Mathematics - 2012-10-14 (page 2 of 3)

Two crates of masses 12.0 kg and 20.0 kg respectively, are pushed across a smooth floor together, the 20.0 kg crate in front of the other. The acceleration is $1.75\, m/s^2$

Calculate the action-reaction forces between the crates.

Charlie

the crates are conected?

Argon

5:14 PM

@Charlie They are, I assume, adjacent and the 12.0 kg is pushing the 20 kg

Charlie

hmm

Argon

This uses, of course, Newton's third law.

Argon

5:30 PM

Is the answer $20.0 \cdot 1.75 \,m/s^2 = 35.0 \, N$?

Link

Hi... can someone explain to me why the two girls reach the other side of the river at the same time?

tinyurl.com/9zqdyzw

user19161

Haha, this has really become a physics cum chem chat. I think bio will come next.

Link

since, when I do it, I end up getting bebe reaching first.

user19161

@Link No question in the link.

Link

Its there. b1.

It says They reach at the same time, but I don't get why.

user19161

5:35 PM

@Link I am not seeing it. Maybe only Americans can see it.

Link

hmm

user19161

Different locations view the internet differently due to blocking, legal restrictions etc.

anon

try refreshing it.

user19161

What I see is a bunch of books or links there but no question, without refreshing.

user19161

No difference with refreshing at all.

user19161

5:38 PM

Two people can click on the same google book link and see different things I think.

Charlie

@Argon how did you think?I sually made a drawn and the vectors and things are easier...

user19161

@Charlie Draw a force diagram on each of the boxes and then apply F=ma horizontally eh?

Charlie

@JasperLoy yeah...

@JasperLoy Hello , isn't it?

user19161

@Charlie Hmm, I don't know. Argon should know better than me.

Charlie

@JasperLoy what?

Link

5:45 PM

@JasperLoy, try this: imgur.com/4iYeW

user19161

@Argon Yes, I think so. Just draw a force diagram on the heavier box.

user19161

@Link This definitely looks different.

Jayesh Badwaik

@Link the answer is there in the book. the horizontal velocities are the same.

Link

but i don't get why.

is ut because the river is being used as the reference?

it*

user19161

@Link Dude, the book is just saying that since the horizontal component is the same, they reach at the same time.

Jayesh Badwaik

5:50 PM

@Link what we use as a reference does not matter. although, using the river as a reference simplifies the mental picture.

user19161

You need to understand that velocity of $X$ relative to $Y$ is $v_x-v_y$.

user19161

Here $v_x$ and $v_y$ are the actual velocities of the two objects.

user19161

Relative velocity is as if one of the objects is stationary.

Argon

@Charlie As @JasperLoy said, I used $F_{net}=MA$ horizontally

user19161

Horizontally, the water has no velocity component.

Charlie

5:54 PM

@Argon ok

user19161

The question just says that if the two girls have the same absolute velocity horizontally, of course the relative velocity will be the same as well since the water does not move horizontally.

user19161

Now one must admit that relative velocity is one of the hardest topics in mechanics.

user19161

@Argon Hey dude, no need to acknowledge me for such a trivial observation. =)

user19161

@Argon Well, of course, the more complicated formula is that F=d(mv)/dt as force is the rate of change of momentum. When mass is constant, it is taken out as a factor and a=dv/dt.

Link

ahh.I think i get it I drew a diagram, and that worked out.

:D yay thanks

Argon

5:58 PM

@JasperLoy Nice to know :)

user19161

@Link Draw a velocity diagram using the velocity vectors. That's a standard step.

user19161

@Link did you derive the sin 3A formula? I thought you were kidnapped.

Link

6:13 PM

no, I got it. :D and thanks

user19161

@Link Actually in the above, I think I meant to say that if the girls have the same relative velocity horizontally, then the absolute horizontal velocity is the same as well, but never mind. The absolute velocity is what a stationary observer sees.

user19161

6:34 PM

Any of you notice that when you edit an answer it looks crappy at first? One has to refresh for the math to look correct.

user19161

Hmm, I wonder why this happens. The words just sort of overlap each other.

Argon

@JasperLoy Happens to me too. It is strange.

Peter Tamaroff

@JasperLoy My last 6 answers have all been accepted. I'm on a streak.

Jayesh Badwaik

@PeterTamaroff You are on a roll!!

user19161

@PeterTamaroff I blessed you with my presence you see.

user19161

6:46 PM

Hey I have been the victim of another accept without upvote. Is this answer correct? math.stackexchange.com/questions/213758/…

user19161

@matt You seem to be on a puzzles streak.

Matt N.

@JasperLoy Yes, though not anymore since today. : )

Lucky me.

Can't stand puzzles.

Peter Tamaroff

@MattN. Hey Matt. How are you doing?

user19161

@MattN. Hmm OK, better to focus on your schoolwork, just a thought.

Matt N.

@JasperLoy Yes, exactly.

Jayesh Badwaik

6:50 PM

@MattN. then why were you doing them in the first place? (don't mean to be accusatory, just wondering.)

Matt N.

@PeterTamaroff Thanks, ok. And yourself?

@JayeshBadwaik Because. : )

For practice.

Peter Tamaroff

@MattN. I had a massive headache. Then I realized I didn't have coffee in all the day.

Matt N.

@PeterTamaroff Eww, yes. I know how it feels.

Jayesh Badwaik

@MattN. oh. okay. nice. :-)

user19161

@PeterTamaroff I know why you have a headache. It is because I have been running in your mind all day. =)

Jayesh Badwaik

6:52 PM

@JasperLoy Sheesh.

Peter Tamaroff

Problem of the Day Suppose $f$ has the functional equation:$$f(x+y)+f(x-y)=2f(x)f(y)$$ for each $x,y$ and there is a real $x_0$ for which $f(x_0)=-1$. Prove $f$ is periodic.

user19161

@JayeshBadwaik Sorry, I like to use cliches.

Peter Tamaroff

@JasperLoy Well, don't.

=D

Jayesh Badwaik

@JasperLoy Go strut out your cheesy lines elsewhere, you might get the girlfriend you are moping about.

3

Peter Tamaroff

@JayeshBadwaik $\Huge \star$

user19161

6:53 PM

@PeterTamaroff That's the problem of your day, not our day.

Peter Tamaroff

@JasperLoy Actually, it is

Problem of the week.

Argon

Could someone help me with a LHS=RHS-style proof for a trig identity?

Peter Tamaroff

New prime, guys

@Argon Yeah

user19161

@JayeshBadwaik Well, I don't use such lines with a girl I am seriously in love with. Cliches are only used for non-serious purposes.

Argon

$$\frac{1+\sin x}{\cos x} = \frac{1+\sin x+\cos x}{1-\sin x+\cos x}$$

sperners lemma

6:54 PM

cool Peter

I guess it comes from factoring a mersenne number

Jayesh Badwaik

@JasperLoy But you can use them before you fall in love. :P

Argon

Choose a side and get to the other side somehow. I cheated using $$\frac{1+\sin x}{\cos x} \cdot \frac{1 - \tan x + \sec}{1 - \tan x + \sec}$$

Peter Tamaroff

@spernerslemma It is a "Proth" prime.

sperners lemma

> a number N of this form is prime iff there exists a number a such that a^((N-1)/2) is congruent to -1 modulo N. This provides an easy computational test for Proth primes. Yves Gallot has written a downloadable program for testing Proth primes and many of the largest currently known primes have been found with this program.

Peter Tamaroff

@spernerslemma The guy who found this used a "homemade" computer with 3076 processors

@Argon Why don't you try differentiating? =P

Argon

6:58 PM

@PeterTamaroff Can't. We haven't learnt that yet.

Jayesh Badwaik

@Argon hint Multiply the denominator and the numerator of RHS with an appropriate similar term to somehow give you the term $\cos^2 x + \sin^2 x $ in the denominator among others.

Peter Tamaroff

@Argon Hmm. Ultimately, you want to prove that $$\sec x + \tan x = \frac{{\sec x + \tan x + 1}}{{\sec x - \tan x + 1}}$$

user19161

@Argon Hey you should post such things on main so that we get some rep for answering you. =)

Argon

@JayeshBadwaik I'm too lazy to use the conjugate if that's what you mean.

Jayesh Badwaik

@Argon Bleh. :-)

Write the terms in terms of half-angles

user19161

7:03 PM

@Argon I'll give you a complete solution now if you post on main.

Argon

@JasperLoy Doing it right now :)

@JayeshBadwaik We haven't learnt half angle identities, so I cannot use that either!!

0

Q: Proving Tigonometric Indentiy

I would like to try and prove $$\frac{1+\sin x}{\cos x} = \frac{1+\sin x+\cos x}{1-\sin x+\cos x}$$ using $LHS=RHS$, i.e. pick a side and rewrite it step by step to make it identical to the other side. I found a quick way by doing this: $$\frac{1+\sin x}{\cos x} = \frac{1+\sin x}{\cos x} \cdo...

trigonometry

sperners lemma

Argon the question doesn't make any sense

Argon

@spernerslemma Why not?

sperners lemma

You basically answered it and then said this isn't a vaild answer

user19161

@Argon Done.

sperners lemma

7:12 PM

so it doesn't seem like anything is a valid answer

Argon

@JasperLoy I like!

user19161

@Argon You know what to do...

Argon

@JasperLoy You can accept an answer in 7 minutes... :)

sperners lemma

why isn't jaspers answer rejected on the same grounds as the one in the question?

user19161

@Argon Of course, you can add more steps if you want to yourself if it's an exam and you want to be sure you show everything.

user19161

7:15 PM

@spernerslemma Because I used the rhs denominator so it is not mysterious.

W3Geek

How is dividing by 1/2 the same as multiplying by 2?

3 * 2 = 6

Argon

@spernerslemma Because I don't like my answer. I manipulated the denominator so that the LHS = RHS and I don't really like that.

sperners lemma

3 / (1/2) = 3 * 1/(1/2) = 3 * 2

W3Geek

So the ones cancels each other out?

sperners lemma

a/b = a * 1/b

1/(1/x) = x

user19161

7:17 PM

@W3Geek I see that if you ask this then you have lots of basic stuff to cover, I remember you asked me about programming math books.

W3Geek

confused Symbols are very confusing to me.

Yes I asked about those. I'm watching KhanAcademy videos right now.

sperners lemma

A symbol just means you can replace it with any number

for example you can replace x with 5: 1/(1/5) = 5 or 3: 1/(1/3) = 3

W3Geek

Trying very hard to learn this.

Peter Tamaroff

@W3Geek The general idea is that $(a^{-1})^{-1}=a$

W3Geek

@PeterTamaroff Beyond confusing...

Argon

7:20 PM

@PeterTamaroff ...but then you must know that $a^{-1} = \frac{1}{a}$

W3Geek

Ok, I cannot read that. :(

sperners lemma

well ok looks like people are taking over from me

Peter Tamaroff

@W3Geek Oh, you don't have ChatJax.

sperners lemma

I'm not sure what the value of saying $(a^{-1})^{-1}=a$ is when I already said 1/(1/x) = x

Argon

@JasperLoy Happy?

user19161

7:21 PM

@Argon Sure! =)

Peter Tamaroff

@spernerslemma I don't like division bars =)

Argon

:)

Ian Mateus

@W3Geek if you give to half a kid one chocolate, then the concentration (ratio between the amount of sugar and mass) of sugar in his blood is the same as if you gave two chocolates to one kid.

2

W3Geek

I need to go over fractions I think.

sperners lemma

lol

@W3Geek, do you understand what I said about symbols?

W3Geek

7:23 PM

Yes, I just always find it hard to represent them correctly.

sperners lemma

what do you mean represent?

W3Geek

Represent as in finding a number to replace them.

sperners lemma

you can replace it with any number you choose

you don't have to specially find one

W3Geek

So when you multiply fractions, 3 becomes 3 / 1 correct?

Argon

@JasperLoy How did you know to multiply by $1-\sin x+\cos x$?

@W3Geek Indeed

W3Geek

7:24 PM

then you cross multiply?

user19161

@Argon Like I remarked above, it is simply the denominator of the RHS.

W3Geek

3 / 1 * 1 / 2 = 3 / 2

3 / 2 is 1.5

Argon

Correct

sperners lemma

a/b * c/d = a*c / b*d

Ian Mateus

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

drN

7:30 PM

I have a question about self similar solutions and (discrete) fourier transforms. Is there any way that DFT data could be used to prove self similarity? I have posted this as a question but given the shear number of questions being asked, I thought I'd try here....

*sheer not shear (the fluid dynamicist in me has taken over apparently)

Argon

$$\Gamma(x) : = \int_0^\infty t^{x-1}e^{-t}\,\text dt$$

user19161

@Argon Dude, you deal with the gamma function but ask how to prove a trig identity?

Argon

@JasperLoy Why yes... :)

sperners lemma

he already knew how to prove the identity

Argon

@JasperLoy You see, when I can't use complex exponential XD

user19161

7:35 PM

@spernerslemma Wait, are you the one who came up with the lemma?

sperners lemma

what lemma?

Argon

sperners lemma

no

user19161

Sperner's Lemma.

user19161

7:48 PM

I usually upvote the questions of new users so that they can get enough rep to start upvoting.

Argon

@JasperLoy Upvoting your questions?

:)

user19161

@Argon No, my answers. =)

user19161

This is a disaster. math.stackexchange.com/questions/213821/…

user19161

OK it has been edited by someone who guessed OP mind.

user19161

8:30 PM

@jay Are you still up?

user19161

@W3Geek Just cover addition, subtraction, multiplication and division of fractions.

Matt N.

@JasperLoy Every time I read this I read "Spermer's lemma". : /

2

sperners lemma

lol

user19161

@MattN. Hehe, that's because you are full of sperm like me.

Matt N.

@JasperLoy Probably : )

user19161

8:40 PM

I imagine someone would come in soon and flag me, but let them flag all they want.

Jayesh Badwaik

@JasperLoy kind of.

@JasperLoy flagging would be done only if someone else in the chat is intentionally offended right?

user19161

@JayeshBadwaik Hehe, would you like to do me a favour and look at this answer? math.stackexchange.com/questions/213763/… Hint, hint...

user19161

@JayeshBadwaik Well, I don't know if invisible people could flag. Anyway, does not matter.

Jayesh Badwaik

@JasperLoy duuude. that question is asked by the guy whose profile says "A Graduate student in Pure Math. Currently doing a research on integrals that take values in locally convex spaces." WTF?

user19161

@JayeshBadwaik Yeah WTF. That's why people like me have hope of getting accepted I think.

Jayesh Badwaik

8:50 PM

@JasperLoy Did you see this I posted this on chat some time ago, but did not ping anyone for it.

user19161

@JayeshBadwaik I decided to give an answer after two have been posted because neither showed all the axioms needed.

user19161

@JayeshBadwaik Yes I saw it.

Jayesh Badwaik

@JasperLoy Apparently they thought it was a freshman homework, and decided to give only hints?

@JasperLoy busted!

user19161

@JayeshBadwaik When someone asks this kind of thing, it's clear they don't know anything about the axioms, so it's best to give it all.

Jayesh Badwaik

@JasperLoy okay. notes it down

user19161

8:52 PM

@JayeshBadwaik What? We are not them! Anyway I just really hate it when my answer has no upvotes, so now and then if I wait a while and still no upvote I will try to ping someone in here and say hint hint.

user19161

@JayeshBadwaik There are some questions that the more hints you try to give the more twisted it becomes.

Jayesh Badwaik

@JasperLoy Gosh! No, I was not referring to you! I was referring to how good people are who kept a watch and saw it and kept it in check.

user19161

@JayeshBadwaik I caught someone trying to delete a question the second time today. I rolled back.

Jayesh Badwaik

@JasperLoy yup. unfortunately, I have a tendency to do that a lot.

user19161

I was thinking if I should flag for a mod to lock the post but I think no need to do that.

Jayesh Badwaik

8:54 PM

@JasperLoy good! Hmm. Flagging is best as Qiaochu said in the comment.

You might miss that guy's other questions and then, he might get away with it.

user19161

@JayeshBadwaik Also, I am really trying to get my TeX account to up to 2k rep. I guess I will try to do 100 maximal edits to get 200 rep!

Jayesh Badwaik

and if others see it, then he will get away with the offense of being an habitual offender.

@JasperLoy only 100 are allowed? hmm. I have done less than 10 till now I guess.

user19161

@JayeshBadwaik In this case, he clearly knows what is happening cos it's the second time, so I think I will flag now. Let me find it...

user19161

Here math.stackexchange.com/questions/208836/…

user19161

Actually he did it thrice, WTF!

Jayesh Badwaik

8:58 PM

@JasperLoy WTF!!

user19161

@JayeshBadwaik Why can't these people ask their fellow students for help instead?

Jayesh Badwaik

BTW, the bar at the bottom says 11 flags remaining. What does it mean? Do I get only 11 flags?

@JasperLoy yeah!

user19161

@JayeshBadwaik Per day.

Jayesh Badwaik

@JasperLoy okay. good.

user19161

@JayeshBadwaik Such numbers may change with rep or other factors I think.

Jayesh Badwaik

9:01 PM

@JasperLoy okay.

user19161

@JayeshBadwaik No, I mean I only need to do about 100 more.

Jayesh Badwaik

@JasperLoy okay.

user19161

@JayeshBadwaik Let me recall some of my flags in this room. One was "looks like my balls" and the other was "I am naked now". I am surprised they did not flag every occurrence of the f word.

Jayesh Badwaik

@JasperLoy hmm. f*** is okay. the other two sentences are kind of suggestive if you know what I mean.

but still, I personally would not have flagged it, going by the context I know this rooms often has.

user19161

@JayeshBadwaik I don't say such things on the main site, but I think it's alright for this chat, as long as it's not too much.

Jayesh Badwaik

9:06 PM

@JasperLoy yeah.

user19161

@JayeshBadwaik Some people would think that f is not OK and those are OK, just opinions.

Jayesh Badwaik

@JasperLoy A context is a context is a context.

user19161

@JayeshBadwaik No, in this case it is just what various people consider flaggable or not, not really the context, which is often clear.

user19161

Some countries you can walk completely naked, others you get fined, and others you get jailed, and others you get killed.

Jayesh Badwaik

hmm. My rules of flagging are:
1. Someone intentionally and specifically insults me directly even after I have given him a chance to apologize once.
2. I feel someone is intentionally and specifically insulting/bullying some other guy in the room even after I have given him a chance to apologize and I feel the guy being insulted is not going to flag the behavior himself due to pressure probably.

user19161

9:13 PM

@JayeshBadwaik My rules of being aggressive to another person in real life are: if you abuse me, I will retaliate in whatever way I feel like at that moment.

Jayesh Badwaik

@JasperLoy Yup. I am never aggressive myself. But I have enough verbal and some physical ammunition to take care of any aggression against me.

user19161

@JayeshBadwaik I guess it is not ammunition literally. Speaking of which, I obviously have handled real bullets in the army.

user19161

I remember the demo given by my platoon commander. He fired at a watermelon 100 metres away and it burst into pieces.

Jayesh Badwaik

@JasperLoy No, its not ammunition literally. But I will not shy away from carrying one for self-defence. Not always, but on rare occasions when I feel the need. You have been in army!!! I have been in National Cadet Corps and I have done my shooting lessons as well among others.

user19161

@JayeshBadwaik Of course, you know where I am from.

Jayesh Badwaik

9:19 PM

@JasperLoy ohh. How long?

user19161

@JayeshBadwaik Actually I can't shoot in the night because of astigmatism, just can't see. But in the day I can get a perfect score for shooting.

user19161

@JayeshBadwaik 2.5 years.

Jayesh Badwaik

@JasperLoy Nice! I had on an average around 85% accuracy for 50m targets with air rifles (HFT). Haven't touched them for almost two years now.

@JasperLoy Okay. So, all singapore civilians would have 2-3 years of break in their normal life? It would instead go into armed forces? (not criticizing it, just asking.)

user19161

@JayeshBadwaik Only those with bananas.

Jayesh Badwaik

@JasperLoy Hmm.

user19161

9:25 PM

@JayeshBadwaik Israel is different of course. Even those without bananas have to do it.

Jayesh Badwaik

@JasperLoy Israel's case can be understood on the conditions in 1947.

user19161

@JayeshBadwaik I think everyone here should do it too. It has been shortened to 2 years now.

Jayesh Badwaik

@JasperLoy Hmm.

skullpatrol

Wars are for warriors.

hi @PeterTamaroff

Yo @Argon

Argon

@skullpatrol Heyy

@JayeshBadwaik ...And 1973

Jayesh Badwaik

9:41 PM

@JasperLoy can you tell me which part of your country you live in?

@Argon Yeah. That was more important than 1947 actually I might think. But 1947 started the trend I will say.

user19161

@JayeshBadwaik Hmm, why do you want to know?

Jayesh Badwaik

@JasperLoy Curious. I was looking at the google maps and hence, just thought...

You don't have to tell me if don't want to.

user19161

@JayeshBadwaik Sengkang.

Jayesh Badwaik

@JasperLoy okay.

Argon

@JayeshBadwaik It's good to see you know your modern history!

user19161

9:45 PM

@Argon I only remember the history of my life.

Argon

@JasperLoy I thoroughly enjoy history, especially ancient history.

Jayesh Badwaik

@Argon well, I find it fascinating. When I read about how ben gurion gave orders to disassemble rifles and then bring the parts in israel and reassemble them (to avoid detection of smuggling during british occupation). I was like "wow"!

Argon

@JayeshBadwaik I know some people who were in the Israeli army.

Jayesh Badwaik

@Argon okay.

Argon

@JayeshBadwaik In fact, I knew someone who participated in operation Velvetta when they brought aircraft into Israel by painting a light coating of paint over the roundel to make it look British :)

Jayesh Badwaik

9:51 PM

@Argon Cool!

user19161

@jayesh I now have exactly 1800 rep on TeX so I need to do 50 edits in Nov and 50 in Dec to get 2k this year.

Jayesh Badwaik

@JasperLoy Nice.

user19161

Hey @argon I like Just For Laughs.

Argon

Does anyone know a good numerical analysis book?

@JasperLoy :) Me too!

user19161

@Argon Confession: I know nothing about NA.

Jayesh Badwaik

10:01 PM

@Argon what do you want to study in it? I have a book by Hamming which is really good and basic. Somewhat theoretical though.

user19161

@Argon I now imagine you are the naughty boy in it.

Argon

@JasperLoy Haaaaa!

Jayesh Badwaik

@Argon This One

Argon

@JayeshBadwaik I wanted some material on Chebyshev economization, if possible.

user19161

@Argon I think that DPMMS has fairly good notes on numerical analysis.

Jayesh Badwaik

10:03 PM

@Argon Does it make use of chebyshev polynomials and what you want is basically an analysis of chebyshev polynomials?

Argon

@JayeshBadwaik It uses Chebyshev polynomials to approximate infinite series.

@JasperLoy e.g. damtp.cam.ac.uk/user/na/PartIB ?

Or damtp.cam.ac.uk/user/na

user19161

@Argon Well, the last time I checked it out was long ago. It could be any of a number of notes from the lecturer's site or the notes' site, so take your pick.

Jayesh Badwaik

@Argon Strange why I never heard of the name before. Anyway, Hamming has more of a theory as I said, if you want some specific example, I think you should find it on some pdf online. No need to plow through an entire book for that.

Argon

@JasperLoy Looks good, I've bookmarked it

user19161

@Argon Why do you want to learn NA?

Argon

10:08 PM

@JasperLoy I like estimating irrational functions and constants.

user19161

@Argon Hmm, OK. I sort of hate NA. Perhaps you like computational stuff then.

Argon

@JasperLoy I like computer science as well as math, though I believe I understand your dislike of computation.

user19161

@Argon Ah, but which do you like more?

Jayesh Badwaik

@JasperLoy I like them equally. Neither can exists while the other survives. :P :P

Argon

@JasperLoy There's the problem... :) I probably will end up doing something related to computer science, as unfortunately, pure math does not seem to have the same opportunity.

user19161

10:11 PM

@Argon Hmm OK. Good luck! Perhaps one day I will hear of your name!

Jayesh Badwaik

@Argon I saw your question on main. I feel the Robert Israel's answer is quiet good.

Argon

@JayeshBadwaik Didn't check since earlier. I will look

Jayesh Badwaik

@Argon I was referring to this

Argon

@JayeshBadwaik Oh, that's what you meant

Jayesh Badwaik

@Argon I guess you accepted his answer, so understood the basic methods of how the co-efficients are calculated?

Argon

10:14 PM

@JayeshBadwaik He gave me this solution and told me that integrals were used to calculate coefficients.

Jayesh Badwaik

@Argon Yes.

Argon

Thats all great.

However

My numerical analysis textbook (I will tell you the name momentarily) does not mention this at all, and I do not understand where the coefficients are from.

My textbook is called "Elementary Numerical Analysis: An Algorithmic Approach" by Conte and de Boor, published 1972.

Here it is, actually: matematicas.unam.mx/gfgf/sc091/archivos/ConteDeBoor.pdf

Jayesh Badwaik

See this.

${}{}$

Argon

@JayeshBadwaik Interesting, they use the integral that R. Israel gave

Jayesh Badwaik

@Argon Do you know linear algebra, inner product and basis?

Argon

10:23 PM

@JayeshBadwaik I know about orthogonal and orthonormal functions from some differential stuff, but I don't know inner product and basis.

@JayeshBadwaik Thanks for your help, I have to eat dinner now

Jayesh Badwaik

@Argon Okay. It might do you good to learn a little about them, since a lot of such expressions use the idea of the functions implicitly if note explicitly. Also, see [this](Also see this).

@Argon Enjoy!

Charlie

@jayesh Are you there?

@JasperLoy The one who never answers...

user19161

@Charlie Hello honey.

Charlie

@JasperLoy Hello bee!

@JasperLoy know if Jayesh went to sleep?

@JasperLoy OOHHHHH!!!! you know I'm crazy about curves, right?the other day I saw some intersting curves in water!!! life a $\sin$ but it was a little more directed to the right...

user19161

10:39 PM

@Charlie What was it? Some animal in the water?

Charlie

@JasperLoy no, some drop was falling but there was the pressure of the water plus gravity, so the drop was falling but going to the right (??)

user19161

@Charlie Hmm, the water must have curved because of your presence.

3

Charlie

@JasperLoy interesting theory...

but unlikely

Jayesh Badwaik

10:53 PM

@JasperLoy That was moses.

user19161

@JayeshBadwaik No, that was God. Moses is only a pencil in the hands of the master.

Transcript for

$Mathematics$ Mathematics