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9h
comment Solving Simple Partial Differential Equation
Last line should be $\ln x - \ln y$, not $e^x-e^y$. Hence, a function of $x/y$, or, if one prefers, a function of the polar angle only (not the radius); this last formulation also allows $x$ and/or $y$ to be negative.
14h
answered Why is the matrix product of 2 orthogonal matrices also an orthogonal matrix?
15h
comment Solution of $xu_x + yu_y = 0$
OK, if you tell me where your problem is. Are you familiar with polar coordinates, to begin with?
17h
answered Solution of $xu_x + yu_y = 0$
1d
comment Correct bounds for simple triple integral in rectangular coordinates?
OK, in that case your second attempt seems fine. Those values of $(x,y)$ for which the plane $z =1-x-y$ goes below the $xy$-plane must be excluded, just like you have done in your sketch (which isn't bad at all, by the way!).
1d
comment Correct bounds for simple triple integral in rectangular coordinates?
I would ask for clarification from the teacher who gave you that homework problem. It's unclear (to me at least) exactly what solid is intended. Are you quoting the exact phrasing of the problem?
1d
comment Functional derivative or chain rule?
The concept of "partial derivative with respect to a function" doesn't make sense. You take partial derivatives with respect to a variable (where it is understood that this variable is one of the variables in a given coordinate system, and that the other variables are to be held constant).
1d
reviewed Approve Hamiltonian of a system being given, find the expressions of generalized coordinates and momenta
2d
comment How to prove that in $\{0\} \cup \{1, \frac{1}{2}, \frac{1}{3}, …\}, 0$ is not isolated
You just gave the answer! Round $1/\epsilon$ upwards to get your $k$.
Aug
29
comment All continuous functions are analytic
Have you tried setting $f(z)=\overline{z}$, for example, to see at which step you argument breaks down?
Aug
25
comment Help explain “3d algebra”
It's a transformation $F$ satisfying the identity $F(\mathbf{a}) \cdot \mathbf{b} = - \mathbf{a} \cdot F(\mathbf{b})$. If you write its matrix $A$ with respect to some ON basis, it will be skew-symmetric: $A^t = -A$.
Aug
25
comment Help explain “3d algebra”
And asking for "concrete examples of such $\pi$" is a strange request. There is only one map $\pi$, namely the one defined by the given formula... But if you want to write it in terms of coordinates, you can think of $\pi(\mathbf{a})$ as the skew-symmetric $3\times 3$ matrix $[0,a_2,-a_3;-a_2,0,-a_1;a_3,a_1,0]$ (if $\mathbf{a}=(a_1,a_2,a_3)$).
Aug
25
comment Help explain “3d algebra”
It seems that $\Lambda^2(\mathbb{R}^3)$ here denotes the space of skew-symmetric linear transformations of $\mathbb{R}^3$. Usually it means the so-called exterior square of the vector space $\mathbb{R}^3$, so the notation is somewhat strange, unless some previous section explains how to identify the elements of that space ("bivectors") with skew-symmetric linear transformations. Anyway, without knowing some more context of what this is supposed to be used for, it's hard to give any references.
Aug
25
comment Help explain “3d algebra”
Very obscure indeed; that was clearly written for a reader who already knows the material!
Aug
21
comment Why $e^{-n\pi i} + (-1)^{n}i$ is divergent?
I was referring to the formulation of the original question (and the tag divergent-series, which seems out of place).
Aug
21
comment Why $e^{-n\pi i} + (-1)^{n}i$ is divergent?
Series or sequences? It's not the same thing!
Aug
19
answered How to Translate two Equations for a “+/-”
Aug
19
comment How to Translate two Equations for a “+/-”
And if you ever want anything else, try detexify.kirelabs.org/classify.html. :-)
Aug
19
comment Is it meaningful to take “exterior products” of vector fields?
Nothing completely standard that I can recall. I searched the web and found $\mathcal{T}_k(M)$ in a few places, but I think you would have to explain whatever notation you choose to use.