Reputation
361
Next privilege 500 Rep.
Access review queues
Badges
3 12
Impact
~14k people reached

  • 0 posts edited
  • 0 helpful flags
  • 34 votes cast
Nov
25
comment Proving harmonic function is zero
I think you meant the boundary of omega. Hint: use a connectivity argument.
Nov
25
comment Exchanging Series with Integrals: when is it possible?
Note that by linearity, it's always possible to do this for finite sums. For infinite sums, it becomes a matter of exchanging a limit and an integral which you can use Fubini's convergence theorem, monotone convergence theorem, Vitali's convergence theorem, etc.
Nov
25
comment Convergence of $\sum_{-\infty}^{\infty}e^{-\pi tn^2}$
Thank you very much. I had an inkling that it was this simple.
Jul
6
comment Prove that $V$ is the direct sum of $W_1, W_2 ,\dots , W_k$ if and only if $\dim(V) = \sum_{i=1}^k \dim W_i$
I think you mean the sum of the dimension of the span of $B_i $ is the dimension of $W_i $.
Jul
4
comment Let $f=g$ on $[a,b]/E$ where $f\in \mathcal{R}[a,b]$ and continuous on $[a,b]$. Then $g\in\mathcal{R}[a,b]$ and $\displaystyle\int_a^b f=\int_a^bg$.
My question would be if this proof is correct. I saw this problem in an old analysis book and so I thought I would try it out. Sorry, I should have been more clear.
Jul
4
comment Let $f=g$ on $[a,b]/E$ where $f\in \mathcal{R}[a,b]$ and continuous on $[a,b]$. Then $g\in\mathcal{R}[a,b]$ and $\displaystyle\int_a^b f=\int_a^bg$.
Sorry about that, I have corrected the statement in my edit.
May
27
comment $\lim_{n\to \infty} n^{1/n^2}$
Ahh, this is much better. Thanks!
May
26
comment Bounded sequence of positive numbers
Do you mean $r $ instead of $K $?
Apr
14
comment Improper Integral with trigonometric functions
Well this integral diverges so my integral will diverge by the comparison test. Correct?
Mar
17
comment Residue Theorem and Homologous to zero
In your definition of being homologous to zero, if there is a point outside of $G $ that isn't so that the winding number is zero, then wouldn't that mean the the curve does not meet the hypothesis of the RT?
Mar
17
comment Residue Theorem and Homologous to zero
This is the heart of my question I think. If $C_2$ is NOT homologous to 0, then it does not satisfy the hypothesis because in order to use the Residue Theorem, we need a curve that is homologous to 0. I apologize if I'm being stupid here...
Mar
17
comment Residue Theorem and Homologous to zero
So this was my question; we don't consider such curves as $C_2$ for the residue theorem because it does not satisfy the hypothesis. Correct?
Mar
17
comment Residue Theorem and Homologous to zero
Well in this picture the answer is no, you can't deform $C_2$ to a single point and still stay in $K$.
Mar
17
comment Residue Theorem and Homologous to zero
So in this picture, $C_2$ is not homologous to 0? Then for the Residue Theorem we couldn't use a curve such as $C_2$ but can only consider curves that are either $C_1$ or curves that wrap around $H$ in such a way so that the winding number is 0, correct?
Mar
17
comment Residue Theorem and Homologous to zero
I think I'm a little confused here. In this example $f=\frac{1}{z^2}$ and so is analytic on $\mathbb{C}-\{0\}$. Then if our contour is just the unit circle traversed once around this point, shouldn't the winding number be 1?
Feb
19
comment Consider the function
I would try a sequential argument and use the denseness of $\mathbb{R}$.
Feb
19
comment A Step in the Proof of Green's Theorem
Which limits are you talking about? Could you be more specific?
Feb
1
comment If $x_n \rightarrow 0$ and $\{y_n\}$ is a bounded sequence, then $x_ny_n \rightarrow 0$.
Just be careful of your $\alpha$. It must be a point so that $\alpha \in \mathbb{R}^+$. And yes, the same $N$ works because $y_n$ is bounded independent of whether $x_n$ converges or not.
Jan
12
comment Part of Fubini's Theorem with almost everywhere
This question was already asked math.stackexchange.com/questions/1092685/…
Jan
6
comment Tonelli and Fubini and almost everywhere
I had forgotten about this theorem. Thank you.