News and Information for students enrolled in 21-260 Differential Equations at Carnegie Mellon University during the Spring 2007 Semester.
Thursday, March 1, 2007
Borrowed Pencil
I borrowed somebody's pencil in secion G and forgot to return it. If you cannot survive without your precious mechanical pencil, send me an email and I'll get it back to you. Otherwise I'll bring it to recitation next week.
5 comments:
Anonymous
said...
Two questions on the most recent homework:
1. How are we supposed to do the x1x2x3-space graph in 7.8.12? Is there some way to use pplane to do that?
2. In 7.8.17, are we supposed to prove that a vector of that form must be a solution, or just use that information to compute a solution for the given diff eq?
1. You will have to sketch that graph by hand. Start by thinking about how it must look if x1x2x3-space is rotated so that the vectors [1, 1, 1] and [2, 5, -7] lie in the plane of your paper. Then think about what will happen when when it is rotated back to a more normal position.
2. For part (c) take the expression they give for x, then (1) Differentiate with respect to t and (2) Multiply it by the matrix A. Since x is a solution, these two expressions must be equal.
Comparing the terms, you should see that A[xi] = 2[xi] and A[eta] = [xi] + 2[eta]. From there, you should be able to reach their conclusion.
I don't plan on posting solutions online for two reasons. First, it can create problems for teachers at other schools, who may be on a different schedule than we are. Second, electronic solutions tend to be more "persistent" than hard copies. With a click of a button they can be sent to any number of people.
I always operate under the assumption that my students are honorable and upstanding. It seems prudent to avoid creating a moral hazard, though.
Hard copies of the solutions are, of course, available from your TA.
5 comments:
Two questions on the most recent homework:
1. How are we supposed to do the x1x2x3-space graph in 7.8.12? Is there some way to use pplane to do that?
2. In 7.8.17, are we supposed to prove that a vector of that form must be a solution, or just use that information to compute a solution for the given diff eq?
Thanks!
General question: Will past HW Solutions ever be available online? It would make things more convenient and be appreciated...
Anonymous on March 3,
1. You will have to sketch that graph by hand. Start by thinking about how it must look if x1x2x3-space is rotated so that the vectors [1, 1, 1] and [2, 5, -7] lie in the plane of your paper. Then think about what will happen when when it is rotated back to a more normal position.
2. For part (c) take the expression they give for x, then (1) Differentiate with respect to t and (2) Multiply it by the matrix A. Since x is a solution, these two expressions must be equal.
Comparing the terms, you should see that A[xi] = 2[xi] and A[eta] = [xi] + 2[eta]. From there, you should be able to reach their conclusion.
Note: [xi] = "tornado" and [eta] = "n".
anonymous on March 6,
I don't plan on posting solutions online for two reasons. First, it can create problems for teachers at other schools, who may be on a different schedule than we are. Second, electronic solutions tend to be more "persistent" than hard copies. With a click of a button they can be sent to any number of people.
I always operate under the assumption that my students are honorable and upstanding. It seems prudent to avoid creating a moral hazard, though.
Hard copies of the solutions are, of course, available from your TA.
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