Assignment for Week #15

I've posted the reading and homework for Week #15. Follow the link from the schedule page.

Homework #15 is due on the last day of class. Our final exam follows hot on it's heels -- First thing Monday morning. I don't know that the homework can be graded by then, but I will make sure that solutions to HW#15 are available over the weekend. Because of this, I will not be able to accept late homework for this last assignment.

Assignment for Week #13

Well, I was looking at the state of our course, what we've covered recently and our schedule this week. I had initially intended to assign homework due Wednesday this week. Since I cancelled class that day, compensating for our early morning exam, that doesn't seem to make much sense. Monday is the next possible day, but that is right after carnival. I could make the assignment due a week from Wednesday, but then would I have another assignment due two days later?

Ultimately, I decided that there will be no homework assignment for this week. I'll just lump this week's and next week's assignment together and make it all due a week from Friday, i.e. April 27. It will be a bit longer than usual, so you may want to start on it earlier than usual.

SYNOPSIS: No homework this week. Long assignment due next week. Enjoy Carnival. Start your homework early.

Assignment for Week #11

The assignment for Week #11 has been posted. You can find a link on the Schedule page of the Course Website.

Assignment for Week #10

The assignment for Week #10 is available. You can follow the link from the Schedule Page of the course course website.

Just to be clear, in problems 3.1.4, 3.4.12 and 3.5.4, where you are instructed to convert the second order equation to a system, you should find the solution by first solving the system and reading off the solution to the second order equation from that.

Assignment for Week #8

I'm noticing that I never posted a note here for the homework assignment for Week #8. Well here it is. You can find a link to the assignment from the Schedule page of the Course Website.

I notice that a few people have posted homework questions under the "Borrowed Pencil" post. You can ask any other questions you have in comments to this post.

Assignment for Week #7

I posted the assignment for Week #7 on Friday afternoon, but I didn't get a chance to post about it here until now. You can find it by following the link from the Schedule page. There are a couple "home-made" additional problems that I will add on Monday afternoon.

UPDATE: I've added the additional problems to the homework page for Week #7. Try refreshing your browser if they don't show up.

UPDATE: In problem 7.4.2, you should skip part (d). Do only parts (a), (b) and (c).

Assignment for Week #6

There will be a homework assignment for Week #6, but it's likely I won't get to post it until Monday, or maybe Sunday evening. If you are anxious to get started, you can be sure that the problems 7.3.6 and 7.3.10 will be on it. You can get to work on those.

UPDATE: The assignment has been posted. It does, indeed, include 7.3.6 and 7.3.10. You can follow the link from the Schedule Page to find out the other problems.

Sections A and B

In case any of you cannot make it to the office hours today, you can collect your homework and solutions from outside my office. Homeworks 1 to 4 of each section are in a box and you can also find solutions to all the assignments. My office is WeH 7215.

mistakes hw 4

In the set of solutions that I wrote to hw 4 there are two mistakes, but I don't want to waste paper and print new copies of the solutions, so I'll just post here the corrections. 1 In exercise number 7.2.1 part d the element in the second raw and first column should be 14, not 7 as I wrote. 2 In the first additional exercise part b all the directions that I draw should be rotated counterclockwise by 90 degrees. So for example for R bigger then 4 and F bigger then 1.5 the answer would be Up Left instead of Up Right etc.

Assignment for Week #4

The reading and homework for Week #4 have been posted. Follow the link from the Schedule Page of the course website.

UPDATE: You should feel free to use the program pplane wherever you are asked to sketch direction fields in a phase plane, or produce sketches of solution curves in the phase plane.

UPDATE: We did not get to cover linear independence of vectors this week, so I have removed problems 7.3.6 and 7.3.10 from the assignment. They will return on the next assignment, after next week's exam.

UPDATE: There is one other bit of information that will help with problem 7.2.22: If you have a matrix (or a vector) with entries that depend on t, then to differentiate that matrix (or vector) you simply differentiate each component separately.

For example the derivative, with respect to t, of [f(t) g(t)] is

[(df/dt) (dg/dt)].

I've asked your TA's to comment on this in tomorrows recitation.

Assignment for Week #3

The reading and homework for Week #2 have been posted. Follow the link from the Schedule Page of the course website.

There are a couple "homemade" problems this week. They are available in a pdf file linked from the assignment page. You only need to complete the first two (this week). Early next week I'll post a new pdf file with only those problems you need to complete.

UPDATE: For problem 2.3.15 you will want to use dfield, or some other technology. You will find it quite difficult to complete the integration by hand. Additionally, problem 2.5.7(b) makes some comments about the phase line for the differential equation in question. You should actually show the phase line in your solution. Problem 2.5.20(b) is also simplified greatly by looking at the phase line, though it is not, strictly speaking, necessary.

Problem 2.3.8

I've been asked to comment on problem 2.3.8, in which you are asked to find the rate of return required for an investment of $2000 per year to grow to $1,000,000 over the course of 40 years. To complete this problem, as noted by commenter "anonymous" to this post, you must solve an equation of the form (e^(rt)-1)/r=[constant].

I didn't remark on this earlier, because I though commenter Jeffrey addresses the situation adequately. You will have to find some way to solve this numerically. If your calculator has a "solver" you can use that. Another method would be to graph the function f(r)=(e^(rt)-1)/r-[constant] and determine (by inspection) where it crosses the x-axis. Newton's method could, in principle, be employed, but it gets unwieldy rather quickly.

Assignment for Week #2

The reading and homework for Week #2 have been posted. Follow the link from the Schedule Page of the course website.

A number of the problems will require you to use some sort of computer technology. I would recommend the Java applet dfield, which I will be demonstrating in class on Monday and/or Wednesday.

UPDATE: I've made a slight modification to the homework exercises for Week #2. I've removed 1.1.27 and 2.1.15 from the assignment, and added 1.2.16, 2.3.4 and 2.3.8.

UPDATE: I've also removed 2.2.22, and added 2.3.6.

Assignment for Week #1

The reading and homework assignments for Week #1 have been posted. Follow the link from the Schedule Page of the course website. You will have to take a short tour of the Policies page before you can view the Exercises.

The assignment for this week should not be especially strenuous. If you have any questions or concerns, though, I encourage you to post a comment under this entry. Your TA's and I will try to review the comments and respond as needed. Probably not at 2:00am, though.

Alternatively, if you see a question you feel like answering, you can go ahead and do that too.

UPDATE: I've corrected the pdf file to correct the typo in problem 1.3.2. I've also corrected the due date in the pdf file: Friday 19 January.