Math 385 Section C2 Homework, Spring 2003

Beginning of Announcements.

Final exam study sessions: Sunday and Monday, 11 and 12 May, 5-6:30pm in Altgeld 143.

Quiz 5 Solutions are available at the Quiz page.

Office hours will be in the Engineering Hall 406B1 computer lab on Tuesday 5-6pm and Wednesday 2-3pm.
Office hours in my office are Thursday 3-4pm, Friday 11am-noon, and Monday 11am-noon.
Let me know by email if you want to meet at some other time.

The median scores on the Homeworks so far are:
8.25, 9, 7, 9.5, 9, 9, 9.5, 8.75, 9, 10, 9 (all out of 10)
The median scores on the Quizzes so far are:
5, 1, 3, 3, 4 (all out of 5)
The top score on Test 1 was: 75/75, median 36/75. Approximate A: 56-75, B: 42-55, C: 30-41, D: 24-29, F: 0-23.
The top score on Test 2 was: 91/100, median 58/100 Approximate A: 73-100, B: 60-72, C: 48-59, D: 36-47, F: 0-35.

End of Announcements.

Homework can be turned in during class, or to the box outside my office 376 Altgeld Hall. To be accepted, every homework must start with a cover sheet (either print 12 copies of this, or else use the individual links below). All homework must be stapled.

I encourage you to form groups of two or three to discuss the homework problems. After discussing them, each of you should write up your own solutions.

Late homework will be accepted only if you have made prior arrangement with me. Exceptions will be made, for example, in case of serious illness or family emergency.

I will drop your 2 lowest homework scores, over the semester. But some of the assignments will be announced as mandatory (i.e. they cannot be dropped).

Homework # 1
Cover sheet
Hand in the following:
Homework 1 Supplement (print this off)
Section 1.1: 9, 13, 19, 24, 33 (and solve for v(t)), 35
Section 1.2: 3, 9, 18 (acceleration is nonconstant, so eq. (11) does not apply)
Due Wednesday 29 January, 5:30pm
Supplement Solutions
Homework # 2
Cover sheet
Section 1.3: Project 1 Due Wednesday 5 February, 5:30pm
Homework # 3
Cover sheet
Section 1.4: 8, 16, 17, 28, 46, *58 (extra credit)
(In #46, first consider (Delta t)=1 month and find a formula for (Delta P). Then consider (Delta t)=1/2 month, and find a formula for (Delta P). Generalize to get a formula for (Delta P)/(Delta t), then let (Delta t) tend to zero.)
Section 1.5: 14, 19, 20, 29, 34
(In #19 it should be y'+y cot x=cos x, not y'+y cos x=cos x as some books have.)
Section 1.6: 14, 16, 29, 49 (Aside: #49 is the default example in Iode.)
Due Wednesday 12 February, 5:30pm
Homework # 4
Cover sheet
Section 2.2:
Consider the following two equations:
(a) (dx/dt) = x^2 - x - 6
(b) (dx/dt) = cos2x
For each equation,
(i) find all "equilibrium" x-values (also called "critical points", on p. 89),
(ii) draw the phase line,
(iii) determine the stability or instability of all equilibrium x-values,
(iv) plot enough solution curves (either by hand or with Iode) to make the picture clear in all regions of the tx-plane,
(v) find the general solution by hand (for example by using the method of partial fractions to integrate, or by looking up integrals from a table).
[Check: do your plots in part (iv) basically agree with your solution formula in part (v)?]

Section 2.4: Project 2 (*Question 5 on this project is for extra credit.)
Due Wednesday 19 February, 5:30pm
Mandatory
Homework # 5
Cover sheet
Section 3.1: 5, 10, 19, 36, 37, 46, 48
Section 3.3: 9, 22, 42, 43(b)
Due Wednesday 5 March, 5:30pm
Homework # 6
Cover sheet
Problem on solving large linear systems
Section 3.1, 3.3: Project 3
Section 3.4: 3, 13, 14
(And for # 13, 14: determine whether the system is overdamped, critically damped, or underdamped. Check: plot your function x(t) using "Plot arbitrary function" in Iode to make sure the graph looks like Figure 3.4.11 or 3.4.12.)
Due Wednesday 12 March, 5:30pm
Mandatory
Homework # 7
Cover sheet
Section 3.4: 5 (first read the instructions above the problem), 6, 23 (here m=100, and you should express omega in radians per second), 31
(you can use the binomial series on page 514; it is just the Taylor series of f(x)=(1+x)alpha around x=0)
Section 3.5: 3, 4, 8, 9, 13, 25, 26
Due Wednesday 19 March, 5:30pm

This is a good time to give me feedback on the course: what topics are you finding difficult, how much time are you spending doing the homework, is my writing too hard to read on the board, do I speak too quickly, do you feel comfortable asking me questions...? You can do all this anonymously, here. (If you have comments specifically about Iode or the computer projects, then they are best submitted here).
Homework # 8
Cover sheet
Download Homework 8.
And here's the solution to a related Neumann exercise from class.
Due Friday 4 April, 11am
Homework # 9
Cover sheet
Download Homework 9. Due Thursday 17 April, noon
HW9 Solutions
Homework # 10
Cover sheet
Section 9.3: 9, 13, 15 [Hint: for 13 and 15 you might want to use results from Example 1 in Section 9.3]
And do the Fourier series project.
Due Wednesday 23 April, 5:30pm Mandatory
Homework # 11
Cover sheet
Download Homework 11 Due Wednesday 30 April, 5:30pm
Homework # 12
Cover sheet
Download Homework 12. Due Wednesday 7 May, 5:30pm.
Mandatory
Short Solutions