MATHEMATICS 423:01 -- HOMEWORK ASSIGNMENTS  Spring 2011

Only the problems with an asterisk (*) should be handed in for grading.

 Assignment Chapter/Section Due date 1 1.1: 3,7,8*,10,11; 1.2: 1,3,6*,8,10* Thursday, Jan 27 2 1.3: 5,6*,9; 1.4: 1,2,4*,6; 1.5: 1,2,3* Thursday, Feb 3 3 1.6: 2,4*,5; 2.1: 1,5*,6; 2.2: 1,2*,3,5 Thursday, Feb 10 4 2.3: 4,5,6*; 2.4: 1,2*,15,16; 2.5: 1,2* Thursday, Feb 17 5 4.1: 2,3,4*; 4.2: 1,2*,3*,4 Thursday, March 3 6 5.1: 2,5,8*,9; 5.2: 1,4*,7*,11 Thursday, March 10 7 5.3: 2,3*,6,9*,11a,13* Thursday, March 24 8 5.4: 2*,7,8; 5.6: 1,8*,9* Thursday, March 31 9 6.1 2,4,5*,8*,9; 6.2: 3,4*,6,7 Thursday, April 14 10 6.3 1,2,3*; 7.1: 2,5,7,8,9* Thursday, April 21 11 8.1 3; 8.2: 1,2*,3,9,11* Thursday, April 28

Hint for problem 1.4.4: Integrate the differential equation between 0 and x to get a formula for u'(x) in terms of u'(0) and the integral of f. Then integrate again to get a formula for u(x). By evaluating this second formula at x=l, you can find an expression for u'(0), so this term may then be eliminated. In the integrations described above, you will need to do the cases when x in (0,l/2) and x \in (l/2,l) separately.

Hint for problem 2.1.5: Consider the following 6 cases (1) x-ct < x+ct < -a, (2) x-ct < -a < x+ct < a,
(3) x-ct < -a < a < x+ct, (4) -a < x-ct < x+ct < a, (5) -a < x-ct < a < x+ct, (6) -a < a < x-ct < x+ct.

Hint for problem 7.1.9: Use Green's identity to write (grad w_i, grad w_j) = -([w_i]_{xx} +[w_i]_{yy}, w_j) for i = 1 or 2. Use Maple to compute the integrals.

Hint for problem 8.1.3: Use the points x + Delta x, x - Delta x, x + 2 Delta x, and x - 2 Delta x.

Solutions to the problems that you are asked to hand in will be posted to the Sakai course web page.

last revised 4/13/2011