Problems marked with an asterisk (*) are to be turned in.
Solutions to selected problems from homeworks 13 and 14 are available here.
Homework 14: due Friday, December 13 by 4:00 pm in my office
9.6: 2,6*,17
9.7: 2,8*,16
10.1: 2,7*
Extra Credit Assignment: may be turned in any time up through 4:00 pm on Friday, December 13.
Solutions to selected problems from homeworks 11 and 12 are available here.
Homework 13: due Thursday, December 5 IN CLASS!
9.4: 8,10*,11*
9.5: 1,2*,10,13*
For problem 2 in section 9.5, explain the physical meaning of your solution. Thermal diffusivity constants for various materials can be found in Figure 9.5.3 on page 636 (for use in problem 13).
Homework 12, part 2: due Tuesday, December 3 by 4:00 pm in my office
Homework 12, part 1: due Thursday, November 21 IN CLASS!
9.3: 11,12*,16*
9.4: 1,3*,5
For problem 16 in section 9.3, verify the solution by directly substituting into the differential equation.
Hint: For any of these problems which involve writing a formal Fourier series solution to a differential equation, the first step is to find the Fourier series for the forcing term F(t). Look back at your old homework assignments; you may find that you've already done the work!
Extra Credit Assignment (worth the equivalent of up to one perfect quiz score): may be turned in any time before Tuesday, December 3
Do problems 23, 24 and 25 from section 9.2. For problem 23, you may verify the formulas directly by differentiating the right hand sides. For part (b) of problem #24, you may need to use identities (16), (17) and (18) on page 606.
Solutions to this extra credit assignment are available here.
Homework 11, part 2: due Tuesday, November 19 IN CLASS!
Homework 11, part 1: due Friday, November 15 by 4:00 pm in my office
9.2: 1,2,6*,8,17*
9.3: 1,3,4*,8*,19
Additional problem to be turned in:
Let f(t) be the trapezoidal wave function whose graph is shown here.
(a) Write a formula for f(t) and for its 6-periodic extension to the entire real line.
(b) Find the Fourier coefficients and write the Fourier series for f(t). (Hint: the values of the Fourier sine coefficients depend on the residue of n mod 6, that is, the remainder when n is divided by 6.)
(c) By substituting an appropriate value for t into your equation from part (b), calculate the value of the sum 1+1/25+1/49+1/121+1/169+... Your answer should be a rational multiple of pi squared.
Homework 10: due Thursday, November 7 by 4:00 pm in my office
9.1: 1,2,10*,13,15*,25*
(Hint for problem 25: use a double angle formula together with the formulas in equations (9), (10) and (11) on page 593 to compute the Fourier coefficients.)
Homework 9: due Friday, November 1 by 4:00 pm in my office
3.6: 15,18*,28*
3.8: 2,3,4*,13*,16*
Homework 8: due Thursday, October 24 by 4:00 pm in my office
3.5: 8,10*,26,34*,43*,47,53*
3.6: 1,4*,19,24*
For problems #1 and #4 in 3.6, write your anwer in the form of equation (8) on page 208.
Note: there is a typo in the statement of problem #24 in 3.6.
The external force should be
notF(t) = F_0 cos^3(omega t),
(Hint for this problem: use the result of 3.5 #43(a).)F(t) = F_0 cos^2(omega t).
Homework 7: due Thursday, October 17 by 4:00 pm in my office
3.4: 1,4*,10,15,16*
3.5: 1,4*,5,16*,31,40*
Homework 6, part 2: due Tuesday, October 15 by 4:00 pm in my office
Homework 6, part 1: due Thursday, October 10 by 4:00 pm in my office
3.1: 1,8*,37,40*,43,46*
3.2: 9,16*,17,31*
3.3: 3,7,10*,23*,26,35*
Homework 5: due Thursday, October 3 by 4:00 pm in my office
2.1: 1,18,20*
2.2: 1,6*,21*
Homework 4, part 2: due Friday, September 27 by 12:00 noon in my office
You can work on this project in any of the following EWS labs: 57 Grainger, 406-B1 Engineering or 252 Everitt. There will be office hours in the 406-B1 lab on Wednesday, Sept. 25 from 6-7pm and Thursday, Sept. 26 from 4-5:30pm, staffed by myself and Prof. Laugesen.
Second IODE lab: was completed during class on Tuesday, September 17. (You do not need to turn this in.)
Homework 4, part 1: due Thursday, September 26 by 4:00 pm in my office
2.4: 2,4,6*
2.5: 2,4,6*
2.6: 2,4,6*
There are really just three problems here, each having three parts. Each problem (#2, #4 and #6) involves a single differential equation, which you should first solve exactly (by the methods of Chapter 1) and then approximate numerically using (i) Euler's method (section 2.4), (ii) the improved Euler's method (section 2.5) and (iii) the Runge-Kutta method (section 2.6). You only need to turn in your answers to problem #6. Compare the approximations which you find with the exact answers. What conclusions can you draw about the accuracy of these three methods? Take a look at the statements about the error in these methods on pages 117, 120 and 129.
Homework 3: due Thursday, September 19 by 4:00 pm in my office
1.4: 1,9,12*,22*,31,36*,46*
1.5: 3*,9,12*,33,36*
1.6: 3,6*,16*,17,31,32*,54,55*
Homework 2, part 2: due Friday, September 13 by 12:00 noon in my office
You can work on this project in any of the following EWS labs: 57 Grainger, 406-B1 Engineering or 252 Everitt. There will be office hours in the 406-B1 lab on Wednesday, Sept. 11 from 6-7pm and Thursday, Sept. 12 from 4-5:30pm, staffed by myself and Prof. Laugesen.
First IODE lab: completed during class on Thursday, September 5. (You do not need to turn this in.)
Homework 2, part 1: due Tuesday, September 10 by 4:00 pm in my office
1.2: 1,4*,8*,23,24*
Homework 1: due Tuesday, September 3 by 4:00 pm in my office
1.1: 3,8*,13,17,20*,33,34*,40*