Recent content by dm4b

Well, I came up with the following if anyone is interested. I still don't feel good about this. Not even sure it's correct. If anyone has improvements, I am all ears! We want to show that the integrand term is even in the following integral, for any function S(jw) $$...

By the way, I found a link to the proof, page 339 in the following PDF: https://www.cds.caltech.edu/~murray/books/AM05/pdf/am08-complete_22Feb09.pdf

I am reading a proof in Feedback Systems by Astrom, for the Bode Sensitivity Integral, pg 339. I am stuck on a specific part of the proof. He is evaluating an integral along a contour which makes up the imaginary axis. He has the following: $$ -i\int_{-iR}^{iR}...

Hello, I am currently reading about the Residue Theorem in complex analysis. As a part of the proof, Mary Boas' text states how the a_n series of the Laurent Series is zero by Cauchy's Theorem, since this part of the Series is analytic. This appears to then be related to convergence of the...

... keeping it under the integral (of S) and differentiating by parts works out here. However, is there a way to achieve this with just tensor manipulation? I thought so, but I may not be remembering correctly.

Hello, In Schawrtz, Page 116, formula 8.23, he seems to suggest that the square of the Maxwell tensor can be expanded out as follows: $$-\frac{1}{4}F_{\mu \nu}^{2}=\frac{1}{2}A_{\mu}\square A_{\mu}-\frac{1}{2}A_{\mu}\partial_{\mu}\partial_{\nu}A_{\nu}$$ where: $$F_{\mu\nu}=\partial_{\mu}...

Thanks again for the recommendations, much appreciated!

Thanks, I just ordered the Niven text, it was pretty cheap on Amazon. Other one looks pricey, but I may have to get it!

Hello, I was interested in learning more about complex analysis. Also, very interested in analytic continuation. Can anyone recommend a good text that focuses on complex analysis. Also, is there a good textbook on number theory that anyone recommends? Thanks! <mentor - edit thread title>>

I figured out the answer to this, if an admin would like to delete the OP. Didn't see a way to do that myself

In Matthew Schwartz's QFT text, he derives the Schrödinger Equation in the low-energy limit. I got lost on one of the steps. First he mentions that $$ \Psi (x) = <x| \Psi>,\tag{2.83}$$ which satisfies $$i\partial _t\Psi(x)=i\partial_t< 0|\phi...

Thanks, this also helps. (Fixed the typo in the OP, as well). Gonna read up on all this some more and give it some thought - it's slowly all coming together.

Thanks, I will check out that article. I am better appreciating the connection, but still struggling with the following. I work in the aerospace industry, specifically we deal with modeling and simulation environments for aerospace flight vehicles. Quite often those generators (the matrices)...

Or, maybe I should phrase my question more simply as ... what does the vector cross product have to do with rotations?

Hello, I’m not completely appreciating your comment. Can you provide more detail how the vector cross product relates to the Lie algebra?