Bill Goodwine's Courses

If you have any questions that you would like me to answer to help you prepare for the final, please post them below and I'll answer as soon as I can.

About how many questions should we expect? How will they be distributed from the material on the previous 3 exams?

ldillon1 wrote:About how many questions should we expect? How will they be distributed from the material on the previous 3 exams?

I haven't written it yet, but a reasonable expectation would be proportional to the previous exams, so 120/75*5 problems.

Can we use the textbook/class notes for the final like we have been able to for all of the other tests?

Also will 1st and 3rd tests from this year and their respective answers be posted on this website?

For problem 4.6 on Homework 6, the answer key says that xss = 1/16*(cos(4t+pi/2) + cos(4.2+pi/2)). However, Figure 4.17 says that the phase angle for r=1 should be -pi/2. Is that a typo in the solution, or am I missing something?

kpulliam wrote:Can we use the textbook/class notes for the final like we have been able to for all of the other tests?

yes, the same rules as the first three exams.

kpulliam wrote:Also will 1st and 3rd tests from this year and their respective answers be posted on this website?

No I generally don't post solutions for exams because students have had all semester to go over them with me. Exam 2 was an exception this year.

tbest wrote:For problem 4.6 on Homework 6, the answer key says that xss = 1/16*(cos(4t+pi/2) + cos(4.2+pi/2)). However, Figure 4.17 says that the phase angle for r=1 should be -pi/2. Is that a typo in the solution, or am I missing something?

I don't have access to the answer hey right now but unless there was something very unusual about the problem it should be minus. In general it depends on your choice of sine or cosine and plus or minus phi. However if it used the book's form I'm pretty sure it should be minus.

If you cannot post the solutions to the previous exams can you post the questions, I seem to have misplaced mine from Exam 1.

eklaus wrote:If you cannot post the solutions to the previous exams can you post the questions, I seem to have misplaced mine from Exam 1.

I just put the first exam from this year at the top of the page with all the other exams. I typed the first response on my phone. I should add too that I don't even have the solutions. I do them in the exam with the students by hand, then we grade the exams. They might be in my office, but they certainly aren't in a form that is legible/perfect enough for me to post to help you prepare for the final.

Will we be provided with a table of integrals for various complex functions like we were on exam 1?

pmangels wrote:Will we be provided with a table of integrals for various complex functions like we were on exam 1?

You need to be able to integrate by parts. I'll provide a table for more complicated integrals if needed.

If we are solving a series solution for a differential equation, and due to the variables we end up with in one of our series something like a_n*t^(n+4), would we set n+4 = m and have a starting m value of m=-4, or would we have to set all of our other series to start at t^(n+4) and solve for the values that are left out?

This is from Question 1 on exam 3 from 2012.

dkelly7 wrote:If we are solving a series solution for a differential equation, and due to the variables we end up with in one of our series something like a_n*t^(n+4), would we set n+4 = m and have a starting m value of m=-4, or would we have to set all of our other series to start at t^(n+4) and solve for the values that are left out?

If I accurately understand your question either way is ok. It all works out consistently.

For homework 3, I keep getting the solution: mx'' - xpg(1+u) = -uplg . The solution says u-1, is that an algebra error?
Thanks!

ethomass wrote:For homework 3, I keep getting the solution: mx'' - xpg(1+u) = -uplg . The solution says u-1, is that an algebra error?
Thanks!

Yes, it should be \mu - 1.