I would recommend Nonlinear Systems by Khalil
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We used this textbook in my Computational Complexity course:
https://greenteapress.com/wp/think-complexity-2e/
Super interesting. Lots of projects you can do in it.
This is a super easy to read book about complexity:
https://www.amazon.com/Golden-Ticket-NP-Search-Impossible/dp/0691156492
The EdX course seems to focus more on LP theory and for example also discusses the simplex solution algorithm. That's helpful for understanding what a solver actually does you tell it to optimise your model. A downside is that they only seem to focus on continuous problems.
The Coursera course appears to be more of a tour d'horizon of mathematical programming approaches, discussing many applications and models. This is very helpful to get a broad understanding of what sorts of problems can be solved using mathematical programming models, but it does not really help you understand how these models are solved. Of course, the second and third courses in the OR specialisation will remedy this knowledge gap somewhat, but then you have to commit to more than just a single course.
I think you will learn more from the three course specialisation on Coursera, but you might also want to pick up a standard textbook on linear optimization as a reference work/aid during the course, like Bertsimas' and Tsitsiklis' book. Then you are sure to get a solid understanding of the basic mathematical programming tools used in the OR field.
> One reply here mentioned that bias changes as a function of current meaning the state of the system can be dependant on what came before it. Wouldn't this be considered hysteresis?
I am not 100% sure whether to call it hysteresis. It's likely that it's another non-linearity. There are more non-linearities than just hysteresis ;) Non-linear modeling is truely a field on it's own and it's really hard to explain in a reddit comment. Besides that, I really don't understand a lot of the material myself.
What I would do is try to find the time domain transfer function of your system and then try to transform it to a state-space or laplace domain (laplace only works after linearisation). I don't know about how to do it for non-linear systems (I am still in grad school, but I get my non-linear courses next year).
If you really want to learn about non-linear systems, my classmates recommend this book: https://www.amazon.com/Nonlinear-Systems-3rd-Hassan-Khalil/dp/0130673897
Be prepared to do some insane math though.
> I don't understand the connection to PWM.
Frankly I don't understand that either. It could also be that the person from the image in your original post is shifting the bias voltage up/down. That way the the ratio of positive/negative voltage (also some form of duty cycle) changes.
If you push the average voltage up, you get closer and closer to the saturation point on the positive half and further away from the negative half. This leads to asymmetric distortion (distortion only on the top half and no distortion on the bottom side). If this is the case then my previous comment is nonsense and completely irrelevant to this post (oops).
It doesn't look like he is modeling a tube amplifier at all.
I think that Linear Models with R by Faraway is pretty good. And it's not terribly large/long, and not very expensive as textbooks go. Faraway also has a follow-up book Extending the Linear Model with R, which will get into other models including logistic.
Luenberger is excellent if you are working at the portfolio level.
https://www.amazon.com/Optimization-Vector-Space-Methods-Luenberger/dp/047118117X
I've got a fucking stack I'm working through, but I'll definitely add it to the pile. Thanks for the recommendation.
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Maybe your school library has Programming for Mathematicians. I have enjoyed reading it, but it is a little-known book.
It's funny you mention Hahn-Banach, because I recently came across this book which you might find useful. Read the reviews to see if it might help.
Also Googling the title and author might prove useful . . . .
No too scientific but quite easy introduction is Straffin's Game Theory http://www.amazon.com/Game-Theory-Strategy-Mathematical-Library/dp/0883856379/ref=sr_1_1?ie=UTF8&qid=1353588814&sr=8-1&keywords=straffin+game+theory. It is not a pure scientific book more like popular science type. Good to read in train.
>Mainstream economics is also value free.
In that case, I don't want to hear any more trite about curbing irrational decision making from mainsteam economists.
>d) This seems like a bit of a cop out to me. It's too hard to model human behaviour, so there's no point in even trying? Instead, we'll just make shit up.
"making shit up" is exactly what mainsteam economists are doing through the use of their pathetically incomplete models of human behavior.
It would be worth your time to to some serious reading on complex problem solving. http://www.amazon.com/How-Solve-Heuristics-Zbigniew-Michalewicz/dp/3540660615