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.
17 comments:
Several of the homework questions ask us to "plot a direction field" and use it to answer some questions. Should we include a copy of this direction field with our homework, or is it sufficient to just answer the questions?
You should provide the direction field. You can either draw it by hand (it is humanly possible) or use the dfield program, in that case you can just give a printout.
Problems where you need to provede a direction field:
1.1: 2 and 30
2.1: 4 and 22
what scale should we use for the graphs?
Could you please try to avoid doing this in the future? It's rather disheartening and discouraging to see new homework problems after thinking the assignment is done.
I agree, I would greatly appreciate if this was not done in the future. Also, if this is to happen again, it would be appreciated if an e-mail was sent out. I may not have noticed this if I hadn't done everything except the last question.
anonymous at 10:22,
You should play around with the boundaries and choose a region that displays all the "interesting" information. Now "interesting" is pretty vague, but, for example, if some solutions are increasing and some are decreasing, you should make sure that both types of solution appear in your graph.
anonymous at 10:43,
I don't generally change the assignments once they are posted. That kind of defeats the purpose of posting them a week in advance. I would say this happens not more then once or twice a semester, so chances are we're past that now!
anonymous at 10:32,
While I did not send a mass email to the class, I did announce the change during Monday's class. I'll plan to announce the change again during Wednesday's lecture.
On 1.1 #40, is that y' = 3sin(t)+ 1 + y, or 3sin(t+1)+y of 3sin(t+1+y) or any other possible combination?
Quick question - for 2.3.6b, are we supposed to just solve the differential equation or are we supposed to derive it? I've read it a couple times and I'm really not sure what it's asking.
Thanks!
for 2.3.8 c, i was left with a factor of (e^(rt)-1)/r on the right side, and we are asked to solve for r. i was wondering if there is a special trick for doing this?
I just did that part on my calculator. You can graph it and use it to find the zeros. I'm not sure of how to do it on a TI-83, but on a TI-89, there's an option on the math menu.
Robert,
1.1 #30 reads
y' = 3sin(t) + 1 + y
2.3 #6 In part (b), you are asked to show h(t) satisfies the equation. Since you don't have an expression for h(t), you can't differentiate and verify. For the same reason, you cannot solve the given equation and check.
So derive the equation : Equate the rate of outflow to the change in volume of liquid in the tank, as asked. Then find alternate expressions for both these.
How do you intergrate e^(t + ln(t))?
e^(t + ln(t)) should be the same as e^t * e^(ln(t)) which should be te^t
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