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Jan
28
comment What are some interesting, atypical mathematical topics that a student who has taken an introductory calculus sequence can learn about?
Try convex analysis.
Jan
23
comment Strong solutions to an elliptic PDE
Now I. should up vote your part of the answer!
Jan
22
revised Strong solutions to an elliptic PDE
added 92 characters in body
Jan
22
comment Is f(x)=-log(x) a closed function?
A subset of $\mathbb{R}$ is closed if every convergent sequence in said set has it's limit in the set. Do you see now, why it is closed?
Jan
22
comment Is f(x)=-log(x) a closed function?
The same as $[b,\infty)$…
Jan
22
answered Strong solutions to an elliptic PDE
Jan
22
answered Is f(x)=-log(x) a closed function?
Jan
20
comment $f \in \mathcal{L}^1(\mathbb{R}) \cap \mathcal{C}^1(\mathbb{R}),f' \in \mathcal{L}^1(\mathbb{R}) \Longrightarrow f \in \mathcal{C}_{0}(\mathbb{R})$
That is some kind of Sobolev embedding (of $W^{1,1}$ into $C_0$), see the derivation before Exercise 19 here: terrytao.wordpress.com/2009/04/30/245c-notes-4-sobolev-spaces
Jan
19
comment What is the equation for this wave?
Related to a cycloid?
Jan
18
comment Introducing $\mathrm π$ and polar coordinates in real analysis
Actually not. Forster estimates the error in the cosine series similarly to Leibniz (since it is alternating).
Jan
18
answered Introducing $\mathrm π$ and polar coordinates in real analysis
Jan
15
reviewed Leave Open Set Theory intersection and union
Jan
15
reviewed Close Necessary and sufficient condition for Euclidean geometry to hold?
Jan
13
revised Source term in a PDE
corrected grammar and spelling
Jan
11
comment Application of the mean value theorem to find $\lim_{n\to\infty} n(1 - \cos(1/n))$
I think that @abel's comment deserves to be the accepted answer. It is so spot on and (I guess) very much in the spirit of Heuser...
Jan
7
reviewed Leave Closed Mathematical concepts that permeate algebra, geometry, and analysis?
Dec
26
comment How nuclear norm is convex whereas weighted nuclaer norm is not?
The singular values are ordered by definition. That's the key...
Dec
25
comment Functional derivative of $\int \left( \frac{df^2 }{d^2 x} \right)^2 dx$
Integration by parts, two times (neglecting boundary terms).
Dec
19
comment What are some applications of elementary linear algebra outside of math?
That's neat but actually a fake application. No image codec ever used the SVD of the full images. Back in the days when digital images were just a few hundred pixels wide computer were to slow to be practical and nowadays images are too large to perform a SVD on them. And anyway, JPEG(2000) and PNG are just way better.
Dec
19
comment Radius of convergence, prove that $\sum\limits_{n=0}^{\infty} a_n z^n$ converges absolutely for every $z \in \mathbb{C}$ with $|z| < R$
$\rho = R - \epsilon/2$ is between $R-\epsilon$ and $R$…