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00:01
@Simply the intial hint given was that $\int_{-\infty}^{\infty} \frac{e^{x}-1}{x}dx = \frac{1}{2i}\int_{-\infty}^{\infty}\frac{e^{x-1}}{x}dx = \frac{\pi}{2}$
So I used that to start off
@Zophikel I believe it should be $e^{ix}$
@Simply oh ok it's just a latex typeo sorry
Ah, okay then
sorry man been drilling at this problem for hours :( i'm getting latex fever
@Zophikel x.x that's rough
00:03
@Simply I had to use symbolab to do some results for me since I was getting tired
typing this will take a couple of hours maybe days due to my last finial
@Simply I hate latex :(
^
latex is evil
T_T Ugh, you people lol
@SimplyBeautifulArt Why post it yet again? I'm glad you like your post.
@Riker latex is not evil it just has it's prices
@amWhy @Riker ASKED FOR IT!
>.>
00:06
I did :p
@SimplyBeautifulArt Then thou art cleansed and free of wrong-doing, and the wrath befalls upon Sir Riker!
:P All you man @Riker
lol
Oh @Simply there's a crazy integration by parts method for integrals of the form $\int_{a}^{b}Q(X)/P(X)$
It's a really nice method lets you avoid partial fractions at least
@Zophikel Do tell then
00:10
@Simply I used the method while doing the exercise it's actually really interesting and handy
@Simply see here:
17
Q: Is there a rule of integration that corresponds to the quotient rule?

The Chaz 2.0When teaching the integration method of u-substitution, I like to emphasize its connection with the chain rule of integration. Likewise, the intimate connection between the product rule of derivatives and the method of integration by parts comes up in discussion. Is there an analogous rule o...

^ There's actually a famed Russian who used to use a similar technique
@SimplyBeautifulArt Dos't thou forgive me?
@amWhy Oh, of course.
@Simply really handy wow analysis can be a bag of tricks but you gain a tool to do something
lol @amWhy
@Zophikel Does not always work, but those methods are generally the first things you should check for
00:13
@Simply I know
Sometimes using these method you just get another integral
lol
so then on the new integral you've gotten from the old on you just use another technique I see it all the time MSE
@Simply let me guess there's a more elegant way to appoarch that situation
@Zophikel $Q(x)/P(x)$ or the problem you're trying to solve right now?
@Simply nahh already done it latexing what I have currently
the step i'm on applying the estimation lemma I have to simplify two integrals before going on got one of them now I have to go for the other
I'd actually just use Frullani's integral...
*cough*
00:18
@Simply true very true, but doing it the long hard way makes me understand it better
@SimplyBeautifulArt, and up for grabs for the daring! Any takers for a closing vote (the fifth, on the current 4 closevotes) on this question? The asker has asked eight questions since joining 4 days ago, gained 150+rep in that time, but has posted nothing but "problem statements"!
@Simply it seems you've picked up a little real analysis
@Zophikel Yeah, true
@amWhy Taken already
@Simply looking back at my work it seems the books are balanced
@Zophikel and what do you mean by that?
00:21
@Simply every step seems vaild
@Simply the only thing I see wrong in my work are latex typo's
@SimplyBeautifulArt Yay! TU
@amWhy It's usually TY for thank you
00:23
Well, I'm being unique, then TU: Tank You!
@SimplyBeautifulArt Would you like to "take" this one down?
x.x
:D I HAVE AN ANSWERER!
1
A: you probably read this wrong!

DeusoviHidden in the text is a Taking the link, Take that number and

00:38
@SimplyBeautifulArt Wooo hoooo! Pretty much nailed it (except for the "Beauti" part, and the concatenation of "art" with "full"
@SimplyBeautifulArt ty... and TU!
Having latex troubles anyone know how to fix:
$$\frac{(-1)^{er}-1}{{-r}}\bigg\vert_{\pi}^{0}+\int_{\pi}^{0}{(-1)^{er}}-1 \frac{(-1)^{\frac{er \theta}{(re^{i \theta}(re^{i \theta}}{(re^{i \theta})^2}$$
 ^ ?
one minute it worked next minute nothing
Well...
that's a lot of { and }
$$\frac{(-1)^{er}-1}{-r}\bigg\vert_{\pi}^{0}+\int_{\pi}^{0}\frac{(-1)^{er}-1}{} \frac{(-1)^{\frac{er \theta}{(re^{i \theta}(re^{i \theta}}{{(re^{i \theta})^2}}}}{}$$
00:51
Ahh ok
This removes the error, as you didn't have enough } in your thing
though its probably not what you want
@Simply yeah
@Simply almost got it
$$\frac{(-1)^{er}-1}{{-r}}\bigg\vert_{\pi}^{0}+\int_{\pi}^{0}{(-1)^{er}}-1 \frac{(-1)^{\frac{er \theta}{\pi{}}}}{(re^{i \theta})^2}$$
№, looks like you got it
∫_π^0? Those bounds seem a tad off, why is π on the bottom?
@Simply are you taking about: $\left|\int_{\partial D} \frac{e^{rei\theta}-1}{re^{\theta}}\right | \leq \max_{z \, \in \, \partial D}\left|\frac{e^{rei\theta}-1}{re^{\theta}} \right |\int_{a}^{b} \gamma'(\frac{e^{rei\theta}-1}{re^{\theta}})$
@Zophikel Was talking about the other integral you just put up
Was just curious as to why the bounds were like that
00:59
Ahh ok @Simply that from applying IBP for integrals of that form
@Simply then I applied Ferynman's Integration trick after using that technique to get the final answer
Latexing this is going to take a while soo..... it might be a couple of days
Well, I'll have to continue this tomorrow. Time for bed now ‮@Zophikel
see ya @ylpmiS
lol
:P You don't ping me like that
01:03
I'll ping you however I want, s@ba
Welp, okay ‮@EricStucky
01:18
More latex troubles any help plz:$$\frac{(-1)^{er}){-r}+\int_{0}^{\pi}\frac{(-1)^{eir \theta-2 \theta}}{\pi}}{r}}}$$
the second ) should be a }
maybe? what are all those }}}s for at the end?
yeah you just have hella extra }s I think; three of the four last ones aren't doing anything.
loll hella extra }s
01:32
@EricStucky exercise that I've halfway worked through: mathb.in/143584
                                                                                        ^ Note not finished yet
01:44
@EricStucky how does the proof look so far
there are some Grammar errors
I don't really have time tonight to remember complex analysis well enough to check your proof, sorry
it's all right
anyone got any ideas on how to do this?
@TheGreatDuck Directional Derative
yeah but applied in what way?
and I only know x,y,z
01:56
@TheGreatDuck not sure
@TheGreatDuck what appoarchs have you tried
@Zophikel I don't know surface geometry so I have no clue.
Duck: I know that, in very generic terms, what you are asking is how to solve an integrable system. In general this isn't possible but if $d$ is small enough (and assuming, say, that the surface is smooth) it should be feasible.
To solve an integrable system, you need local coordinates and, yeah, the derivative.
So I think that means you need to have some way, at least near $A$, of turning $x,y,z$ into $m,n$.
interesting @EricStucky
02:04
@EricStucky can you write a computer algorithm for solving a parametric equation in reverse?
if so, fantastic!
(this is for a program)
I have a derivative thing that is mostly working. Good enough for my purposes.
I mean even if it's a polynomial system you don't have any hope of getting an analytical solution. But of course you only need numerics for the computer anyway.
But yeah, numerically you're just solving a system right? And you might as well linearize and assume the system is linear; and you can update that in time.
02:09
@EricStucky in this problem i'd use the computer just for the computations alone
(or you could probably do something fancy)
@EricStucky alright. What if we were to instead refer to just smooth surfaces. Any surfaces in particular that you know of that might be feasible? I'm basically trying to make a thingy walk upon a surface.
@EricStucky are you referring to my derivative? No. It actually takes the derivative by using the different rules for elementary functions. My functions are abstract objects of nested functions. The only issue is the exponentials due to... 0.
(no I'm not)
I mean, yeah, if you stick to polynomials with degree less than 4, you should be fine.
"fine" being a relative word, here :P
ehhhh I maybe rescind that.
what about a tube in space?
yeah, that'll work
02:11
oh wait duh
I already have confirmed that works
tube plot algorithm. In order to make a 3d model of a tube you have to essentially due it's geometry. Weird stuff.
of course, if it were a multivariate function m and n would be known.
oh but the arclength comes from the integral!
if you know $m$ and $n$ at any given point... aren't you just done with this subproblem?
no
i want to map A to B using a local isometry
O.O
that's a very strong restriction >.<
02:13
I want to walk a certain distance on the surface from A in some direction V to B
@EricStucky isometry is probably a bad choice of words since only one point is being moved
think of it as the sort of math occurring in your favorite "guy walking on stuff in space" game.
if you know what I mean. :p
yeah, I do get the concept :P
okay, I need to finish this blogpost, and if I have more time tonight I'll ping you and start thinking again
@EricStucky perhaps the 'trick' to solving this isn't to find m and n but rather to parameterize the surface in a particular way. Just as tube plots break when the tube is not parameterized via it's arclength.
 
5 hours later…
07:00
Morning all
 
3 hours later…
SBM
SBM
09:31
Good afternoon
Hello @SBM.
SBM
SBM
09:44
Hello
Hope you had a good day
09:54
Just morning here, but thank you.
Hope you're having a good day.
Find any books you like?
SBM
SBM
10:08
Yesterday was a shock.
how so?
SBM
SBM
No point thinking of it again though
10:50
@Zophikel lol
SBM
SBM
tomorrow's going to be a day of eating nothing but fruits
lovely
Hm, is ‮?ydal a @Mithrandir
of course not
@SBM healthy...
10:52
don't be silly
Lol, I'm too silly
Say, anyone have the link to the voting place?
It's not directly there on mobile
Nvm, I found it
SBM
SBM
oh voting?
SBM
SBM
Oh
 
1 hour later…
12:03
Candidate scores are low-ish, or am I being picky?
SBM
SBM
12:20
Idk
12:49
@TheGreatDuck: I now know enough to confidently say that, if I sit down with the notation for a few hours, I could figure out what is going on here. In fancy language: your object is traveling along a geodesic on a Riemann surface, which means that if you have a general method for transforming x,y,z into m,n (or at least, a method in general near A), then we can use the geodesic equation to solve for the path. Then we can compute the arclength at any given $t$ and solve for B.
@EricStucky can you gauge the perquisites for the this paper: liu.diva-portal.org/smash/get/diva2:872439/FULLTEXT02.pdf
To use that equation, we need to compute the Christoffel symbols for the surface, which seems like they will turn out nice (for nice $f$), but also seem mildly painful to work out from their general definition. You might be asking: in all these fancy words, where is the derivative? The answer is that the geodesic equation is a differential equation. But like, an actual honest differential equation; no manifold mumbo-jumbo translation needed.
SBM
SBM
What? Hello btw
Zoph: looks like most of the prereq work is functional analysis: you need to know what an $L^p$ space is, some comfort working with norms, and at least a vague familiarity with the Cauchy principal value. It looks like it's trying very hard to avoid needing to know any complex analysis, in particular. (He mentions distributions in the prose a couple times but without reading the proofs I can't tell if he really assumes you need them.)
hi SBM
@EricStucky interesting I thought it would be Real Analysis with tools of Lesbugese Integration
since he uses $L^{p}$ spaces
Do you think tools of tools from the basics of measure theory should suffice for reading this paper
SBM
SBM
13:06
$L^p $ space?
Lesbugese integration?
@SBM yeah
@EricStucky do you think tools from Lesbugese integration would suffice
13:21
...yes, but morally no. After my first course in measure theory I wouldn't have been prepared to read that paper.
but we didn't talk about norms or L^p spaces in any depth, which I guess we could have. So I think it's just what you want to call things.
@EricStucky what do you mean by morally
I meant what I said
if the word bothers you then skip it
when I first looked at that paper, I intially taught that that tools form measure Theory/ Integration Theory would be enough
please stop pinging me
sorry
13:25
as I said, it just depends on what you mean by that
I mean, sure, you can define an Lp space with a Lebesgue integral, and from that you can do Cauchy-Schwarz and Hölder and convolutions and so on
I initially meant what would be the best prerequisite knowledge or tools required I taught that Lesbugese integration would be enough
but usually those things are not covered in a measure theory course to the comfort level you need to be to read that paper
Dang :(
Do you of any lecture notes or books on measure theory for undergrads that cover things on a deep enough level
Hello ‮@Zophikel
Hi @Simply
13:32
ylpmiS@ does that ping you?
I learned measure theory from Papa Rudin (Real and Complex Analysis). Whether or not that's an undergraduate text is left as an exercise to the reader.
But I don't recommend it, actually, if that paper is the goal (it gets a little distracted). Maybe try the Princenton Lectures, Book III?
Princeton's Lectures should seem good
It does not ping me ‮@Mithrandir
I found some lecture notes covering things on a deeper level:
13:34
hmmm
But I think Princeton's Lectures on Analysis Book 3, should be a great help thanks for the advice mate sorry if I sound like a noob
Those look fine Zoph, except that the exercises are pretty skimpy.
npnp
I gotta run tho :P
SBM
SBM
Where do I learn about them?
And How do you get those reverse pings @SimplyBeautifulArt ?
@SBM What're you talking about? ‮@SBM
@SBM ‮@SBM
:-)
SBM
SBM
What are spaces?
13:43
You mean that?
SBM
SBM
no
SBM
SBM
not that
SBM
SBM
I saw someone talking about $L^p$ spaces but I don't understand what that means
13:44
@SBM those are resluts and tools that from Measure Theory it's a prequiste for what i'm working on
SBM
SBM
oh
Measure Theory?
SBM
SBM
Oh
@Simply and @SBM i'm working on understanding HHT which requires measure theory and complex analysis at the minimal level
SBM
SBM
13:46
HHT
Guess I've got a lot to learn
should be fun though
@Simply i've got a long way to go but i'm making progess
SBM
SBM
Where do I get to learn about it?
@SBM about what? ‮@SBM
SBM
SBM
About measure theory, complex analysis and HHT?
13:52
@Zophikel Don't we all? ‮@Zophikel Don't we all?
@SBM Hm, you got any recommendations ‮?@Zophikel
@Simply don't have my laptop on me for right now, but for dealing with Measure Theory you should have grounding in real analysis
SBM
SBM
real analysis?
SBM
SBM
Oh
where do I start learning about it?
@SBM I suppose you could google "Real analysis PDF"
SBM
SBM
14:05
What is a metric space?
>.<
In mathematics, a metric space is a set for which distances between all members of the set are defined. Those distances, taken together, are called a metric on the set. A metric on a space induces topological properties like open and closed sets, which lead to the study of more abstract topological spaces. The most familiar metric space is 3-dimensional Euclidean space. In fact, a "metric" is the generalization of the Euclidean metric arising from the four long-known properties of the Euclidean distance. The Euclidean metric defines the distance between two points as the length of the straight...
SBM
SBM
oh so much to learn don't know where to start from
@SBM have you do calc
^
He has
basic calc
SBM
SBM
yes
I know the basics of calculus
not much
14:19
@Simply how would you define a function mapping between two metric spaces
reading through something having trouble extracting the intution
SBM
SBM
oh
14:53
@EricStucky I worked around the issue altogether. I'm using the polygonal surface of the 3D model itself as the geometry to use. Locally, any two faces or triangles of the surface should be Euclidean, so it's mostly just a matter of find where something hits an edge and how it wraps to the other triangle. It would be the better way to do it.
SBM
SBM
triangles?
SBM
SBM
3D models seems cool
k
now you can read to your heart's content.
Suppose that ${X, d_{x}}$ and $(Y, d_{y})$ are metric spaces. Let $E$ be a subset of $X% and suppose that $f: E \rightarrow Y$ is a function from $E$ to $Y$. Let $p \in X$ be a limit point of $E$ and suppose that $q \in Y$ Then: $$lim_{x \rightarrow p}f(x)=q$$
So from the defintion is $E$ one the metric spaces, what is function mapping to
SBM
SBM
15:09
Uh could you use $\text{when writing text}$
\text
a bit hard to read
@SBM he shouldn't use text for his ordinary text outside of latex.
Let $E$ be a subset of $X%
there's yer problem
@doppelgreener hi
@TheGreatDuck yeah I know i'm trying to get the intution behind the defintion
No...
look at what I put in bold
ler latex has a mistake in it
Hi! I received a flag request to clean up some TEX code. What can I do for you? It's not parsed in my browser -- do you want to just repost it, or do you need it edited?
15:15
I suggest just reposting it with corrections, and optionally I could remove the original message.
@doppelgreener i'll just repost latex dosen't render in my browser
@doppelgreener that '%' is supposed to be a $
Suppose that ${X, d_{x}}$ and $(Y, d_{y})$ are metric spaces. Let $E$ be a subset of $X$ and suppose that $f: E \rightarrow Y$ is a function from $E$ to $Y$. Let $p \in X$ be a limit point of $E$ and suppose that $q \in Y$ Then: $$lim_{x \rightarrow p}f(x)=q$$
it doesn't render in chat
@Mithrandir yeah it does
15:16
If it's not causing any harm I'll leave the original message intact.
@TheGreatDuck hmm, never has for me after a long while in this room
did you readd the bookmark?
Ok, so y'all are using an external renderer.
there was a 'patch'
@doppelgreener actually, it's the official MSE one. It just isn't integrated into chat (yet).
15:18
Well, that's what I mean -- something not integrated into chat, but external to it instead.
ah ok
i thought you meant it was not part of MSE
:p
as in something a random guy made
anyone got an answer for my question
SBM
SBM
ok
wait
no
go post it on the main site
oh ok
SBM
SBM
15:23
I couldn't um understand.
15:45

 The Universe of Quack

Where you are free to do proofwriting and generally hang out.
SBM
SBM
15:57
uh oh
@Zophikel hm, not really sure
16:42
@doppelgreener Hello and welcome to my realm ‮@doppelgreener
16:55
@SimplyBeautifulArt greetings, ty your majesty
17:12
@SimplyBeautifulArt people referring to you as royalty now? Do I need to bow every time I log in? :P
SBM
SBM
Good night!
Night @SBM. Hope you're enjoying your newfound treasure trove.
17:43
@shredalert of course
@amWhy wait, what edit?
You mean to my answer?
@SimplyBeautifulArt I had seen the first line evaluated to $-1$ without the dx....you immediately edited appropriately. Never mind about that, I upvoted your answer, then my upvote was countered by a downvote...then last I saw you were positive again. Nice answer.
Lol, yeah...
Good day sir ‮‮@EricStucky
@SimplyBeautifulArt I was there responding to a commenter (below the question)...
@amWhy I saw
Good day sir ‮‮@Mithrandir
18:05
@SimplyBeautifulArt o/
One hour left
Indeed
@projectilemotion I am now interested in this
@SimplyBeautifulArt Need your magic, here: math.stackexchange.com/questions/2287860/… (However you see fit to use it!)
@amWhy do you do integrals like the one we were just at?
The one at my link immediately above, which you helped close? Or the earlier one?
The earlier one
18:18
Hi @SimplyBeautifulArt, interested in what?
@projectilemotion the answer I just had
Yes, I saw
It's been awhile. I don't typically work with $d(\lfloor x\rfloor - x)$ :P
Yep, @SimplyBeautifulArt, it comes up a lot in Laplace Transforms
18:29
Did you see my update?
On the integral with the floor function?
Yes, I did
Wonder if my logic works
Well, considering the dirac delta function, intutively it should
$\int_a^b \delta(x)=1$ as long as $a<0$ and $b\geq 0$.
All assignments for the semester done. Just an exam left now. :D
I reckon I'll finish my logic book in 2 weeks too. :D
Who's up for spending a vote to close one more post on this MSE day? (hint hint @SimplyBeautifulArt, though anyone so inclined may cast the winning vote!): math.stackexchange.com/questions/2287900/…
18:45
@amWhy :)
@projectilemotion $\ddot\smile$
I flagged it
@projectilemotion Indeed, your comment is good!
@shredalert $\ddot\smile$
@amWhy Thanks, I was wondering whether this meta post would be suitable in this case.
@amWhy oops, I'm too late it seems
19:02
@SimplyBeautifulArt Well, ya just missed the fun!! Actually, closing isn't really fun, but it helps release the angst when encountering miserable questions (not the fault of the question, but the asker!).
@amWhy I think this one should be closed, though I'll give the OP a chance
-1
Q: Double integral with a product of Delta functions

jssDoes this integral equal 1? $$ \int_0^1\int_0^1 \delta(f(x,y)-fx\times fy)d(fx,fy) $$

:P
Welp, I'll be back later
@projectilemotion agreed.
@SimplyBeautifulArt Cya, Bya, Wya, Yaya, ... continues to illiterate...
@amWhy I'm going to go back to Zorich's analysis books after my summer of logic and set theory. I shall learn from those two volumes! face set in determination
19:18
@shredalert raises glass for a toast: Here's to the summer!!
5
@amWhy raises drinking horn!!!
I was defeated previously because of lack of background.
@shredalert Ye shall never more be defeated!
never again!
19:46
@amWhy indeed to the summer
Is something happening in the Math.SE chat room?
I heard something about flags in the Math.SE chat room, was checking
00:00 - 20:0020:00 - 00:00

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