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
I've asked your TA's to comment on this in tomorrows recitation.
6 comments:
Hi,
For Section 9.5, we are suppose to draw dx/dt and dy/dt where both contains x, y and t. How do we do this in dfield?
I'm not sure how I should approach the problems in 9.5. It is not listed under the readings, should it be? Was this material covered in class with no intention of our reading the chapter?
anonymous,
For the problems in Section 9.5, you will not be able to use dfield. You will want to use the program "pplane" as we did in class. This program works much like dfield, but has places to enter two differential equations.
Pplane will not handle systems that are nonautonomous, i.e. the RHS depends explicitly on the independent variable. The problems on the homework are autonomous, though.
drewshaver,
The reading in Section 9.5 relies on a number of techniques that we have not yet covered. This is the reason that (i) no reading from that section was assigned, and (ii) parts (c) and (d) of the problems were not assigned.
Much of the two problems from 9.5 can be completed using the program pplane. There may be some differences in terminology between my Friday lecture and the text: the critical points in part (b) are what I've called "equilibrium points". Part (e) of the problem refers to a "phase portrait." This is simply a representative set of solutions in the phase plane, similar to the pictures I produced in class.
Are you going to post the solutions to the homeworks? I haven't seen them anywhere.
Thanks,
Hi Anonymous
Solutions to HWs are distributed in recitations in a dead-tree-format. If you are missing some of the solutions you can get them from your TA during office hours.
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