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.
8 comments:
For question 2.3.15, are we supposed to use d-field to help in the plotting of the curves based on initial values. I was wondering if this is why there is a little mouse symbol next to the problem.
anonymous at 3:31,
You have it exactly right. You can use dfield to plot (approximate) solution curves with initial values for y_0 between 1/2 and 1.
In general the "mouse" icon indicats problems where technology will be helpful/useful.
On questions like 2.3.15b, where we are asked to estimate a critical point by zooming in and graphing in dfield, should we include zoomed in graphs around our estimated point, or is it sufficient to just give a numeric answer?
anonymous at 1:17,
I think in this case you don't need to show the zoomed in plot. You should give an indication of how you found the answer, though.
For instance, you might highlight (circle) the region of the graph you zoomed in on, and write something like "a closer view of this region reveals that the initial condition satisfied by [the appropriate solution] is [whatever the initial condition is]."
I hope that helps.
In additional problems, it mentions using the dfield program to use Euler's method. I can't figure out how to do this within dfield. Can I just do it by hand, or should I be doing something that I don't know about?
To use Euler's method in dfield, click options->ODE solver in the phase plane window.
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