The h Bar

0celo7

12:02 AM

the animals are doing well

user54412

blog as Einstein

ACuriousMind

Oh, then I can also say that I've read Einstein!

Brilliant idea

0celo7

ha

can someone pls help me with that calculus equation

my ODE book just states it

what would Einstein blog about

skill patrol

The Evidence

:-)

0celo7

lol

ignore that

skill patrol

12:11 AM

lol

user54412

I feel like Secret now

ACuriousMind

@0celo7 So, I've not fully checked if this gives the right result, but do you know the formula for the angle between to intersecting lines given their slopes?

0celo7

@ACuriousMind I know of it

could not tell you what it is

ACuriousMind

After you've remembered or derived that one, you just need to compute the slopes and plug it in.

0celo7

12:16 AM

how on Earth do you derive this :O

there needs to be a triangle somewhere...

mathforum.org/library/drmath/view/68285.html

you need a crazy trig identity

ACuriousMind

These things are annoying.

0celo7

@ChrisWhite not sure what you're trying to tell me here

user54412

@0celo7 $\tan\beta = r \mathrm{d}\theta/\mathrm{d}r$ :P

ACuriousMind

Yeah, that'd be the physicists' proof :D

0celo7

what the heck

can't make out what that's about :O

is the black line a circle

user54412

12:20 AM

yes

ACuriousMind

Damn...I don't know trig in English

I have to look up all the words

user54412

think of the black-blue-green triangle as being in the tangent space if it helps

0celo7

tangent space of

user54412

P

0celo7

still trying to figure out what's going on

where is beta

user54412

12:22 AM

If you move an infinitesimal dt along the parameterized curve, you will go r d\theta in the theta direction and dr in the radial direction

user54412

beta is the angle between the blue and straight black lines

0celo7

AH

the blue line is the tangent

thanks!

just had to figure out the picture lol

user54412

one day I'll get a proof-by-diagram into a publication

ACuriousMind

Drawn by hand, of course.

0celo7

yeeeeessss

user54412

12:24 AM

(this may very well be the day I decide to become a crackpot)

0celo7

exactly that quality

skill patrol

@ACuriousMind do you TA freshmen in English?

ACuriousMind

@ChrisWhite Why would you become one by conscious decision?

0celo7

ok time to do it using the slope formula

ACuriousMind

@skillpatrol No, the BSc is taught in German.

0celo7

12:25 AM

@ACuriousMind when the evidence strikes him

obe

tfw my parents tell me to close the window or they will take my computer.

ACuriousMind

That...is an unusual situation. I don't know what face that is :D

user54412

2 hours ago, by 0celo7

CLOSE THE WINDOW

0celo7

@obe you're gonna get some sickness

jesus

23 secs ago, by Chris White

2 hours ago, by 0celo7

CLOSE THE WINDOW

obe

Like cold, though I'm forced to now.

0celo7

12:27 AM

99 out of 100 times your parents are right when it comes to your health

ACuriousMind

28 secs ago, by 0celo7

23 secs ago, by Chris White

2 hours ago, by 0celo7

CLOSE THE WINDOW

user54412

Sep 11 at 16:20, by ACuriousMind

Sep 3 at 15:15, by ACuriousMind

Please do not recurse

0celo7

$$\tan\beta=\frac{\tan\theta-y'}{1+\tan\theta y'}$$

skill patrol

STAAAP the recursion :D

ACuriousMind

@ChrisWhite Excellent :D

0celo7

12:28 AM

well this is gonna be awk

I'm bad at calculus

skill patrol

1 min ago, by Chris White

Sep 11 at 16:20, by ACuriousMind

Sep 3 at 15:15, by ACuriousMind

Please do not recurse

0celo7

$$y'=\frac{dy}{dx}=\frac{dy/dr}{dx/dr}$$

is that right?

ACuriousMind

@0celo7 Do you even chain rule?

0celo7

probably not

@ACuriousMind no

HDE 226868

@0celo7 Yes.

0celo7

12:30 AM

it can't be right

I just get $\tan\theta$

ACuriousMind

@HDE226868 Well, it should really be written $\frac{dy}{dx} = \frac{dy}{dr}\frac{dr}{dx}$.

HDE 226868

$$\frac{dy}{dx}=\frac{dy}{dr}\cdot\frac{dr}{dx}$$

0celo7

what the hell is that

ACuriousMind

A MathJaX fail :P

0celo7

indeed

skill patrol

12:32 AM

:-/

0celo7

haha

HDE 226868

Weird. I've had that before, too. :P

0celo7

ok well this doesn't make sense

according to this, the slope of the tangent line is just tan theta

unless I'm really dumb

which I'm not excluding ofc

HDE 226868

No more fancy \mathrm s for me.

user54412

@0celo7 If any trig formula works for 0 and pi/2, it works for all values :p

skill patrol

12:34 AM

^

ACuriousMind

@0celo7 Have you computed $\frac{dr}{dx}$ instead of dividing by $dx/dr$ as you wrote?

0celo7

what's the difference

::ducks::

ACuriousMind

@0celo7 I'm not that sure, since it sometimes goes over well, but it's safer to not do the latter

0celo7

doing the other thing

do you at least agree with

8 mins ago, by 0celo7

$$\tan\beta=\frac{\tan\theta-y'}{1+\tan\theta y'}$$

$\tan\theta$ is the slope of the radial line

HDE 226868

@0celo7 Take the function $y=x^2$.$$\frac{dy}{dx}=2x$$Because (if you treat the derivative as a ratio)$$\left(\frac{dy}{dx}\right)^{-1}=\frac{dx}{dy}$$you could say that$$\frac{dx}{dy}=\frac{1}{2x}$$but it's often simpler to just find the inverse (i.e. $x(y)$) and compute $\frac{dx}{dy}$ from that.

0celo7

12:37 AM

what the heck

you have an equality in the denominator of a fraction

pls teach me this wizardry

HDE 226868

Damn it, \frac isn't on my side today.

0celo7

also your $\mathrm{d}x/\mathrm{d} y$ is wrong

ACuriousMind

Just look here:

Inverse functions and differentiation

In mathematics, the inverse of a function is a function that, in some fashion, "undoes" the effect of (see inverse function for a formal and detailed definition). The inverse of is denoted . The statements y = f(x) and x = f −1(y) are equivalent. Their two derivatives, assuming they exist, are reciprocal, as the Leibniz notation suggests; that is: This is a direct consequence of the chain rule, since and the derivative of with respect to is 1. Writing explicitly the dependence of on and the point at which the differentiation takes place and using Lagrange's notation, the formula for the...

HDE 226868

^^

0celo7

@HDE226868 like everything here is wrong

the derivative of $2x$ is not $2x$ :/

user54412

12:40 AM

@HDE226868 what you should have said: "Frak, \frac isn't on my side today."

HDE 226868

Oh, damn. I meant $y=x^2$, not $y=2x$. I got ahead of myself. I should check my work more often.

@ChrisWhite What the frak? Yep.

0celo7

ok, $$\frac{\mathrm{d}r}{\mathrm{d}x}=\frac{x+yy'}{r}$$

maybe

ACuriousMind

Maybe you also need to take the partial derivative...

0celo7

what

ACuriousMind

(not sure, low brain power)

0celo7

12:42 AM

this is too hard

I like the physicist's proof way better

7 mins ago, by 0celo7

8 mins ago, by 0celo7

$$\tan\beta=\frac{\tan\theta-y'}{1+\tan\theta y'}$$

is that even right?

HDE 226868

Potentially stupid question here: Is it possible, using the Lorentz force law, to analytically get an expression for the position of a charged particle as a function of time under the influence of electric/magnetic fields that change in space?

0celo7

no

now do my homework

ACuriousMind

@0celo7 Stop panicking, chug through the calculations and see if it gives the right result. If it does, celebrate. If it doesn't, start over.

0celo7

@ACuriousMind not sure what to chug through

I'm failing at basic calculus

HDE 226868

@0celo7 I'm not sure if I should be glad that my suspicions were confirmed, or annoyed that that would mean more work for diminishing returns.

bolbteppa

12:46 AM

Are you guys trying to derive this math10.com/en/geometry/trigonometry-and-geometry-conversions/… ?

0celo7

@HDE226868 I said that randomly

tutorial.math.lamar.edu/Classes/CalcII/PolarTangents.aspx

apparently we're stupid

HDE 226868

@0celo7 Oh.

user54412

@HDE226868 what other force would there be?

0celo7

wait what

ok that's assuming $\theta$ is the parameter

HDE 226868

@ChrisWhite Nothing else. It would be in a horizontal plane (ideally; I'm talking about an experimental setup here).

. . . that may or may not ever be built.

NeuroFuzzy

12:49 AM

@HDE226868 What do you mean? I mean $\dot{x}=-\phi'(x)$ isn't exactly something where you can solve $x$ as a function of time...

HDE 226868

@NeuroFuzzy Basically, if I can figure out the electric and magnetic fields in a given region of space, and I know the mass, charge, and initial velocity of a particle in that space, can I use the Lorentz force law to come up with an explicit expression for its position?

That probably didn't help.

0celo7

@ACuriousMind I don't know what to chug through anymore

I've been defeated

NeuroFuzzy

@HDE226868 Okay, but a simpler problem to start out on would be to "solve $\dot{x}=-\phi'(x)$ for $x$ as a function of time", right?

and that seems like kind of a weird question because at least as far as I can tell you can't do anything to that expression generally (I mean maybe a general power series solution)

HDE 226868

@NeuroFuzzy Okay, true. $\phi(x)$ is a scalar field, right?

NeuroFuzzy

yeah

HDE 226868

12:53 AM

@NeuroFuzzy Yeah, that would be the only thing I can think of.

0celo7

ok, that's wrong too

you so need some partial derivatives....

too complicated, @ChrisWhite your proof wins

DanielSank

Discussion topic: Is math a language? In what sense, if any, can mathematics be considered a language? Surely notation and syntax are important in mathematics, but is there something more? Compare against natural language which is intimately tied into abstractions such as emotion, much as mathematical expression is tied to math's own abstractions.

obe

Yes because you can read it without referring to what the symbols denote in another language.

DanielSank

Good point.

0celo7

But any math text has non-math language in it.

DanielSank

1:00 AM

Also a good point.

0celo7

Try writing a topology proof without words.

user54412

@obe Can you? I don't see this being immediately true (or false).

obe

@0celo7 Try learning another language from a book that is written in that language.

DanielSank

So math textbooks are actually written in a pidgeon language :D

@ChrisWhite I don't think my brain translates math to English internally.

0celo7

@obe Math does not have symbols for all the words we use in proofs, does it?

Maybe it does.

DanielSank

1:01 AM

I'm pretty sure when I read a mathematical expression it goes to the same place that natural language does, with no intermediate steps.

user54412

If we raised a child with pure math and no elements of natural language, would they understand the math? The same as we "understand" it?

0celo7

Just look through something like HE...a lot more words than symbols.

DanielSank

@ChrisWhite Woah. Probably not the same way.

I wonder if you can learn math without the help of another language. Interesting!

obe

@ChrisWhite For example I don't read $\frac{d}{dt}$ as d by dt in my head.

DanielSank

Right, you just see a derivative.

And maybe you feel slopey or something.

Maybe you feel like integrating something.

0celo7

1:03 AM

@obe I do.

DanielSank

@0celo7 That's cuz you're young :P

Give it time.

Im younger though.

It was a joke.

I know.

:D

1:04 AM

:D

user54412

@DanielSank But what indeed is your concept of derivative?

user54412

Is it primitive?

DanielSank

@ChrisWhite Yes. I'm 99% sure that it is as primitive as "blue" or "happy".

user54412

Or do all abstract mathematical concepts build upon (concrete and/or abstract) natural language elements?

DanielSank

@ChrisWhite Similarly to how a note on a musical staff has no English meaning to me.

ACuriousMind

1:05 AM

The boring answer here is: It depends on what exactly you mean by math, I think.

DanielSank

@ChrisWhite For me, no. At least, I don't think so. Not any more.

@ACuriousMind It's not boring to be precise! Only philosophy professors frown on precision.

user54412

@DanielSank "Not any more." That's interesting. I think we agree then that in practice we all learn math by building a dictionary between math and whatever other language we have on hand.

obe

@DanielSank Exactly, you don't read F B E A D G in your head when you play piano.

DanielSank

@ChrisWhite Sort of.

obe

The same way you don't read the derivative as d by dt.

DanielSank

1:07 AM

Although I'd argue that so long as you're translating math to natural language you really haven't learned math yet.

obe

How?

I'd say that means you learned it well.

user54412

Or you haven't lost touch with reality yet ;)

DanielSank

@ChrisWhite and really, what teaches a student better about derivatives, words or a diagram :)

obe

Because you can translate it.

DanielSank

I'd argue the diagram, which surely is not a piece of natural language.

1000 words and all that...

0celo7

1:08 AM

@DanielSank Do you not read equations at all in English when you see them?

obe

Does anyone do that?

DanielSank

@0celo7 I don't think so.

obe

That's weird.

0celo7

That's impressive.

I read every part usually.

DanielSank

Especially if the equations relate to something with which I'm familiar.

I mean, when I see $Z = \sqrt{L/C}$ I don't even see the pieces of the equation any more.

0celo7

1:09 AM

I'll skip indices most of the time.

obe

Ok math is a pseudo-language.

DanielSank

My brain is just like: resonator/impedance/linewidth all at the same time.

obe

Because it depends on other languages as of now.

or it is still in alpha.

DanielSank

^ lol

0celo7

Ok what if I show you something from geometry which you're (perhaps) not familiar with.

DanielSank

1:10 AM

Example? Let's try this.

0celo7

::gets out BLT::

DanielSank

Bacon lettuce and tomato?

I asked for an equation, not a sandwich.

0celo7

erm

@tex people

how do I do an i or j with a bar instead of a dot

user54412

\imath

0celo7

@DanielSank what does $g_{i\bar\jmath}=\partial_i\partial_{\bar\jmath} K$ mean

(BLT is a string theory textbook)

DanielSank

1:12 AM

hang on.

Turning on mathjax

obe

@0celo7 How can you know what a word in english means before you have seen it?

DanielSank

Ok, @0celo7, here's what my brain did when I saw that expression:

ACuriousMind

@DanielSank Okay so: Formal logic is a language. Most of mathematics can ideally be expressed as statements in first order logic. In that sense, it's a language. But all the "real" semantics behind the expressions (like the picture in your head when reading a derivative) are completely absent from it, and can't be expressed in that language.

0celo7

@obe I'm not arguing

obe

I didn't say you are.

ACuriousMind

1:15 AM

Now you're arguing about whether he was arguing, great.

DanielSank

The first thing that happened was it tried to produce notions for the $g$ and $K$. Interestingly, it ignored the $\partial$ symbols. It failed on $K$ and so tried to attach meaning to $g$ and found the notion of metric. Interestingly, I think because I have no context, "metric" was somehow lexical, without any real meaning.

0celo7

did you get metric because I said geometry

btw that's the expression for a Hermitian metric in terms of the Kahler potential

DanielSank

@0celo7 I don't think so. I think that $g$ with indices is inextricably bound to relativity in my brain's associations table.

0celo7

it has nothing to do with relativity in this context

DanielSank

@0celo7 I understand that. That's not the point at all.

0celo7

1:16 AM

I know

just saying

DanielSank

Interestingly, I did not feel my brain search for word meanings for $K$. It just totally crashed in its attempts to ascribe meaning to the symbol and the whole process aborted.

At that point I felt a change in context as my mind fell back on what I can only describe as conversation with my own inner voice.

obe

This is really weird.

0celo7

UCSB did a number on you

DanielSank

@ACuriousMind Indeed.

@0celo7 What do you mean?

@obe What is really weird?

0celo7

that's way more introspection than I've ever done

or am capable of

@ACuriousMind argh now I want to start reading string theory again

DanielSank

1:18 AM

@0celo7 Your brain is a pretty interesting computer. It's worth hacking around.

0celo7

but no time

and no one to help

DanielSank

The tracebacks you get when something fails are fascinating.

0celo7

want another?

user54412

@DanielSank I see your brain runs on Python, with its automatic tracebacks.

DanielSank

@ChrisWhite Heh. Brain tracebacks are stored in volatile memory though, and have an element of quantum mechanics: you can screw them up by trying to access them.

ACuriousMind

1:22 AM

@DanielSank But, conversely, these "real" semantics we attach to it often aren't the precise meanings of it, but only the meaning in special cases, like how we always imagine 2D or 3D geometry for things that can be arbitarily high dimensional.

DanielSank

@ACuriousMind Not sure I follow that.

HDE 226868

@0celo7 I'll try it. My brain successfully associated $g_{ij}$ with a metric, although I then got sidetracked into thinking that $K$ was (Gaussian) curvature, and the idea fell apart after there.

Also, it should be easier to think of an equation I don't know.

0celo7

next one: $\nabla\phi=\mathrm{d}\phi+\rho_*(\tilde\omega)\wedge\phi$

DanielSank

@0celo7 Similar experience.

0celo7

@ACuriousMind what does it mean to you

you should have a p. good idea

ACuriousMind

1:27 AM

@DanielSank Okay, let me try again: All the "counterintuitve" examples of things in math - like a everywhere continuous function that is nowhere differentiable - come from places where the pictures in our head do not agree with that the math really means (which you get by just applying the rules of logic to the logical statements).

DanielSank

The $\nabla \phi$ got parsed immediately as a "gradient" which in my head means there's some cloud filling up space which involves some kind of "paths" in it determined by the composition of the cloud.

ACuriousMind

So, one could say it is a language in itself, and one could perhaps say that we are translating (sometimes inaccurately, because our own language/imagination lacks a precise equivalent) it when reading it.

DanielSank

@0celo7 but then everything fell apart when I didn't recognize the rest and I fell back to that inner voice.

ACuriousMind

@0celo7 It's a covariant derivative for a connetion $\tilde{\omega}$.

HDE 226868

My brain looked at the whole equation at once and noticed the common term, $\phi$, which I always associated with scalar fields (even if it isn't one). I didn't translate it in my head; I just left it as a primitive entity. I actually did pronounce the other operators (I assume they're operators . . . ?), and read them out: gradient, derivative (?), something like a wedge product.

0celo7

1:28 AM

@ACuriousMind yes

DanielSank

The voice started doing things like "Wedge product. Are there forms here? Are we integrating something..."

0celo7

$\phi$ is a spinor

obe

owned.

DanielSank

@ACuriousMind Uh, ok. I think maybe you're missing the point of this.

0celo7

@DanielSank I knew he would immediately recognize it

@DanielSank so your inner voice said "wedge product"

DanielSank

1:29 AM

Crap, I mis-pinged that last comment.

Sorry @ACuriousMind. That was meant to go to @0celo7.

@0celo7 Yes, as I said.

Once the pattern recognition failed my brain fell back on conversational methods.

0celo7

@HDE226868 covariant derivative, exterior derivative, induced isomorphism, connection form

not sure how the spinor is a form, but I don't know much about spin bundles

ACuriousMind

@DanielSank Like searching for the meaning of an idiom before thinking about the words it's made up of, right?

DanielSank

@ACuriousMind Yes, or even reading the letters of a word you don't know.

When you read you almost never actually parse the words into letters.

0celo7

ok, it's a spinor valued form, that's why

ACuriousMind

@DanielSank So...we're tending towards it being a language, hm?

DanielSank

1:32 AM

@ACuriousMind I think so?

ACuriousMind

What's wrong with your reply function? :P

DanielSank

It seems to set off similar processing pathways.

@ACuriousMind I suck at internet.

0celo7

:(

but you work at Google

DanielSank

@0celo7 So what?

You think the guys who program all your video games are amazing pro level gamers?

;)

HDE 226868

218

Q: Thinking and Explaining

How big a gap is there between how you think about mathematics and what you say to others? Do you say what you're thinking? Please give either personal examples of how your thoughts and words differ, or describe how they are connected for you. I've been fascinated by the phenomenon the que...

^ Related to what's being talked about.

DanielSank

1:38 AM

Hahahaha, that first comment.

HDE 226868

Interestingly enough, 5/15 top-voted questions on MO appear to be soft-questions. Including this one.

ACuriousMind

That is not surprising, is it?

HDE 226868

Well, accessibility to everyone will absolutely raise votes, but on a site with an highly active professional community - and given what a lot of Math Overflow's questions seem to be like - I wouldn't have thought it.

I don't truly know the community well enough to gauge it, though.

ACuriousMind

But that active community splits into many subfields. These are the questions where they all come together

HDE 226868

That makes sense.

Anthony

1:52 AM

@DanielSank Yeah, thanks again.

user54412

2:05 AM

So I've been a part of this one collaboration since it started 2 years ago. And today I just learned that apparently we have both a public website and a name for ourselves.

DanielSank

@ChrisWhite Haha, nice.

skill patrol

@HDE226868 that should've been asked on mathed.SE

dmckee

2:35 AM

@ChrisWhite What will they think of next.?

In particle physics choosing names is usually handled in a very forthright way sometime after the decision to put in a proposal for a project and the awarding of the first actual money.

A period of open nominations, then a vote usually. And sometimes another vote after the original name is vetoed or turns out to be currently in use by someone else.

Speaking of names EGADS! has been running for some time now, and they got the go ahead for the full scale project, but sadly the original name has been dropped.

I mean, who wouldn't want to work for GADZOOKS!

user54412

The same people who wouldn't want to work with SExtractor

dmckee

symmetrymagazine.org/article/july-2015/…

@ChrisWhite Uhm ... tell me they at least pronounce it "ess-extractor".

user54412

@dmckee I can't guarantee that.

dmckee

Ouch.

user54412

Ok, if I put a picture of myself on my webpage, what should it be? (there aren't many pictures of me)

user54412

2:48 AM

the "wait you're taking a picture of me?" look

user54412

the "bearded and pondering deep thoughts" look

dmckee

That is one that the sober, elder statesphysicists would have vetoed.

0celo7

don't you hate playing a sequel, then going back top play an earlier game and it being disappointing

user54412

the "bearded addict going into a relapse" look perhaps?

0celo7

I'm trying to play Splinter Cell: Conviction on Realistic mode

I'm missing the cover melee kill from Blacklist so bad

dmckee

2:51 AM

@ChrisWhite I can only grow a descent beard on the front half of my face and don't want to trouble of maintaining a goatee, so I usual go with "too baby faced to be a professor".

user54412

there's always the "just arrived back in civilization after an unspecified time in the wilderness" picture

dmckee

Though I'm finally beginning to look close to my age, so I'll have to chose a new one.

@ChrisWhite Very popular look, that.

@0celo7 I had the opposite reaction to a bunch of the CoD games. World at War had the best story line and storytelling and Modern Warfare came in second.

0celo7

3:40 AM

@dmckee I was thinking more in terms of game mechanics.

For instance, Splinter Cell: Blacklist has this mechanic where if an enemy is close enough to you while you're in cover, you can stab them in the throat and drag the body behind cover. This isn't present in Splinter Cell: Conviction and if you try to do the same thing, you'll expose yourself and get detected/killed.

So while I'm really glad that I just finished Conviction again, that part really irked me.

There's another thing where you can whisper to attract the attention of a nearby guard...which is also really helpful if you don't want to shoot the guy but aren't close enough to drag him behind cover.

In terms of story...that can vary from game to game but the quality generally decreases as they milk the series further.

Secret

Continue on the overthought problem 2 days ago...
Stuck on delta derivative (or unit impulse distirbution) integral in red

Unit impulse distributon
$$f'(t)=\int_{-\infty}^{\infty}f(w)u_1(w-t)da$$
$$\int_{-\infty}^{\infty}f(w)\delta'(w-t)da=\left.f(w)\delta(w-t)\right|_{-\infty}^{\infty}-\int_{-\infty}^{\infty}f'(w)\delta(w-t)da=-f'(t)$$
$$\therefore "-u_1(w-t)=\delta'(w-t)" \forall w$$
In particular, when $a=2t$:
$$"-u_1(t)=\delta'(t)"$$

Charges and currents
$$\rho(t)=\lambda(x(t))\delta(y(t))\delta(z(t))$$

The issue is that, if the use the rules above, I get a weird $"\frac{d0(t)}{d0}"$ term which does not make sense

0celo7

4:03 AM

uh

no one is gonna read that one

waaaaay to long

Secret

4:15 AM

Ok let me single out the piece I have issues with:
$$-\int_{-\infty}^{\infty} \delta'(y)v_y(y) dy$$

If we use integration by parts we will obtain

$$-v_y'(0)$$

But we cannot have zero as a variable in the derivative, so how to evaluate this integral?

PS $v_y$ is just a function, it is not a partial derivative wrt y of v

0celo7

4:31 AM

what

zero as a variable in the derivative?

Huy

5:58 AM

wazup @0celo7

Secret

6:22 AM

https://en.wikipedia.org/wiki/Distribution_(mathematics)

Ok nvm, I solved it
I first need to differentiate the test function (in this case $v_y(y)$) by the variable y, and then evaluate the resulting integral at y=0

The unit impulse distribution convention, that is $"u_1=-\delta'"$ obscured this procedure

Now to finish computing the results...

DanielSank

6:47 AM

Is it possible to come up with a question which you'd down vote but would not vote to close?

0celo7

@Huy holy fuck look at the time

Huy

wat

it's 8am

0celo7

Rainbow 6 Vegas 2 swallowed 4 hours

Huy

lol

0celo7

gnight

Huy

6:57 AM

n8

user54412

@DanielSank I'm sure I've done that at some point.

0celo7

Back

user54412

Like something that lacks any research effort but isn't homework-like nor unclear.

user54412

7:14 AM

Ok, everyone always says sans-serif fonts are easier to read or something, especially on screens.

user54412

Can anyone name a common sans-serif that doesn't look awful in section headings?

user54412

The most tolerable I can find is Verdana, but the x-height is enormous. h's could pass for n's.

Secret

(cont. from above...)
Integrate over all space
$$\int_{-\infty}^{\infty}\dot{\lambda}(x)dx-\int_{-\infty}^{\infty}\lambda(x)dx 0-\int_{-\infty}^{\infty}\lambda(x) dx 0+\int_{-\infty}^{\infty} \lambda(x)a_x(x) dx+\int_{-\infty}^{\infty} \lambda(x) dx a_y(0)+\int_{-\infty}^{\infty}\lambda(x)dx a_z(0)+\int_{-\infty}^{\infty} \frac{d\lambda(x)}{dx}v_x(x)dx-\int_{-\infty}^{\infty}\lambda(x) dx \int_{-\infty}^{\infty} u_1(y)v_y(y) dy-\int_{-\infty}^{\infty} \lambda(x) dx \int_{-\infty}^{\infty} u_1(z)v_z(z) dz=0$$

And finally

$$\dot{\lambda}(x)+\lambda(x) +\frac{d\lambda(x)v_x(x)}{dx}=0$$

DanielSank

7:36 AM

@ChrisWhite I use whatever LaTeX uses by default.

Looks great to me.

user54412

Computer modern always struck me as a bit narrow, but looking now the sans-serif isn't as bad in that regard.

user54412

And yes, I am an unappeasable font snob.

user54412

Only organic, tie-dye, free-range serifs for me.

2

Secret

So in short, the continuity equation restricts the form the x component of the current density can take for a wire extending along the x direction

for a charge density of the form given here

Physics Meta

8:20 AM

0

Q: Are questions about mathematics used in physics always off topic?

This question looks in imminent danger of being closed on the grounds that it's a pure mathematics question. This is something that happened a lot when I was more active on the site, and is one of the reasons I'm less so now. I'm wondering (a) whether the on-topicness of maths-as-used-in-physics ...

discussion

skill patrol

@ChrisWhite very...conservative :P

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