Homework 2 Solutions

Due Wednesday, September 8, 2004. Grader: Michaela Logue (Logue.3@nd.edu)
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goodwine
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Homework 2 Solutions

Post by goodwine »

Get them here.

Note: these solutions were composed by the grader, Michaela Logue (Logue.3@nd.edu). They may be superficially different from the notation in class or from the book, but should be substantively correct.
Last edited by goodwine on Thu Jun 15, 2006 4:43 pm, edited 1 time in total.
goodwine
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Questions

Post by goodwine »

goodwine wrote:Someone emailed the following questions to me:
At first, I couldn't get the soln to #1 because I wasn't integrating from t0 to t, but the example in the book (pg 37) doesn't do that integration either. I was wondering why that was.
I assume you are talking about computing the integrating factor. That is an indefinite integral and further more, the constant of integration is assumed to be zero. I don't quite follow this question since the solutions made by the TA also compute it the same way. Am I looking in the right place w.r.t. your question?
On #6, you integrate again from t0-t, but to get the answer, t0 has to equal 0. I thought that only happened if there was an initial condition x(0)=...
Hmmm. I still don't quote see where your question is coming from. I don't see any integral with a lower limit of t_0 on the sixth problem. Can you point me to a more specific place?

You have flexibility to pick t_0 using VoP. The solutions aren't 100% clear on it, but you can pick t_0 to be whatever you want (withind the domain of the solution). Usually if you have logs, picking t_0 to be 1 simplifies things more than picking t_0 to be zero.
For all equations where you have to solve for the homogeneous equation first, do you only find c1 and c2 after you combine the homogeneous and non homogeneous?
Yes! Otherwise the solution wouldn't match the initial conditions, in general.
For these homeworks, I've had to use Maple (I don't own or know how to use Matlab) for some of the integrals (partly because I am a bit rusty, but plan to look back over old texts), how much is that going to hurt me on an exam? Will there be fairly complex integrals on exams?
I expect that you can integrate, for example, by parts and other techniques of similar sophistication. I expect that you know how to integrate polynomial, most standard trigonometric, exponential functions and compositions thereof. Since most of my exams are open book, you can bring reference material with you, but if you have to spend a lot of time looking stuff up, it may cause trouble.
I don't really understand the Variation of Parameters method. I can plug and chug, but thats as far as it goes. Would you have any suggestions that might help me?
This is going to seem like I'm dodging the question a bit. It's not always the case, but for VoP the derivation in the book is actually quite good. Have your read the couple pages preceding the theorem that gives the equations?
Finally, I don't know anything about programming and I'm still waiting on the book to arrive (I ordered it off the internet). Is there going to be any time that there will be a help session for beginners in C.
I'd try the office hours for the TA's that I sent out last Friday. If that fails, I'd try one of your friends that went to the help session. If that fails, I'd email one of the TA's and ask if you can set up a time to meet one-on-one. If you try all that and are still having trouble, send me an email.
Bill Goodwine, 376 Fitzpatrick
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