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Jan
31
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.
Jan
31
comment Homework Help - Calculus III / Physics / Force-Work Problem
@Math Student: That's what I thought ; )
Jan
31
answered Homework Help - Calculus III / Physics / Force-Work Problem
Jan
29
accepted Wronski matrix of a discrete evolution and condition
Jan
28
awarded  Peer Pressure
Jan
27
comment Find the expectation
@Debanjan: No, there might be cleverer ways of computing this expectation value.
Jan
27
revised Find the expectation
deleted 80 characters in body
Jan
27
answered Find the expectation
Jan
27
answered On variance of a random variable
Jan
27
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.
Jan
27
accepted 2 step Runge Kutta method with parameter $\Theta$
Jan
26
answered Characterizing units in polynomial rings $R[X]$
Jan
26
asked 2 step Runge Kutta method with parameter $\Theta$
Jan
26
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?
Jan
26
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?
Jan
26
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 $F[x]$.
Jan
25
asked Wronski matrix of a discrete evolution and condition
Jan
25
answered Chain rule for multi-variable
Jan
25
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.
Jan
25
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.