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What are the conditions on a linear time invariant system for a PI controller to converge to a specified set point? Specifically, given the system: $$begin{array}{l}y^prime =...
Asked on 12/06/2021
1 answerSuppose that $h_{1},cdots,h_{n}in mathbb{R}^{p}$ are $n$ constant vectors, $g(lambda)$ is a$p-$demensional function of a vector $lambda in mathbb{R}^{p}$ defined as below:begin{equation}g(lambda)...
Asked on 12/06/2021 by yyzheng
1 answerI am pretty sure this is elementary, but I am having a hard time understanding winding number (although intuitively I think I get it). My reference is Brown & Churchill...
Asked on 12/06/2021 by 10understanding
1 answerI started learning time series analysis and I have one small "home task".$$X_t = Z_t + 0.5Z_{t-1} + 0.5Z_{t-2}, sigma^2=1 \Find: gamma(0), gamma(2) text{ and autocorrelation...
Asked on 12/06/2021 by Hillbilly Joe
0 answerThis was originally a typo in my textbook* and I spent a lot of time trying to solve it. Lost and confused I turned to desmos which gave me some...
Asked on 12/06/2021
3 answerI’m trying to establish what the combined probability would be for a certain event to occur, where there are 2 teams involved, and I know the probability of the event...
Asked on 12/06/2021 by Gav
0 answerThe $n$th term $a_n$ of any series has a closed form representation if the nth partial sum $S_n$ has a explicit, closed-form representation; specifically, $a_n =...
Asked on 12/05/2021
1 answerI have a question regarding the following proof in Spivak's Calculus. (I excerpted the post by Kepler 9 years ago)Theorem 7-1:If $f$ is continuous on $[a,b]$ and ...
Asked on 12/05/2021 by toronto hrb
1 answerShow that: $$limlimits_{Nrightarrowinfty}sumlimits_{n=1}^Nfrac{1}{N+n}=intlimits_1^2 frac{dx}{x}=ln(2)$$My attempt: We build a Riemann sum with: $1=x_0<x_1<...<x_{N-1}<x_N=2$ $x_n:=frac{n}{N}+1,,,,ninmathbb{N}_0$ That gives us: $$sumlimits_{n=1}^N(x_n-x_{n-1})frac{1}{x_n}=sumlimits_{n=1}^N left(frac{n}{N}+1-left(frac{n-1}{N}+1right)right)frac{1}{frac{n}{N}+1}=sumlimits_{n=1}^N frac{1}{N}frac{N}{N+n}=sumlimits_{n=1}^Nfrac{1}{N+n}$$ We know from the definition, that:...
Asked on 12/05/2021 by CoffeeArabica
3 answerPart 1 is easy, but struggling to see how it helps with Part 2. Part 1 Find $frac{dy}{dx}$ if $y=xe^{-x}$. Part 2 Hence show that $int xe^{-x}dx=-xe^{-x}-e^{-x}+c$...
Asked on 12/05/2021 by punkindrublic
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