It is not complete, but if you want to use the notes that I am making for this course, you may find them here.
It is probably not a good idea to print much of this book at this time. I plan to modify it quite a bit during the course of this semester.
Course Text

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Course Text
Bill Goodwine, 376 Fitzpatrick
formula for repeated eigenvalues
Looking at the course notes, I think the formula at the top of page 124 (132 by the pdf numbering) is missing some exponents.
Specifically, shouldn't it be t^2 in the second term and (...)^m1 on the last term?
Nothing major, just thought I should point it out so it can be fixed when the course notes are revised.
Specifically, shouldn't it be t^2 in the second term and (...)^m1 on the last term?
Nothing major, just thought I should point it out so it can be fixed when the course notes are revised.
It looks like the formula on the top of page 124 in the pdf notes is the same as the formula in problem 6 of HW 4. But I was having trouble applying it to the HW solutions and getting the same answer.
Looks like page 125 has a good example. For each generalized eigenvector, use the formula with as many terms as the multiplicity of your eigenvectors. Then add up each solution you get from each generalized eigenvector, and any solutions you got from any normal eigenvectors.
These notes are very helpful, especially when the book does not cover what is in lecture. Sometimes having a hard copy to back up what is done in class is good, or sometimes I'll have an error in my notes from copying down something wrong. Other times there are small errors from class notes that nobody points out, and small errors in important formulas can lead to several minutes of frustration when things aren't working out.
Looks like page 125 has a good example. For each generalized eigenvector, use the formula with as many terms as the multiplicity of your eigenvectors. Then add up each solution you get from each generalized eigenvector, and any solutions you got from any normal eigenvectors.
These notes are very helpful, especially when the book does not cover what is in lecture. Sometimes having a hard copy to back up what is done in class is good, or sometimes I'll have an error in my notes from copying down something wrong. Other times there are small errors from class notes that nobody points out, and small errors in important formulas can lead to several minutes of frustration when things aren't working out.
Nope, you're right about the formula being different. In the pdf notes, like you said, it looks like it is missing the ^(m1) for the last term, as in the HW4 assignment.
Not sure about the t^2 in the 2nd term, but I don't think so. I think the HW4 is correct. Hopefully Dr. Goodwine will post here and let us know.
Not sure about the t^2 in the 2nd term, but I don't think so. I think the HW4 is correct. Hopefully Dr. Goodwine will post here and let us know.

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Re: formula for repeated eigenvalues
Yes, that formula is incorrect. I've fixed it in the current version. What I gave in class is correct.jlarson2 wrote:Looking at the course notes, I think the formula at the top of page 124 (132 by the pdf numbering) is missing some exponents.
Specifically, shouldn't it be t^2 in the second term and (...)^m1 on the last term?
Nothing major, just thought I should point it out so it can be fixed when the course notes are revised.
I'm sorry about the long delay replying to these. Usually I click on "watch this topic" on everything and hence get an email whenever anyone posts anything, but I forgot to to so in this case (I've done it now, though!).
Bill Goodwine, 376 Fitzpatrick
typo
Looks like the equation at the bottom of section 7.1, defining the Laplace transform needs an equals sign.
F(s) = the integral from 0 to infinity of f(t)e^(st)dt.
Also, to match the equation given later in section 7.3 the lower limit should be 0 not 0. (but that might be intentional considering the discussion in 7.3).
F(s) = the integral from 0 to infinity of f(t)e^(st)dt.
Also, to match the equation given later in section 7.3 the lower limit should be 0 not 0. (but that might be intentional considering the discussion in 7.3).

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Re: typo
Thanks, I fixed the equal sign. That's intentionally zero until the discussion in 7.3, but thanks for pointing it out anyway  it could have easily been an oversight.jlarson2 wrote:Looks like the equation at the bottom of section 7.1, defining the Laplace transform needs an equals sign.
F(s) = the integral from 0 to infinity of f(t)e^(st)dt.
Also, to match the equation given later in section 7.3 the lower limit should be 0 not 0. (but that might be intentional considering the discussion in 7.3).
Bill Goodwine, 376 Fitzpatrick
just a couple typos
I was reading through the course notes while studying, and I noticed a of things, nothing major.
Hoping is spelled wrong (Hopeing) in 8.9.2 Example, page 324.
Also, the references for the figures are showing up as ??, which might just be a Latex problem.
Exactly is spelled wrong (exaclty) on page 326, 3rd paragraph.
Also, it would be nice to put the values for n on rule three of the root locus plotting rules (Table 8.2), (n = 0, 1, ... (n_pn_z) like when the rule is first introduced on page 301.
Hoping is spelled wrong (Hopeing) in 8.9.2 Example, page 324.
Also, the references for the figures are showing up as ??, which might just be a Latex problem.
Exactly is spelled wrong (exaclty) on page 326, 3rd paragraph.
Also, it would be nice to put the values for n on rule three of the root locus plotting rules (Table 8.2), (n = 0, 1, ... (n_pn_z) like when the rule is first introduced on page 301.