# Matt N.

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 Jan31 comment How do I find Orthogonal Projection given two Vectors? @Math Student: If you would like to edit your question you can click on the word "edit" in the bottom left corner of your question. Jan31 comment Homework Help - Calculus III / Physics / Force-Work Problem @Math Student: That's what I thought ; ) Jan31 answered Homework Help - Calculus III / Physics / Force-Work Problem Jan29 accepted Wronski matrix of a discrete evolution and condition Jan28 awarded Peer Pressure Jan27 comment Find the expectation @Debanjan: No, there might be cleverer ways of computing this expectation value. Jan27 revised Find the expectation deleted 80 characters in body Jan27 answered Find the expectation Jan27 answered On variance of a random variable Jan27 comment 2 step Runge Kutta method with parameter $\Theta$ Thank you! I padded the table because I am scared of implicit methods. Seriously: thank you so much, I have no idea why I filled the table with zeros. Jan27 accepted 2 step Runge Kutta method with parameter $\Theta$ Jan26 answered Characterizing units in polynomial rings $R[X]$ Jan26 asked 2 step Runge Kutta method with parameter $\Theta$ Jan26 comment Wronski matrix of a discrete evolution and condition Second example: using $\Psi^h y = y + h f(y)$ again, this time to solve $\dot{u} = (\alpha - \beta v)u$, $\dot{v} = (\delta u - \gamma)v$, I get $$\Psi^h y = \left( \begin{array}{c} u + h(\alpha - \beta v) u \\\ v + h(\delta u - \gamma)v \end{array} \right)$$ but I don't know what to do now. Can you tell me how to proceed from there? Jan26 comment Wronski matrix of a discrete evolution and condition Many thanks. I like your answer to my first question, it's very clear. As for my second question: I'm not entirely satisfied. For example: $\Psi^h y = y + hf(y)$ then trying to solve $\dot{y} = f(y) = (\alpha - \beta y)y$ yields $\frac{\partial}{\partial y} \Psi^h y = 1 + h \alpha - 2h\beta y$ which is a scalar so the maximal determinant is just the maximum value of the function $1 + h\alpha - 2h \beta y(t)$, for $t$ in the domain. Is this correct? Jan26 comment Construct an isomorphism between fields @elgeorges: If I change $F$ to $F[x]$ my comment would be wrong. What I can do if you like is write "If $R$ is a ring and $I$ and ideal of $R$ then $R/I$ is a field if and only if $I$ is a maximal ideal of R." Then you can replace $R$ with $F[x]$. Jan25 asked Wronski matrix of a discrete evolution and condition Jan25 answered Chain rule for multi-variable Jan25 comment How to Quantify $\limsup \limits_{i \to \infty} \; E_i = \bigcap \limits_{k=1}^{\infty} \bigcup \limits_{i=k}^{\infty}\; E_i$? If $S_i \subset S_{i + 1}$ then $S_i = S_i \cap S_{i+1}$ so the number of sets you can construct by intersection and union from sets $S_i$ with $S_i \subset S_{i+1}$ is the number of sets $S_i$, i.e. you don't get any new sets. Jan25 comment How to Quantify $\limsup \limits_{i \to \infty} \; E_i = \bigcap \limits_{k=1}^{\infty} \bigcup \limits_{i=k}^{\infty}\; E_i$? @hhh: I think if you have no information about your sets then you cannot know. For example, if you have $A \subset B$ then $A \cap B$ won't give you a knew set.