc, 21, 25. Note book typo in 21, they mean f(r) = -c/|r|, not f(r) = -c/(|r|^3).
17.2 1, 4, 7, 8, 15, 16, 17, 21.
sols12.pdf solutions
Grading: 31 points, distributed as follows: (Note: If the main point of an integral is to do the iterated integral computation, do it by hand. If the main point is setting up the integral, for example in applications, then feel free to use technology (graphing calculator, MAPLE, etc) to get the answer from the correctly set-up iteration.
16.8 3, 5, 12 = 3 points each.
17.1 10 = 1 point, 15, 17 = 2 points each; 20a,b = 1 point each, 21 = 4 points.
17.2 1, 7, 8 = 2 points each; 15 = 3 points, 17 = 2 points.
Due Friday, April 8:
16.6 1, 6, 7, 9;
16.7 1, 5, 9, 10, 15, 21, 25, 27, 28.
sols11.pdf solutions
Grading: 19 points, distributed as follows: (Note: If the main point of an integral is to do the iterated integral computation, do it by hand. If the main point is setting up the integral, for example in applications, then feel free to use technology (graphing calculator, MAPLE, etc) to get the answer from the correctly set-up iteration.
16.6 1 = 2 points, 6 = 3 points, 7 = 2 points.
16.7 5, 10 = 2 points each, 15 = 3 points, 21 = 3 points, 28 = 2 points.
Due Friday, April 1:
16.3 1, 5, 9, 13, 14, 16, 19, 23, 25, 33, 34, 37.
16.4 1, 5, 11, 12, 15, 19, 27.
16.5 3, 9, 12.
sols10.pdf solutions
Grading: 24 points, distributed as follows: (Note: If the main point of an integral is to do the iterated integral computation, do it by hand. If the main point is setting up the integral, for example in applications, then feel free to use technology (graphing calculator, MAPLE, etc) to get the answer from the correctly set-up iteration.
16.3 5, 14, 16, 25, 34 = 2 points each.
16.4 5, 11, 12, 19 = 2 points each.
16.5 3, 12 =3 points each.
Due Friday, March 25:
15.8 28, 29. Remember in 28 the book has a typo... the right side of the second equation is the sum of the yi, not the sum of xi*yi.
15.9 1, 3, 5, 9, 10, 11. Do 9 both ways: using Lagrange multipliers, and the 15.8 way of using the constraint to eliminate a variable.
16.1 1, 5, 8, 9, 10, 16;
16.2 5, 7, 11, 12, 13, 14, 17, 18.
sols9.pdf solutions
Grading: 31 points, distributed as follows:
15.8 28a,b = 2 points each, 29 = 2 points.
15.9 3 = 3 points, 5 = 2 points, 9(via Lagrange) = 3 points, 11 = 2 points.
16.1 1, 5, 8 = 1 point each; 9, 16 = 2 points each.
16.2 7, 12, 14, 18 = 2 points each.
Due Friday, March 11:
15.6 1, 6, 12, 13, 17, 18, 19, 20, 29;
15.7 1, 4, 6, 9, 15, 22;
15.8 1, 3, 7, 11, 12, 13, 15, 16, 19, 20, 22, 23.
sols8.pdf solutions
Grading: 31 points, distributed as follows:
15.6 6, 12, 13, 17, 20 = 2 points each.
15.7 4, 6, 9, 22 = 2 points each.
15.8 3, 7, 13, 15 = 2 points each; 19 = 3 points, 22 = 2 points.
Due Friday, March 4:
15.3 1, 2, 3, 5, 7, 8, 10, 11, 27abc, 28;
15.4 2, 9, 11, 12, 15, 17;
15.5 1, 9, 14, 15, 17, 19, 20, 24, 25, 31.
sols7.pdf solutions
Grading: 27 points, distributed as follows:
15.3 2, 5, 7, 8, 27abc = 1 point each.
15.4 9 = 1 point, 12 = 2 points, 17 = 1 point.
15.5 9, 14, 15, 17 = 2 points each; 19 = 3 points; 24 = 2 points;; 31c = 3 points.
Due Friday, February 25:
14.7 2a, 3a, 4a, 5a, 6a, 7, 8, 9, 13, 15, 17, 23, 27, 35, 36.
15.1 1, 9, 10, 11, 17, 18, 23, 24, 25, 27, 33, 35, 41.
15.2 1, 13, 17, 25, 27, 39, 47.
sols6.pdf solutions
Grading: 30 points, distributed as follows:
14.7 2a, 4a, 5a, 7, 8, 9 = 1 point each; 35 = 2 points, 36 = 1 point.
15.1 9, 10, 11, 17, 18, 41b = 2 points each.
15.2 13, 17, 27 = 2 points; 39b, 47b,c = 1 point each.
Due Friday, February 11:
13.4 16, 17, 21, 23, 31, 38, 41.
13.5 10, 17, 20, 36 (this problem is expanded, see prob36.pdf ) , 52, 53, 55.
14.5 15, 23. Also sketch the curves in 15, 23. For 15 sketch the curve onto the cylinder y^2+z^2=1. For 23 use the auxillary "cylinder" y^2-x^2=1, whose cross section is a hyperbola. 28, 36, 52, 64.
sols5.pdf solutions
Grading: 31 points, distributed as follows:
13.4 16 = 1 point, 23 = 3 points, 41 = 2 points.
13.5 10, 17 = 3 points each; extended 36: a=1, b=2, c=1, d=2, e=2 points; 52 = 1 point, 53 = 3 points.
14.5 15 = 3 points (2 points length, 1 point picture), 28 = 4 points.
Due Friday, February 4:
14.6 2, 5, 7, 8, 9, 13 14, 21, 22, 25. Note several additional problems from last week.
13.1 3, 6, 9, 13, 17. In 3, 6 also verify that dy/dx = (dy/dt)/(dx/dt) by computing both expressions directly.
14.4 23, 25.
14.5 1, 7.
sols4.pdf solutions
Grading: 30 points, distributed as follows:
14.6 2, 7, 8, 9, 13, 14 = 2 points each. On these problems you get 1.5 points if your surface is of the correct type with the axes in correct locations. Another .5 points for the quality of your picture.
13.1 6a,b,c,extra = 1 point each, 13, 17 = 3 points each.
14.4 23, 25 = 2 points each.
14.5 1, 7 = 2 points each.
Due Friday, January 28:
14.3 3, 5, 9, 10, 11, 13, 15, 19, 21, 25, 26;
14.4 5, 9, 17, 19, 28, 29a, 30a;
14.6 2, 5, 7, 8, 9, 14. Actually, section 14.6 is postponed until next week.
sols3.pdf solutions
Grading: 23 points, distributed as follows:
14.3 5, 10, 15 = 2 points each; 19ab = 1 point each, 19c, 25 = 2 points each.
14.4 5 = 1 point, 9, 19 = 2 points each; 28, 29a = 3 points each (1 point for derivation, 2 points for computation).
Due Friday, January 21:
hwset2.pdf assignment
sols2.pdf solutions
Grading: 27 points, distributed as follows:
Ib(law of cosines) = 2 points.
13.2: 2 = 1 point, 9 = 2 points, 17 = 2 points.
13.3: 2df, 4c, 5a, 16, 23 = 1 point each, 33a = 2 points.
14.2: 5 = 2 points, 7 = 1 point, 15 = 3 points, 29b = 1 point, 33, 43 = 2 points each, 45 = 1 point.
Due Friday, January 14:
hwset1.pdf assignment
sols1.pdf solutions
Grading: 20 points, distributed as follows:
1 = 4 points: 2 points to show inside parallelegram is square, 2 points to equate area computations and deduce Pythagorean Theorem; 2abcdefg = 1 point each, 3abc = 1 point each, 4abcd = 1 point each, 5 = 2 points.