Calculus stuff

Sir Cumference

Jan 13, 2016 21:50

Howdy

0537

Did you learn calculus?

Sir Cumference

Figured out integration and differentiation, head to toe

So yes?

I really don't know any other calc stuff besides those

0537

Didn't you watch the lectures?

Sir Cumference

I can't, my internet is too crappy

0537

dl them.

Sir Cumference

Jan 13, 2016 21:52

I sorta used them while also reading from sites on integrals and derivatives

0537

you should be ok, move on to linear algebra and multivariable calculus.

Sir Cumference

I tried. "6 days remaining"

Wait really?

I haven't learned hyperbolic functions, taylor series, etc.

0537

the details will come to you as you progress.

yeah go for it.

Sir Cumference

Wait, I got just one question

for calc

A derivative is the slope of the tangent line for a function or point on a function. The integral is the area between the x-axis and the function, right? So how are the two related?

I get how they can be found similarly, but that's all I see.

Completely different concepts to me

0537

well do you know the fundamental theorem of calculus?

ACuriousMind

Jan 13, 2016 21:55

@SirCumference Uh, by the fundamental theorem of calculus?

Sir Cumference

Nope...

Oh. "The fundamental theorem of calculus is a theorem that links the concept of the derivative of a function with the concept of the function's integral."

0537

so like the definite integral definition.

Sir Cumference

Er, I never really looked into the definition. I just assumed that when no domain is given, I'm looking for the definite integral. Otherwise, I'd be looking for the indefinite integral...

0537

$\int_a^b f(x) \, dx = F(b) - F(a)$

Sir Cumference

Yeah, I know that

0537

Jan 13, 2016 21:58

then you know the relationship between integration and differentiation...

why did you ask then?

Sir Cumference

I'm reading the definition. I know that finding the integral is essentially doing backwards differentiation.

0537

right the antiderivative is defined such that $F'(x) = f(x)$

Sir Cumference

But I still don't get how the two seemingly foreign concepts bear any resemblance. Shouldn't there be an obvious similarity between the slope of a tangent line and the area under the curve?

I can't find one

I can link them by the fundamental theorem, but I still don't know why the two definitions are so unrelated

or seemingly unrelated

0537

read the wiki?

it describes it well.

0celo7

Turns out there's two different J.M. Lees who have diff geo books

Sir Cumference

Jan 13, 2016 22:03

All right, I think I got it now...

0537

you are ready to walk through the door now.

Sir Cumference

So I'll ask question 2: doing ∫f(x)dx would find the area between f(x) and the x axis, right?

0537

welcome to the world of university level math.

Sir Cumference

So is there any way to find the area between two functions?

0celo7

Yes.

0537

Jan 13, 2016 22:05

yeah.

you can figure it out yourself.

Sir Cumference

So would I call it "taking the integral of one function with respect to another?"

0celo7

That's a bit much.

No.

Sir Cumference

Er...

0celo7

@SirCumference If $f(x)\ge g(x)$ on some interval $I$, then the area between the two functions is simply given by $\int_I[f(x)-g(x)]\,\mathrm{d}x$.

Sir Cumference

Oh, it's that simple?

0537

Jan 13, 2016 22:06

^

yeah though for some curves

Sir Cumference

Huh.

0537

you may have to change the bounds of integration.

TanMath

we talking about calculus? yay!

Sir Cumference

Like which curves?

TanMath

so what are you talkmg about specfically?

like what is the question?

Sir Cumference

Jan 13, 2016 22:07

@TanMath Getting the area between two functions

Er, I dunno if I'm really ready for higher math though. I've only spent 30 mins learning calc. So I only know integration and differentiation.

TanMath

@SirCumference that's simple...it is the integral of f(x)-g(x)dx assuming f(x) is bigger...

0537

0celo7 already said that.

TanMath

@SirCumference good job! you learnt calc in 30 mins!

Sir Cumference

Hooray?

TanMath

@0537 oh...

Sir Cumference

Jan 13, 2016 22:09

It's a 3-4 class subject.

0537

basically it can become complicated if one of the curves is a not a function.

Sir Cumference

I only touched upon two important things

0537

so you will have to find intersection points and do more than one difference integral.

Sir Cumference

Okay?

0537

@SirCumference no it's not.

it's like a 5 month subject.

calc 1&2 that is.

Sir Cumference

Jan 13, 2016 22:10

I meant calc 1-3/4

TanMath

calc is easy!

Sir Cumference

But still, just 30 mins probably leaves me clueless on some stuff

@TanMath Well integration and differentiation were

0537

you spent more than 30 mins dude.

TanMath

everything is...ok?

0537

though it's still little, since you used bad resources.

TanMath

Jan 13, 2016 22:11

you going on to calc 2 then?

Sir Cumference

Not 30 mins in total. 30 mins on each. Still not very good

TanMath

calc 2 is pretty neat...

0537

vector calculus is really cool.

FenderLesPaul

said no one ever

TanMath

@0537 yes...

calc 3, i think is cooler...

but i know very little about it..

Sir Cumference

Jan 13, 2016 22:13

So my next question is kind of idiotic: why does one say "take the integral of [function] with respect to x"? Does this mean that that they want the area between the curve and the x axis?

0537

@TanMath what year of university are you in?

TanMath

but i love taylor series...

0537

@SirCumference with respect to $dx$, because that's your differential.

TanMath

@0537 2nd year...

@SirCumference yes...

FenderLesPaul

@TanMath why do you have a "..." in all your sentences?

Sir Cumference

Jan 13, 2016 22:14

Oh, so what if I said "with respect to (something else)"

TanMath

@FenderLesPaul idk...it is a habit!

Sir Cumference

What would some other options be?

FenderLesPaul

fair enough

0537

@SirCumference then it would either be a different question or not make sense.

Sir Cumference

Okay...

TanMath

Jan 13, 2016 22:15

@SirCumference well if you said with respect to y, then the function must be in terms of y...

Sir Cumference

Oh

0537

$\int f(x) \, d(potato)$ lol doesn't make sense.

TanMath

otherwise, the integral would be equal to y, i guess...yeah guys?

Sir Cumference

@0537 You sure? Makes sense to me

TanMath

lol

calc 3 is about having multiple variables to differentiate and integrate...

so an in depth explanation would be found in calc 3

0537

Jan 13, 2016 22:17

no that's differential equations.

Sir Cumference

All right, last question: Leibniz's notation for derivatives doesn't exactly make sense to me. Is "dy/dx" a random way of saying Newton's "f'(x)"? Or what's the meaning?

What does "d" stand for?

0537

@SirCumference it's a different way.

Sir Cumference

Or should I care?

TanMath

the dy is a differential...same for dx...

0537

$\frac{d}{dx}$ is the differential operator, applied to a function $f(x)$ it gives you its derivative which is $f'(x)$.

Sir Cumference

Jan 13, 2016 22:18

I know, but why exactly is it $d/dx$? I see $dx$ in integrals too

TanMath

dy is like the infintely small change of y and same of dx...it kinda shows the definition of a derivative...

2

0537

$dx$ is called a differential.

TanMath

i just said that...

Sir Cumference

Excuse my ignorance, I'm still new to this

0537

@TanMath I didn't see.

Sir Cumference

Jan 13, 2016 22:19

Ooooh...

A'right, makes sense now

TanMath

it shows that a derivative is the slope at an individual point...

@SirCumference makes sense now?

Sir Cumference

Yep

0537

@TanMath slope of what? lol

TanMath

of the function being differentiated...

Sir Cumference

The tangent line, I assume

0537

Jan 13, 2016 22:20

yeah.

Sir Cumference

Or yeah...

0537

you didn't say that.

there can be multiple slopes at a point on a curve.

TanMath

no...

FenderLesPaul

this conversation is amusing

Sir Cumference

How...?

0537

Jan 13, 2016 22:21

@TanMath dafuq?

slope does not imply tangent.

as far as I know.

TanMath

@0537 there can't!

Sir Cumference

Er, how could a point have multiple slopes?

0537

a point by itself?

Sir Cumference

A slope is just $∆y/∆x$

ACuriousMind

@SirCumference You should think of $\mathrm{d}x$ as an infinitesimal change in $x$. Likewise, $\mathrm{d}f$ is the infinitesimal change in $f$ when $x$ changes by $\mathrm{d}x$ - think of $\mathrm{d}f = f(x+\mathrm{d}x)-f(x)$. Now writing $\mathrm{d}f/\mathrm{d}x$ for the derivative is supposed to symbolize that the derivative is the slope of the function at that point, like the slope of a linear function is $\frac{f(x+\mathrm{d}x)-f(x)}{\mathrm{d}x}$ for a real number $\mathrm{d}x$.

Sir Cumference

Jan 13, 2016 22:24

Ah, now it makes sense why $dy/dx$ essentially means "instantaneous slope"

FenderLesPaul

Calculus is a lie.

Sir Cumference

$∆y/∆x$ is slope, but this would be an instantaneous change...so it would have "d" replace "∆", right?

0537

kind of.

it's a limit though.

Sir Cumference

Well yeah

0celo7

@ACuriousMind Is the set of $(k,l)$ tensors just $\mathrm{Hom}(V^{\ast k},V^l)$?

ACuriousMind

Jan 13, 2016 22:27

@SirCumference Yes, the $\mathrm{d}$ is supposed to represent that. It doesn't work rigorously like that without much further effort, though. Just accept writing $\mathrm{d}x$ as a single symbol, and don't think of the $\mathrm{d}$ as being something applied to $x$.

Sir Cumference

Okay, thanks

ACuriousMind

@0celo7 Yes.

Sir Cumference

Makes more sense now

$user image$

Bernard Meurer

Would anyone more familiar with the US College system be able to explain what should I read out of this?

0celo7

@ACuriousMind ok, but what if $\mathrm{d}$ is the exterior derivative

ACuriousMind

Jan 13, 2016 22:29

@0celo7 You can't divide by an exterior derivative.

Sir Cumference

So what now? Can I go onto analysis or...?

0537

@SirCumference why would you do that?

Sir Cumference

Interested in it

0celo7

@ACuriousMind I was trying to be a smartass but it's not working...ignore me

ACuriousMind

@0celo7 k

0537

Jan 13, 2016 22:30

@SirCumference then say goodbye to physics for a while.

Sir Cumference

Wait what... .-.

0celo7

@SirCumference probably not

ACuriousMind

@0celo7 Don't project yourself onto others ;P

Sir Cumference

But one of the reasons I started learning calc was to learn higher physics stuff

._.

0537

then why do you want to do analysis now?

Sir Cumference

Jan 13, 2016 22:32

Next time @0celo7 asked "Where's the equations?" I'd be like "Here. Ha."

Or something...

Again, it's interesting

Learning about more infinity

FenderLesPaul

@BernardMeurer they send that to everyone I believe, I wouldn't read too much into it

they sent me that email when I applied

(fill disclosure I didn't get in)

0537

@SirCumference just read the wikipedia page about infinity.

Sir Cumference

@0537 Why wouldn't I be able to learn calc and analysis

0537

well it will slow down your progress of learning physics.

Sir Cumference

There's still more I'd like to get into

Bernard Meurer

Jan 13, 2016 22:34

@FenderLesPaul The ammount of emails they send is just abusive (@0celo7). I always get confused on what the hell is going on

Sir Cumference

Yeah, but I can take my time with physics. No reason to go fast

Especially if I can learn some other stuff too

FenderLesPaul

@BernardMeurer honestly it's better for your own mental state if you don't worry about things or constantly try to quantify whether or not you can get in

I'm only saying that because I'm the same way

and it just doesn't help at all

until you get an email from them about admissions decisions just don't read into any of their general emails

Bernard Meurer

@FenderLesPaul I truly try, it's rather difficult. Specially when google inbox makes my whole house vibrate and flash when I get an email

0537

@BernardMeurer what?

FenderLesPaul

@BernardMeurer I understand it's hard. I have the same problem.

But if you don't think about it, you will be de-stressed.

Bernard Meurer

Jan 13, 2016 22:38

@0537 Not reading emails and ponderating upon the meaning of each comma on the email while waiting for college applications to yield results

0celo7

@ACuriousMind mother duck why

that hurts me

Bernard Meurer

@FenderLesPaul I'm currently coding in BASH, I'll never be de-stressed I believe hahaha.

0celo7

FenderLesPaul

@BernardMeurer :p

Bernard Meurer

The fact that an if statement is closed by a fi is enough to traumatize anyone

how ugly is that even

ACuriousMind

Jan 13, 2016 22:41

@0celo7 Did you have that saved for such a moment? :D

TanMath

hello...

@SirCumference everything makes sense now?

0celo7

@ACuriousMind maybe

Sir Cumference

@TanMath Yeah

0537

@TanMath how was what I said wrong though?

TanMath

@0537 that a point can have multiple slopes?

that is so wrong...

0537

Jan 13, 2016 22:44

there can be multiple slopes at a point on a curve.

TanMath

not possible

0celo7

@ACuriousMind Is the bundle of tensors equal to the tensor product of vector bundles?

Or is that true by definition and I'm blöd

0537

@TanMath yeah, just rotate the tangent line.

0celo7

wtf are you people talking about

a point does not have a slope

0537

if I'm being retarded.

^

alarge

Jan 13, 2016 22:45

@BernardMeurer You know how case is closed in bash? Yeah...

TanMath

@0537 no! then it isn't tangent!

Sir Cumference

Rotate the tangent line? It wouldn't be tangent to the function

0537

yeah.

so?

it's still a slope at a point.

ACuriousMind

@0celo7 How do you define the bundle of tensors if not by that?

TanMath

it isn't a tangent line!

0537

Jan 13, 2016 22:46

I didn't say it was.

ACuriousMind

@0537 wat

0537

you didn't imply tangent line.

TanMath

@0537 oh... so by that logic, a point can have infinite number of slopes

0537

yeah.

Sir Cumference

Okay, so you can change the tangent line's slope. But what good would a "non-tangenty" line do for you

0537

Jan 13, 2016 22:47

@TanMath that's what i'm saying.

DanielSank

@BernardMeurer When I need a refresher I usually read the python docs.

0537

@SirCumference nothing.

Sir Cumference

.-.

ACuriousMind

@SirCumference No -y needed. "tangent" and "non-tangent" are already adjectives

Bernard Meurer

@alarge Thanks man, thanks a lot for reminding me something that will keep me from sleeping tonight...

Sir Cumference

Jan 13, 2016 22:48

@ACuriousMind Oh yeah... ._.

0537

@TanMath when you said it shows that a derivative is the slope at an individual point...

you weren't being precise.

Bernard Meurer

@DanielSank Huh, didn't even know the Python docs covered Regex, great addition! Thanks a lot!

0537

because a point can have infinite slopes.

Sir Cumference

Now you're just arguing semantics

0celo7

@ACuriousMind Easily: the disjoint union of tensor products of tangent spaces

Sir Cumference

Jan 13, 2016 22:48

Crap

0celo7

@ACuriousMind also what's the TeX for a disjoint union

0537

that's all i was saying.

ACuriousMind

@0celo7 And your definition of "tensor product of vector bundles"?

@0celo7 \sqcup

Sir Cumference

"semitics" Thanks autocorrect...

TanMath

@0537 you are making a big deal...i bet @SirCumference knows what i mean...

hey @DanielSank

0537

Jan 13, 2016 22:49

@TanMath be more precise. lol

TanMath

big deal...

0537

big deal for me.

Sir Cumference

Bar fight starting

TanMath

@SirCumference did you understand what i meant?

Sir Cumference

Yeah

TanMath

Jan 13, 2016 22:50

@SirCumference lol

ACuriousMind

::breaks bottle::

2

Sir Cumference

XD

TanMath

@SirCumference so that is all that matters...

@0537 bye...

0537

@ACuriousMind hopefully not on our heads. lol

@TanMath what?

0celo7

@ACuriousMind disjoint union of tensor products of fi....oh

ACuriousMind

Jan 13, 2016 22:51

@0537 Nah, on a table. Broken bottle is the traditional bar fight weapon, right?

@0celo7 Exactly :)

0celo7

@ACuriousMind boot knife in the glorious south

TanMath

@0537 i do not want to have a bar fight...so I a, leaving before anything happens!

0537

@TanMath dude the discussion was over...

Physics Meta

1

Q: Is it OK to ask a question that you previously asked in other SE site?

I was wondering if it was accepted. In my case, for instance, I asked a question in other SE site (astronomy) that would be also on topic here. Unfortunately it didn't get much attention since that site is smaller. I was wondering if I could ask it here too. I've read the FAQ and it doesn't seem ...

0537

and i'm a calm person.

0celo7

Jan 13, 2016 22:52

watch out for that ayy lmao @ACuriousMind! He'll shank you!

Sir Cumference

@0537 He says as he takes out a knife

0537

@SirCumference D:

0celo7

you can be calm and still murder people

2

ACuriousMind

@0celo7 I waited for you say that ;)

Sir Cumference

That's the most screwed up type of murder

When the murderer doesn't care

ACuriousMind

Jan 13, 2016 22:54

You dream about me?

4

0celo7

@ACuriousMind awk

ACuriousMind

lol, coward

0celo7

@ACuriousMind NO...

0537

I had a dream where 0celo7 was teaching me relativity.

remember?

TanMath

what is going on?

0celo7

Jan 13, 2016 22:54

you're just obsessed with me @ACuriousMind and want me to dream about you

TanMath

@0537 seriously?

ACuriousMind

@0537 If I remembered your dream that would be pretty messed up...

0celo7

@0537 how would I remember your dreams

Sir Cumference

@TanMath 0celo7 is dreaming about ACurious

0celo7

Jesus no

Sir Cumference

Jan 13, 2016 22:55

Do with that as you will

0celo7

At least not intentionally

0537

@ACuriousMind I implied that I shared that with you guys before.

Sir Cumference

You can dream intentionally?

ACuriousMind

^

FenderLesPaul

@0537 I read that wrong

I thought you said "0celo7 was touching me relatively"

4

0celo7

Jan 13, 2016 22:55

I was dreaming about Mordin Solus obviously

FenderLesPaul

that makes more sense

Sir Cumference

^

0celo7

and it carried over

0537

@FenderLesPaul go away lol

0celo7

@SirCumference uh, yeah

ACuriousMind

Jan 13, 2016 22:56

@FenderLesPaul How does one touch relatively

0537

you can touch relativistically.

TanMath

^

FenderLesPaul

@ACuriousMind it's a tumblr term

you wouldn't know!

ACuriousMind

wat

FenderLesPaul

just for full disclosure

I had a dream that @0celo7 was touching me relatively

3

Sir Cumference

Jan 13, 2016 22:58

So then would @0celo7 be your relative?

FenderLesPaul

@0celo7 just told me it wasn't a dream

ACuriousMind

Great job, the star wall finally returns to its usual non-sensical content!

2

0537

@JohnDuffield

0celo7

@0537 what

TanMath

@0537 he is following your footsteps...

ACuriousMind

Jan 13, 2016 22:59

wat

0celo7

@ACuriousMind Honestly, I do not remember dreaming about you

ACuriousMind

@0celo7 oooooh :(

0celo7

sorry

TanMath

so sad...

0537

=(

TanMath

Jan 13, 2016 23:00

@ACuriousMind is sad...

Sir Cumference

@0celo7 You broke his heart

TanMath

^

0celo7

@SirCumference I'm not into gingers anyway

ACuriousMind

@SirCumference My what?

TanMath

you should have lied! at least his heart would be intact...

0celo7

Jan 13, 2016 23:00

it never would have worked

Sir Cumference

@ACuriousMind black hole

0celo7

@ACuriousMind you have a heart in the third game

but then you SPOILER ALERT

FenderLesPaul

what the fuck is this conversation

ACuriousMind

@FenderLesPaul Not sure it's a "conversation"

Sir Cumference

@FenderLesPaul Fifty shades of ACuriousMind

HDE 226868

Jan 13, 2016 23:02

(Backs away into a corner looking scared)

TanMath

@FenderLesPaul watch the language mister...

0celo7

come here lil' Canadian

0537

who me?

0celo7

time for a relatively lesson

no the other one

The h Bar

Participants