Problems marked with an asterisk (*) are to be turned in.

Extra credit assignment: Sixth (final) IODE project (can be turned in at any time before the last day of classes)

Homework 12: due Friday, December 12 by 4:00 pm in my office

9.7: 2*,8*,9,16*

Homework 11: due Friday, December 5 by 4:00 pm in my office

9.6: 3,4*,6*

9.5: 1,2*,10*,11,14*,17*

For problem 2 in section 9.5, give the physical interpretation of your answer.
Hint for problem 6 of 9.5: look at Example 4 in section 9.4 (page 627).

Homework 10: due Friday, November 21 by 4:00 pm in my office

9.4: 1,4*,7,9*

9.3: 2,8*,12*,15

9.2: Fifth IODE project*

Hint (for problems 12 and 15 of 9.3 and all of the problems from 9.4): Look back through problems from earlier assignments and examples from sections 9.1 through 9.3. For most of the forcing functions which occur in these problems, the Fourier series has already been computed. You are welcome to use such a result in your answer; you do not need to recompute the Fourier series for the forcing function if you can find it in earlier work. Make sure that you give a precise reference if you do quote a result from an earlier section or homework.

Homework 9: due Friday, November 14 by 4:00 pm in my office

9.2: 4,6*,16,17*, Fourth IODE project*

Think about the relationship between your answers for problems 4 and 6 and the answers for problems 15 and 16 from section 9.1 (previous homework assignment).

Extra credit assignment: Additional problems (due along with Homework 9, Friday 11/14 -- but please turn in separately from Homework 9)

Homework 8: due Friday, November 7 by 4:00 pm in my office

9.1: 11,12*,14*,15,16*,25*

3.8: 1,2,3*,13*,16

For problems 11, 12, 14, 15, 16 in 9.1, write a formula for the periodic extension of the indicated function, sketch its graph, and find the Fourier series.
Hint for 9.1, problem 25: use a trig identity to rewrite the formula for f(t).
What can you say about the Fourier coefficients a_n and b_n if n is greater than or equal to 5?

Homework 7: due Friday, October 24 by 4:00 pm in my office

3.6: 1,4*,7,14*

3.5: 1,3,4*,10*,22*,31,32*,35,38*,49

Try doing problem 49 from section 3.5 by both methods (undetermined coefficients and variation of parameters) and see if you can reconcile the answers which you get.

Homework 6: due Friday, October 17 by 4:00 pm in my office

3.4: 3,4*,15,20*,22

3.3: 24*,27,28*

3.2: 2*,3,7,9*,13,16*

Hint for problem 28 in section 3.3: try guessing small integer values as roots of the characteristic equation.

Extra credit assignment: Third IODE project (can be turned in at any time before the last day of classes)

Homework 5: due Friday, October 10 by 4:00 pm in my office

3.3: 1,2*,5,8*,21,23*

3.1: 1,3,6*,10*,19*,29*,45

2.2: 1,4,6,7*,13*

Homework 4: due Monday, September 29 by 4:00 pm in my office Note change in deadline!

2.1: 1,11*,13*,18*,19

2.5: 1,4*

2.4: 1,4*

The problems from 2.4 and 2.5 are linked together. Each problem involves a single differential equation, which you should first solve exactly (by the methods of Chapter 1) and then approximate numerically using Euler's method (section 2.4) and the improved version of Euler's method (section 2.5). You only need to turn in your answers to problem #4. Compare the approximations which you find with the exact answers. What conclusions can you draw about the accuracy of Euler's method versus the improved Euler's method? Take a look at the statements about the error in these methods on pages 117 and 120.

2.4/2.5: Second IODE project*

You can work on this project in any of the following EWS labs: 57 Grainger, 406-B1 Engineering or 252 Everitt.

Second IODE lab: completed during class on Wednesday, September 17. (You do not need to turn this in.)

Homework 3: due Monday, September 22 by 4:00 pm in my office

1.6: 3,5,6*,8*,21,22*,31,34*,54,55*

1.5: 33,36*,additional problem*

Homework 2: due Friday, September 12 by 4:00 pm in my office

1.5: 1,3*,9,14*

1.4: 1,3,5,6*,7,19,20*,31,32*,48*

1.3: First IODE project*

You can work on this project in any of the following EWS labs: 57 Grainger, 406-B1 Engineering or 252 Everitt.
I will hold office hours in the 406-B1 lab on Wednesday, Sept. 10 from 1:30-2:30pm.
Another instructor teaching an IODE section of Math 285 (Prof. Kapovich) will hold office hours in the 406-B1 lab on Thursday, Sept. 11 from 2:15-4:00pm.

First IODE lab: completed during class on Wednesday, September 3. (You do not need to turn this in.)

Homework 1: due Friday, September 5 by 4:00 pm in my office

1.2: 1,6*,8*,12,18*,21,22*

1.1: 3,8*,13,17,20*,36*,40*