The h Bar

Semiclassical

6:00 PM

If you like, it's the solution of $y'(x)=f(x)$ such that $y\to 0$ as $x\to \infty$.

(The integration variable should be different than $x$ eg $u$ but that's a common abuse of notation)

bolbteppa

That's actually an incredible way to look at this condition, nice

0ßelö7

My thought is that your limit will not converge in any meaningful sense.

bolbteppa

That's because your imagination is restricted by something called rigor

Semiclassical

This also fits with Ted's point (made in the math chat) re: convergence of the improper integral---if that DE doesn't have a solution vanishing at infinity, we should expect the improper integral to be divergent

@bolbteppa them's fighting words

bolbteppa

Vaguely I think this derivation breaks down because of the whole $\infty$ part of those integrals, but the formula seems to originate from a Fourier series (i.e. a finite interval) where none of those concerns came up right

IcE my bReaD

6:18 PM

@bolbteppa is that a diss?

Prathyush Poduval

@Blue you can check out baby rudin if you haven't yet, it's a very thorough analysis book and will beat you to death with defenitions. It's still good though

Anonymous

@PrathyushPoduval I plan to start dying next academic session. I just looked up our math syllabus for EE. We have no math courses in 2nd, 3rd and 4th year. That's terrible. I think I'll be be illiterate when I get out of college. :P

Anonymous

On a more serious note, I wish to study Analysis 1, Analysis 2, Differential Geometry and Introductory Topology (and some Abstract Algebra) next academic session (myself, at home). This academic session I want to thoroughly do Multivariable Calculus, basic Real Analysis, Linear Algebra, Integral Transforms and Ordinary Differential Equations properly.

Anonymous

I know about Baby Rudin's book. I've heard it is very good for Analysis.

Prathyush Poduval

yes it is

Sid

6:30 PM

@Blue ...what?

Anonymous

@Sid It is true, man

Prathyush Poduval

@Blue you do it, you don't understand it, you do a easier book, you perfectly understand it

that's how it has been going on for me :P

0ßelö7

Rudin is a meme

there are much better books

Prathyush Poduval

@Blue May cauchy bless yo soul

Anonymous

@PrathyushPoduval I'm trying to strengthen my basic Multivariable Calculus first before going in Analysis 1 and Analysis 2.

Prathyush Poduval

6:31 PM

@0ßelö7 like?

0ßelö7

Abbott

Prathyush Poduval

@0ßelö7 yeah, that was one of my simpler books

I do it alongside rudin. I find him much more rigourous and thorough

@Blue Shouldn't you do it the other way around?

IcE my bReaD

@0ßelö7 yo do you know a better book than fleming to read after abbott?

0ßelö7

@IcEmybReaD Jost

but not for Lebesgue measure

Anonymous

@PrathyushPoduval I don't think so. Look at the pre-requisites here: ocw.mit.edu/courses/mathematics/18-100b-analysis-i-fall-2010/…

IcE my bReaD

6:33 PM

does jost replace fleming for "multivar analysis"

0ßelö7

@PrathyushPoduval I don't know what it means to be more rigorous that Abbott. He has no mistakes as far as I'm aware.

@IcEmybReaD Sure.

CooperCape

@0ßelö7 Hey that's my surname. I soooo wrote that book. K.

Prathyush Poduval

@0ßelö7 well yeah, you're right about that. But i prefer rudin for some reason. Might be cause I liked the defenition-theorum-proof-repeat style exposition.

Anonymous

@PrathyushPoduval Have you finished MV Calculus or you are studying stuff randomly?

IcE my bReaD

@Blue @PrathyushPoduval check out amann/escher vol 1-3.

0ßelö7

6:36 PM

You people...

One only needs one analysis book

IcE my bReaD

I always refer to it but I don't like to use it as my main book because it has TOO MUCH information.

Prathyush Poduval

@Blue no not randomly :P, I'm doing analysis first, then moving on to multivariate

and then some topology

and differential

Anonymous

@PrathyushPoduval That's strange. But if you understand it that's fine I guess

Anonymous

I'm trying to follow the itinerary suggested by MIT. I'll request the math department professors to allow me to take some math courses next year. Otherwise I will study myself.

Prathyush Poduval

@Blue I mainly want to start learning GR, but I wan't to study it without the proper math background

IcE my bReaD

6:38 PM

@0ßelö7 is abbott ---> munkres (topology) ---> jost a solid foundation for intro analysis? (and for further reading)

0ßelö7

@IcEmybReaD Whatever

I'm sure you can figure it out

IcE my bReaD

yeah it seems to be good

but I was not sure about munkres being before jost, or at the same time.

or at least, not all of munkres

Prathyush Poduval

@0ßelö7 how's calculus on manifolds for multivariable calculus?

Anonymous

@PrathyushPoduval I see. GR will take over an year I think. It's a huge topic like QM.

0ßelö7

@PrathyushPoduval I have looked at it like twice. I prefer other books. Personally, I think manifolds have no business in an analysis course.

IcE my bReaD

6:40 PM

@0ßelö7 I agree with this but I don't really have a good reason for it, it just doesn't feel right.

Prathyush Poduval

@Blue Yeah, I'm almost done with griffiths on QM. I'll do shankar after this, it's more of balancing physics and maths now

IcE my bReaD

I like books to be as disjoint as possible in their respective areas.

Prathyush Poduval

@0ßelö7 Which book do you recommend for multivariable, after rudin?

IcE my bReaD

I literally just asked that.

Anonymous

Ted's book, if you can afford it. :P Balarka showed me some illustrations from that book. It looked awesome.

Prathyush Poduval

6:43 PM

ted shifrin? yeah heard of him

Anonymous

@PrathyushPoduval Yeah

0ßelö7

If you understand Rudin there is no reason to be reading pop-math.

Anonymous

He roams around in the Math SE chat. :)

Prathyush Poduval

....pop-math?

0ßelö7

Calculus

Prathyush Poduval

6:43 PM

@Blue Oh nice

0ßelö7

You should have an understanding of multivariable calculus before starting analysis

Prathyush Poduval

@0ßelö7 well then, I fucked things up

Anonymous

That ^

Anonymous

@PrathyushPoduval It's fine. You are in class 12, dude.

Anonymous

Lots of time for you

0ßelö7

6:44 PM

It's hard to develop intuition for rigorous proofs and multivariate visualizations at the same time.

You should be able to clearly picture what you're trying to prove well before you set out to prove it.

Prathyush Poduval

I am able to get the intuition for rudin's proofs

0ßelö7

Then you're a super genius and don't need my help. His proofs are notoriously hard, although I've never looked at the book.

Prathyush Poduval

after thinking over it for a long time, I am able to get the general idea that goes into the proof depending on what neede to be proven

0ßelö7

There might be value in learning analysis from a shitty book. Research papers tend to be horribly written.

Prathyush Poduval

@Blue Yeah. I have holidays now, and 2.5 months more of class to suffer thorugh, after which I'm free to do what I want

@Blue did you buy shifrin's book?

IcE my bReaD

6:49 PM

@0ßelö7 filling summer research applications "relevant experiences: several months of experience in shitty analysis books, ability to decipher research papers of any level of horribleness"

Anonymous

@PrathyushPoduval No ;_;. I wish I could. I'm broke

Prathyush Poduval

@Blue I can't seem to find it online

0ßelö7

Just do OCW

Prathyush Poduval

the ebook

Anonymous

Anyhow, I got the parts I needed from Balarka

IcE my bReaD

6:50 PM

shifrin's book is not a continuation of baby rudin...

Anonymous

@PrathyushPoduval It's not available online

0ßelö7

@IcEmybReaD That was my point earlier.

Anonymous

@IcEmybReaD It's a pre-requisite (has Multivariable Calculus)

Anonymous

Pratyush needs that.

Prathyush Poduval

@IcEmybReaD but still, worth a look

0ßelö7

6:51 PM

@PrathyushPoduval I have Rudin's group theory book. It's quite good.

I use his functional analysis book often.

Prathyush Poduval

I plan on doing group theory from A Zee after all this

IcE my bReaD

lol

Prathyush Poduval

what do you think of the book?

0ßelö7

I have heard it's garbage.

Prathyush Poduval

noted :P

IcE my bReaD

6:52 PM

it's good if you only do physics.

0ßelö7

His GR book is my favorite nonfiction book of all time.

bolbteppa

Lots of nice little nuggets in his group book

Prathyush Poduval

@0ßelö7 I liked his jokes in it very much!

It was very intuitive

IcE my bReaD

but you said you didn't learn GR yet.

though you read zee?

0ßelö7

I am confused too.

Prathyush Poduval

6:53 PM

@IcEmybReaD I read it to get a taste of GR, and left it midway when I realized I needed to get my math-shit together

and now I'm here

Anonymous

@PrathyushPoduval Check out Artin

Prathyush Poduval

But I got pretty much a wonderful taste of GR

IcE my bReaD

@PrathyushPoduval I also read some % of zee's book and it doesn't require analysis/dg background.

were you reading it without knowing vector calculus?

Prathyush Poduval

@Blue Yeah I did, but group theory is not yet on my to-do list

@IcEmybReaD I know vector calculus

IcE my bReaD

before I mean

Balarka Sen

6:54 PM

whats up dramalertnation

Prathyush Poduval

@IcEmybReaD Zee doesn't require, but I wanted to continue Zee with a proper math background and then proceed with a math rigorous gr book

IcE my bReaD

@PrathyushPoduval but you have the proper math background.

Prathyush Poduval

Yo balarka, how you doing?

Balarka Sen

chillin, you?

Prathyush Poduval

@IcEmybReaD For zee maybe, but is it enough for gr?

IcE my bReaD

6:56 PM

......?

Balarka Sen

imma start my day now that it's 12 in the morning

Prathyush Poduval

Awesome, enjoyin' my last week of holidays :,(

Balarka Sen

So university starts from Monday for you?

Prathyush Poduval

@IcEmybReaD So, I just know Vector calculus , linear algebra, 3d calculus, and some analysis shit. You sayin' its enough for GR? Don't you need to know differential geo (Which I don't know)

0ßelö7

@BalarkaSen so are you in college or not

Prathyush Poduval

6:58 PM

@BalarkaSen I'm not in uni

it starts on 6th

Balarka Sen

Oh

dayum

Anonymous

@0ßelö7 It's 12 at night here :P

Balarka Sen

@0ßelö7 Not yet

Prathyush Poduval

waste of time honestly

IcE my bReaD

friend 1: "hey do you know GR?"
you: "nah I only know zee"

Anonymous

6:59 PM

And Balarka is a school kid

Anonymous

;)

Prathyush Poduval

last year to get out of this suffering (school)

IcE my bReaD

@PrathyushPoduval no you don't, all physics GR books cover the basics in the first few chapters.

Sid

Balarka is not human. "Kid" isn't the right term for Balarka

0ßelö7

I'm trying very hard not to get banned

Prathyush Poduval

7:00 PM

@IcEmybReaD Ah yes, even zee does. But I wanted to do the math properly beforehand (personal preference)

0ßelö7

I have a very good joke about that @Sid

Prathyush Poduval

@0ßelö7 Say it 'nd delete it :P

Balarka Sen

@0ßelö7 bring on that shitz

0ßelö7

@PrathyushPoduval Not with this many Indians in the chat :P

Anonymous

BTW @BalarkaSen what's this stuff called: The condition under which we can change the order of integrals (in double or triple or friple or pentaple or :P integrals )?

Balarka Sen

7:00 PM

bring it on you big baby

0ßelö7

Fubini's theorem

Why do you keep asking Balarka about analysis

Balarka Sen

^

0ßelö7

Also Tonelli's theorem

Prathyush Poduval

@Blue you broke ocelo's heart :P

ask him too somedays

IcE my bReaD

@PrathyushPoduval if you do the math properly beforehand you'll be bothered by the lack of rigour from the physics books.

but I guess it depends on the individual.

Prathyush Poduval

7:01 PM

@IcEmybReaD Thats what I'm afraid of

Anonymous

@0ßelö7 Thank you :P

Prathyush Poduval

I hope i don't turn into a mathematician

0ßelö7

I take that very personally

Anonymous

@0ßelö7 Coz what you say mostly goes over my head, except sometimes ;)

IcE my bReaD

@PrathyushPoduval but I think learning basic dg from a physics GR book first will also help you (intuitively) when learning dg from a math book.

0ßelö7

7:02 PM

What the hell dude

Balarka Sen

you can't turn into a mathematicians

IcE my bReaD

correct me if I'm wrong.

0ßelö7

@Blue Stop asking nontrivial questions then

Abcd

Wiki says that coefficient of restitution is defined only 1 dimesnionally. However, what about perpendicular collision of a ball with a wedge inclined at an angle $\theta$? Wouldn't $e$ be 2 dimensional then?

Prathyush Poduval

before, my dreams consisted of hot girls, recently it's full of only epsilon's and deltas :"(

Anonymous

7:03 PM

@0ßelö7 That's not possible. :)

0ßelö7

@Blue Just know that if $f(\vec x,\vec y)$ is continuous in both variables (jointly), then you can change the order.

Again, if your function is discontinuous, give up on life.

Abcd

@Blue Done that problem using momentum conservation and Energy conservation. I don't know why you were referring to Impulse.

Balarka Sen

@PrathyushPoduval Ok I have a joke now but it's inappropriate in front of ya kids

Anonymous

@PrathyushPoduval Hot girls are boring for a true mathematician. Only fake mathematicians like Feynman and Schrodinger were into that stuff.

IcE my bReaD

Oct 19 '15 at 4:00, by 0celo7

this is an adult room now

0ßelö7

7:04 PM

...

Anonymous

@PrathyushPoduval Swear words are for kids. Legends use memes.

Balarka Sen

you angry sardine

you smell like a normie

dmckee

Listen up guys, claims to be an "adult room" aren't stopping the flags. Cut it out.

0ßelö7

Thank you.

Sid

That escalated quickly...

Balarka Sen

7:06 PM

imma delete mine too

Erik the Outgolfer

@dmckee I just came here because of flags...

Balarka Sen

but the angry sardine is ok

bolbteppa

Something bothering me, why is $\delta(\mathbf{r} - \mathbf{r}_0) \mathbf{v}$ the current density for a classical particle?

IcE my bReaD

0ßelö7

@bolbteppa Cuz it's a point flying around

Balarka Sen

7:07 PM

@IcEmybReaD these memes are so good

0ßelö7

these are kid memes

IcE my bReaD

triggered.

bolbteppa

I guess if you say $\rho = \delta(\mathbf{r}-\mathbf{r}_0)$ then $\mathbf{\rho} \mathbf{v} = \mathbf{J}$, velocity density of a point at a point is current...

0ßelö7

yes

bolbteppa

Then $\mathbf{v} = \mathbf{p}/m$ and then to quantum it you symmetrize and voila stupid current density operator (almost)

IcE my bReaD

7:11 PM

are you reading tong's notes?

Balarka Sen

Oh Prathyush actually got banned for that

Oh well

Sid

What was the reason behind the use of the not-so-polite terms?

Abcd

20 mins ago, by Abcd

Wiki says that coefficient of restitution is defined only 1 dimesnionally. However, what about perpendicular collision of a ball with a wedge inclined at an angle $\theta$? Wouldn't $e$ be 2 dimensional then?

0ßelö7

@BalarkaSen I think you would really enjoy GR. Lots of neat pictures

Balarka Sen

7:29 PM

@0ßelö7 I should try that sometime, yeah

Anonymous

@Sid @PrathyushPoduval wanted to prove that he is not a kid. :P

Abcd

Wait for 30 minutes @PrathyushPoduval.

Why are u entering and leaving again and again?

Anonymous

Lol, this is awesome.

Abcd

@Blue It's creepy and strange.

Can you see it too @Blue?

Anonymous

@Abcd Yea

Abcd

7:36 PM

he is coming and going each second.

Anonymous

I think some connectivity issues

0ßelö7

I blame Indian internet

Abcd

lol

Anonymous

Or he set up a bot to distract us

Abcd

@Blue To this extent? Is the connection getting lost within miliseconds.

Balarka Sen

7:39 PM

He's probably refreshing the chat multiple times

CooperCape

everyone refresh to test

0ßelö7

"strictly positive semi-definite"

Abcd

@BalarkaSen One would stop doing that after a certain number of times.

0ßelö7

...what was I thinking when I wrote that

@BalarkaSen what the hell is it supposed to mean

Balarka Sen

Ok, it works

@0ßelö7 looooooool

IcE my bReaD

7:40 PM

@BalarkaSen edgy

Balarka Sen

strictly positive not quite positive

0ßelö7

I need to find a proof I wrote in this chat perhaps 2 years ago

:/

Abcd

lol, first time seeing such a strange thing happening in the chat room.

Balarka Sen

I do that frequently

@PrathyushPoduval Calm your woah

0ßelö7

Aug 23 '16 at 3:54, by 0celo7

I always meant to write down this proof

haha

@BalarkaSen this is not the first time I've searched for it

Sid

7:43 PM

Okay. When someone is trying to prove they are not a kid, doing such antics isn't advisable.

Abcd

@PrathyushPoduval Stop refreshing please.

0ßelö7

ignored

nice, his avatar doesn't do that thing anymore

IcE my bReaD

what the fuck though?

Anonymous

@Sid That :P Swear words are for kids as I said.

Sid

@JohnRennie for some reason unbeknownst to me, you are featured in "People you may know" in my Facebook feed

0ßelö7

7:44 PM

facebook is evil

Anonymous

@Sid You are in my Friend list and John is in mine too. So....

IcE my bReaD

do you have facebook?

0ßelö7

Aug 23 '16 at 3:58, by 0celo7

It's trivial.

@BalarkaSen

Past me is taunting present me

Sid

@Blue ah. That makes sense then.

Balarka Sen

@0ßelö7 beautiful

0ßelö7

7:46 PM

I think I was on crack

Abcd

@Blue What should I do when ball strikes perpendicularly on the wedge? What should I then take $e$ as?

0ßelö7

look at the messages around there

Balarka Sen

ah so the past you took help from the paster you

Anonymous

@Abcd What's the question?

Balarka Sen

and the future you can't make sense of it

Anonymous

7:47 PM

Also, alert: My brain is not working now.

IcE my bReaD

@BalarkaSen transcendence, not even once.

0ßelö7

@BalarkaSen I just made sense of it and it's still not helping.

I think I just need to show that a timelike plane cannot contain a lightlike vector. It seems to be correct.

Abcd

@Blue I know how to do it.

Conservation of momentum

+ value of e needed

I just want to know how to find $e$ @Blue.

0ßelö7

ah no it's wrong

damn 3 dimensions

Mithrandir24601

@Blue It's fine: my brain rarely seems to work

Abcd

7:49 PM

the horizontal component is $v_o \sin theta$ and vertical is $v_o \cos \theta$

IcE my bReaD

@Abcd why does your university use emojis on their problem set website?

Anonymous

@Abcd $e$ is not something you can theoretically determine.

0ßelö7

e=2.5

Anonymous

Either it should be stated in the problem or you need to leave the answer in terms of $e$.

Sid

@IcEmybReaD I am guessing that is actually an online practice set. Not one given by his tutor or uni

Anonymous

7:51 PM

@IcEmybReaD It is not an university problem set

Abcd

@IcEmybReaD Lol, that's a question from my worksheet not from my university's site. I searched for the solution online and landed on brilliant.com where this diagram was there.

IcE my bReaD

oh.

Abcd

@IcEmybReaD And I ain't a university student.

@0ßelö7 NO.

@Blue But I need final velocities in terms of e.

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