Integral square root dx

[@kamilbizon8317]

Apparently in math you can put together two things in seemingly random fashion and dr peyam can prove that they make sense

[@BRORIGIN]

Total clickbait. The thumbnail said sqrt(dx), but got sqrt(dt). Im pressing unsubscribe twice.

[@skyfall-t8p]

Bror Just denote time as x

[@blackpenredpen]

Unsubscribe twice = subscribe

[@insearchofpeace2151]

@@blackpenredpen Well, I really don't want to r/whoosh you as you are a great math tutor. But seriously, your comment is r/whoosh worthy.

[@AlgyCuber]

but if you unsubscribe then there’s no unsubscribe button for you to press, so it’s a pair of docks

[@blackpenredpen]

Kaigun Taisho Borsalino Kizaru What does that mean?

[@blackpenredpen]

Ok, I went through the video.... I need some coffee and then I will watch again....

[@xcalibur6482]

Iam seriously thinking of a math meme right now but i cant imagine one 😂😂.. Maybe I'll think after dinner.

[@buxeessingh2571]

"I need my Brownian motion generator to wake up each morning," seems apt. You can invent the Infinite Improbability Drive for an encore, which would win you The Galactic Prize for Extreme Cleverness.

[@MathManMcGreal]

I need a second cup... or third...

[@blackpenredpen]

@@MathManMcGreal I need expressos now...

[@shayanmoosavi9139]

I know right? 😂😂😂😂

[@nootums]

I can always rely on Dr. πm to blow my mind!

[@GeodesicBruh]

Ming wut

[@blackpenredpen]

You are in trouble now. People will keep asking you to put dx anywhere that they want. (I know I will be in trouble tmr 9am too... hahahhaha)

[@neilgerace355]

You mean ... you can't?

[@wojtekburzynski654]

Integral of 1/dx

[@allaincumming6313]

@@wojtekburzynski654 That's beyond ω, ftw

[@mauriciocaviedes6520]

@@wojtekburzynski654 Please, if someone knows!

[@unfetteredparacosmian]

This integral: *exists* Every single calculus teacher: "Wait, that's illegal"

[@МаксимЮрченков-ы5ь]

Can you integrate 1/dx?

[@Sid-ix5qr]

_Math Teacher_ : Nope, that Integral isn't possible. _Dr. Peyam_ : Hold my beer.🍻

[@blackpenredpen]

In Dr. P, we believe!

[@magnetonerd4553]

Stochastics is a fascinating area of mathematics. I have been learning pure Probability Theory in order to try and understand these processes. Your video has really helped to clear up some of my confusion and misconceptions that I had. Thank you!

[@robertmines5577]

Dr. Peyam, I work in systems biology, and I try to simulate gene circuits in the presence of noise. Most of the time, people in my field are still using the Gillespie-Doob Stochastic Simulation Algorithm (for exact stochastic simulation based on exponential races). Obviously, in cases with multiple concentration scales or time scales, using stochastic integration via Tau-Leaping or Chemical Langevin (Brownian Motion) methods would be a significantly more efficient solution for these problems (since you can specify time steps and avoid oversampling unimportant but fast reaction channels). However, the vast majority of people outside of pure math really cannot handle a rigorous course in stochastic calculus (myself included). I really appreciate that you are making this video series and helping non-specialists to learn this information. This is so important for so many fields of physics, chemistry, biology, and engineering, but most of us would not get this exposure without you.

[@drpeyam]

Thank you! 😄

[@ninakarim9674]

I think the next video is how to find integral of ln(dt)

[@acorn1014]

I think it would have to be the integral of ln(1+dx) or something like that; because, the integrand has to tend to zero, as dx tends to zero.

[@kaanetsu1623]

@@acorn1014 yeah u r right

[@warrickdawes7900]

@2:00 No I'm not joking, and stop calling me "Shirley"!

[@drpeyam]

Hahahaha

[@livedandletdie]

Shirley the best comment you've made...

[@miguelalvarez3740]

Amazing Dr. P! I´m allways have been interested in stochastic processes so I will try to figure out how to add ths new knowledge to my model. Thank you again.

[@mrbenwong86]

I suppose you can sqrt(∫) dx as well.

[@andi_tafel]

This is also clickbait: You didn't solve the integral of sqrt(dx). You solved the integral of sqrt(dt).

[@Joe.O.]

I'm no maths genius and I struggle with basic problems. But your enthusiasm and teaching style is amazing. I sat watching this with no idea what you are talking about but enjoying every moment of your presentation.

[@giannismaris13]

i like your Calculus , but i would like to see some topology or even metric spaces from you!😉

[@KarlChamoun]

try dx^dx

[@tayloraf5108]

Is this throwing shade or just joke? Idek

[@AdityaPrasad007]

Somehow, this professor fits the image of a really nerdy, smart guy..... I love the honest, effusing passion he exudes.

[@AdityaPrasad007]

For a second there I was so happy to have been hearted 💓 but... then I saw how generous Dr is with his love, making me realise how humans sadly only tend to value that which is scarce.

[@pierreabbat6157]

This works only if you put ± before √. Without ±, the integral diverges to infinity as dx (or dt) goes to zero.

[@Rundas69420]

Next logical step after that would probably be integrating f(dx), where f is riemann-integrable xD. But that looks sorta impossible to me. Although it's nice to see the differentials at some other place than the end of "regular" integrals or differential-quotients :D

[@mikewagner2299]

So does that mean if I take your 2nd statement from 3:00 and 11:23 we get: Int(√dt,a->b)~N(0, b-a) =N(0,b) - N(0,a) Whereby FTC implies Int(√dt) ~ N(0,t) [+C = 0 by I.C.] Hardly rigorous but Int(√dt) ~ N(0,t) Does look pretty so it must be true

[@drpeyam]

I don’t think N(0,b) - N(0,a) = N(0,b-a), but I think your other statement is true

[@PeterBarnes2]

Half-integral. Inverse operation to the half-derivative. G(x) = int( sqrt(dx)) = (J^1/2)[1] find G(x) such that (D^1/2)[G(x)] = 1 Depending on how you want to go about it, you might integrate both sides: (J^1/2)[G(x)] = x G(x) = (D^1/2)[x] Which you did a video on: int( sqrt(dx)) = (J^1/2)[1] = (D^1/2)[x] = (2/sqrt(π)) * sqrt(x) Get with it πm!

[@remlatzargonix1329]

Awesome video!....I am interested in stochastic calculus, so if you did more videos like this that would be great! Cheers!

[@dr.rahulgupta7573]

Excellent presentation of the topics in a beautiful manner.Very good .DrRahul Rohtak Haryana India

[@shmarfle47]

Me: has completed multi variable calculus Also me: whaaaaa...???

[@yousteveaaaa]

Would stochastic approach give the correct answer to integral dx instead of integral sqrt(dx) ?

[@bogdancorobean9270]

Writes in title "integral of sqrt(dx)". Proceeds to make a video about integrating sqrt(dt) :x

[@drpeyam]

It’s the same thing...

[@joao_pedro_c]

Watch flammable maths' video on dummy variables and you'll see it's the same thing

[@bogdancorobean9270]

That's exactly what a mathematician might say. Us physicists (otherwise known for our mathematical rigour :) ) know that dx is for space and dt is for time.

[@joao_pedro_c]

@@bogdancorobean9270 I see your point, but I disagree, it's just letters... Just like u can use dt for time nothing stops me to use dJ, for example.

[@bogdancorobean9270]

Leonard Susskind tells this joke in one of his lectures: "You always use epsilon to denote something small. If you want to confuse a mathematician, have epsilon be something big." This was sort of my point, only for physicists. Of course I know it's a dummy variable, didn't mean to sound like a troll :)

[@emmepombar3328]

Is there any generalized form, like the integral of g(dx), where g is any (or a greater subset) function? Or even the integral of f(x)*g(dx)?

[@chasemarangu]

alright I think that u might not be entirely correct; in order to find teh integral we take a rectange sum ofareas of rectangles of side length f(x) and side length dx and so multiply f(x)*dx and we do this for the limit as dx → 0 and also approaches every possible value of f(x) so really its a matter of dx sorta equals 0 and so f(dx)*(x/dx) so its like ∫ (0, x) [ f(dx) ] = x * f(dx)/dx so which diverges faster or does it converge, f(x) or dx? usually the answer will be 0, ∞, or -∞ and in this case its 0 i think the answwers 0

[@drpeyam]

I’m correct; the answer is Brownian motion 😊 Probability is weird

[@chasemarangu]

@@drpeyam Sure. I only dont understand one thing: how come we cant just do the limit as dx → 0 of sum from i=0 to x/dx of ( 1⋅√dx ) it seems to work as an integral calculator for x² and eˣ instead of √dx so i dont see why this wouldnt be correct for √dx as well

[@parsecgilly1495]

I, the integral of sqrt(dx) would calculate it this way: first we easily calculate the differential of order k of x ^n : d (x^n) = n x ^(n-1) dx (first order) d2 (x^n) = n (n-1) x^(n-2) dx (second order) dk (x^n) = n(n-1)(n-2)...(n-k+1) x^(n-k) dx = (n!/(n-k+1)!) x^(n-k) dx (k-order) so, at this point I put: n=1 and k=1/2, so we have: sqrt(dx)=1/((3/2)!) * x^(-1/2) dx, so, the integral of sqrt(dx) is: Integral (sqrt(dx)) = Integral (1/((3/2)!) * x^(-1/2) dx); the second member is easy to calculate, in fact we get: Integral (sqrt(dx)) = 2 * root (x) / ((3/2)!) + Cost ; finally, using the gamma function I get: Integral (sqrt(dx)) = (8/3) * root (x/pi) + Cost if I did not make transcription errors, this should be the exact result

[@drpeyam]

That’s almost the exact same thing as my half derivative video

[@alfiealfie35]

Wouldn't this technically be integral of +/-sqrt(dx) (because either way it would square to dx)? I guess that kinda explains the fact that it is finite, since the erratic behaviour is both increasing and decreasing (and has a mean of 0).

[@loszdog2988]

Yeah. He left this out, although he did heart another comment mentioning it.

[@curtiswfranks]

Around 17:00, what if we let λ vary between partitions? Like, draw from the interval with uniform distribution or something. I am not even sure that this is well-defined, but I want to knock out this dependence.

[@drpeyam]

In that case the limit might not exist. It’s because you choose the same lambda every time that the limit turns out to exist

[@curtiswfranks]

@@drpeyam Wild! This is really interesting. I cannot say that I understand (I readily admit), but it is fascinating just to know that it exists for now. This requires further investigation!

[@curtiswfranks]

What does the little circle mean? Why is that included?

[@drpeyam]

Just to distinguish it from the Itô integral!

[@daaa2299]

integral from a to b sqrt(dx) = integral from a to b 1/sqrt(dx) * dx 1/sqrt(dx) = infinity integral form a to b infinity * dx = infinity right?

[@blackpenredpen]

Damn!!!

[@danielaorozco9995]

I love your enthusiasm for math ❤️ it’s very inspiring

[@zajoliroA]

If you think about the integral analytically, aren’t you summing the square roots of a bunch of tiny changes? How does this result in something that may be different every time?

[@non-inertialobserver946]

What happened with Flammable Maths?

[@drpeyam]

I dunno! 😮

[@himanshumallick2269]

He's planning an endgame version of integral of cos(x)

[@wowZhenek]

Awesome video. Especially the ending, where you explained the relationship to Lebesgue integrals. Also, is there any other examples for different lambdas or only 2 values are used? Coz I also only heard of Stratonovich integral besides Ito's one.

[@drpeyam]

I’m not sure about other examples, but the Ito and Stratonovich are the classical ones! I can also imagine one where lambda = 1, where you are betting on the future, but not sure how interesting it is

[@kingthanatos6093]

Ok who else thinks that Dr Peyam is worthy of wielding Mjolnir? I sure do.

[@Maniclout]

Sooo would this be applied in something like stock predictions for example? It looks and probably is very complicated.

[@drpeyam]

Using this integral, you get what are called stochastic differential equations, and you can use solutions of those to model stock behavior. Look up the Black-Scholes equation for example.

[@nicholasleclerc1583]

12:20 What ? I don't understand... ???

[@skeletonrowdie1768]

that one dislike could not differentiate between the buttons :O

[@drpeyam]

Probably acted like Brownian Motion 😉

[@blackpenredpen]

Aka, being 😵

[@eneapane5831]

I think that one dislike was FlammableMaths😂😂

[@JaGWiREE]

Some love for us stochasticians!!! Brown would be proud.

[@SellusionStar]

Is this black pen red pen over there?

[@blackpenredpen]

Over where?

[@SellusionStar]

@@blackpenredpen in the whiteboard shelf :)

[@blackpenredpen]

@@SellusionStar I wasn't there that day.

[@SellusionStar]

@@blackpenredpen Don't tell me that! I can see the pens right there with my own eyes! 😁😉

[@blackpenredpen]

SellusionStar hahaha

[@That_One_Guy...]

Is the brownian motion you're referring is the brownian motion from biology ??

[@drpeyam]

Yep

[@omgopet]

I'm so proud of my intuition, saw sqrt(dt) in the thumbnail and though to myself "that's just dW". Edit: you are doing the part around 14:00 backwards, you must first define the type of integral (i.e. the value of your lambda). Otherwise, the integral doesn't mean anything. Ito wrote a whole paper chastising mathematicians for this, he argued that dx=f(t)dW is a "meaningless string of characters" unless the interpretation is clearly defined.

[@paulkohl9267]

Non-stochastic version?

[@yeahyeah54]

I studied Brownian motion in university in a mathematical way, i don't understand how you can handle all these different things, i think you are a geniuous

[@drpeyam]

❤️

[@geralln]

Well, since you can put the dx anywhere. What about e^(dx)?

[@josuepimentel6321]

How may I upload spanish subtitles to this video?

[@drpeyam]

That’s a great idea! I’ve just enabled this video for subtitles, let me know if this works

[@josuepimentel6321]

@@drpeyam Thanks! I'll start to write the subtitles!

[@vladimirkuznetsov2058]

What about \int (dx) ^ 2?

[@i_am_anxious02]

If the random variable can be anything, does that mean it can be any constant or anything in terms of x

[@drpeyam]

It could be constant, and any function of “randomness” (whatever that means) to the real numbers. Think for example the gain/loss you get when you roll a die

[@shayanmoosavi9139]

WAIT WHAT? There's such a thing? Well,... There goes my sanity. I miss him. I'm so glad I didn't choose pure mathematics and studying physics instead😂😂😂😂 You gained a sub man :) I'm also subscribed to your friend blackpenredpen. You two are the best.

[@jayamitra4656]

What books on number theory would you recommend after doin burton? Not too advanced please😂

[@drpeyam]

Niven Zuckermann Montgomery is pretty good!

[@jayamitra4656]

@@drpeyam Thanks!

[@mateszabo5487]

Is this the same place where make Blakckpenredpen his videos?

[@drpeyam]

Different universities

[@roygalaasen]

Dr Peyam oh cool! You seem to work so close together that I just assumed that you were working/studying at the same university.

[@sofianeafra7023]

Dr.πm the happiest person on the earth 😂😂 hello please How to solve 5 degre équations ? 😭😭

[@helloitsme7553]

Most of the time you will have to approximate the values. But if you want them exact, sometimes the following works: check if the factors of the constant term are solutions. If so, you know that (x-h) with h the solution is a factor. Then through long division you can get a simpler equation. But not always are the factors of the constant term solutions so this doesn't always work unfortunately. Ask me if you want ways to approximate

[@benjaminbrady2385]

All solutions to any polynomial (including fifth degree) have solutions that are a factor of the constant term divided by a factor of the coefficient of highest degree (x^5 in your case). If there is no constant term, then 0 is a solution and you can divide by x the whole way across to get a polynomial of one degree less. Any other solution is irrational and must either be approximated or factored out through some other algorithm

[@helloitsme7553]

@@benjaminbrady2385 not necessarily every polynomial has these terms that are a factor of the constant term divided by a factor of the leading coefficient. Example : x^2-2=0. Has two solutions: x=√2 and x=-√2. I don't think those are factors eh

[@benjaminbrady2385]

@@helloitsme7553 Yes, anything that is not a ratio of factors is an irrational solution and must be approximated or gotten through some algorithm, if applicable

[@helloitsme7553]

@@benjaminbrady2385 you say all polynomials have these rational solutions but not all of them

[@utnis]

Please may we have more rigour? I don't know what sqrt(dx) means. I am very uncomfortable considering dx as an abstract infinitesimal. I much rather prefer considering dy/dx as the best possible linear approximation for the slope at a point, a geometric intuition. This doesn't feel like calculus. I don't see how I can construct convergent sums or how limits can be applied when the parts of the integral expressions here are stochastic.

[@drpeyam]

It’s completely rigorous! Check out the videos in the description to see proofs of all the facts

[@utnis]

@@drpeyamit is rigourous assuming the sqrt(dx) video is true.

[@Handelsbilanzdefizit]

find a recursive integral a_n+1(x) = integral_[nx,0] a_n(x) dx So that limes n-->infinity a_n+1/a_n = goldenRatio for all 'x' I found it, printed it, framed it and hang it on the entrance of my house. Just to impress visitors :-)

[@ruffifuffler8711]

A case where the symbols generate the idea, which then tries to validate the condensed thought expressed tightly by the symbols, without leaving us in Hairy Wau.

[@dectorey7233]

In what class would you normally see this? Or is this a current topic of research?

[@drpeyam]

You see this in advanced probability or stochastic calculus classes

[@AndDiracisHisProphet]

Or in Statistical Mechanics

[@GabrielPohl]

Is it possible to generalize integral of f(dx)?

[@drpeyam]

I’m thinking about it, nothing obvious comes to mind as of now!

[@GabrielPohl]

@@drpeyam maybe its solvable but not analyticly

[@umbraemilitos]

Time to discuss the fractional calculus, and the calculus of complex order.

[@Bulbulim94]

can u integral 1\dx ? had it in Physics 2 course

[@46pi26]

What kind of godforsaken physics needs this absurdity

[@Bulbulim94]

@@46pi26 i think when we calculated the total resistance of circuit

[@xuhanzhen8126]

Had my pen and papers out and was gonna begin my day enjoying Dr.Peyam's math 5 min later Threw my pen :/

[@johannesh7610]

This is so weird, but fascinating

[@snbeast9545]

Can you integrate dt^dt?

[@drpeyam]

Thinking about it :)

[@balajidodda7701]

I did it assuming Riemann sum and got it as infinity. I didn't understand how you related this to stochastic processes.

[@drpeyam]

That’s the point, it’s not a Riemann sum, it would diverge, that’s why we need this def

[@peterchan6082]

But then after all what exactly is ∫√dx ? I couldn't locate the result at all.

[@drpeyam]

Basically W(b) - W(a), where W is Brownian motion

[@richardaversa7128]

Did we do ln(dx) yet?

[@anonymaus8191]

Exercise for the reader.

[@blackpenredpen]

I want sin(dx)

[@saitaro]

Honestly I can't understand anything about the stochastic integral. How to calculate it? What does it even mean? Can't get my head around it. Hope MIT's edX MOOC on Probability will help me. Or I'm just stupid.

[@mathijs1987j]

I don't understand. Why can you not interpret this as a Stieltjes integral and use Int f(x) d(g(x))=Int f(x) g'(x)dx to get that this integral is Int 1/(2Sqrt(x))dx? (Omitting integration limits for clarity of notation.)

[@drpeyam]

The Stieltjes integral would be d(sqrt dx), but here we mean sqrt(dx), those are two different things

[@mathijs1987j]

@@drpeyam Thanks! So what kind of integral is this one (the sqrt(dx) one)? What do I google to learn more?

[@drpeyam]

I have 3 videos on it! Other than that, it’s called a Stochastic Integral

[@dheerajlalwani4486]

blackpenredpen @bprp @blackpenredpen How about interegrating this 100 times?

[@drpeyam]

Hahaha

[@blackpenredpen]

Hmmm...

[@beezball38]

what the hell did I just watch. I love it

[@neilgerace355]

17:16 "one of the ???? of Riemann integration" sorry I couldn't understand that word there. Also I don't know what "in L^2" means

[@drpeyam]

Chef-d’œuvres of Riemann integration

[@drpeyam]

f is in L^2 if the integral of the square of f is finite

[@MrRyanroberson1]

So... If i remember the definition of an integral that everyone every time tells me is wrong but also gives the exact same answer: Int from 0 to x of f(x)*dx = Lim as h goes to 0 of sum from n=0 to x/h of f(n) * h, where h is basically dx. So instead, it's sqrt(h). Since the function is no longer dependent on x in the inside, x/h = a new x which goes to infinity for all positive x. We get the sum from 0 to x->infinity of sqrt(n), which diverges.

[@crazye7132]

Duuude, watching you drunk is the best thing imaginable. It all make senseeee haha

[@aamirraza2184]

You lzx

[@krishanchandrasahu7338]

Absolutely brilliant sir ji

[@fluffymassacre2918]

I am just nodding my head at this point.

[@aintaintaword666]

So what was the answer again?..

[@drpeyam]

W(b) - W(a)

[@damntoochill]

Just love your energy

[@dgrandlapinblanc]

Amazing and crazy... Thank you very much.

[@IFearlessINinja]

So is this just a rigorous way of saying: "Integral sqrt(dx) = depends. Without any other information, the result cannot be pinpointed, but we can use an infinitely vague function to capture the result." Is that inaccurate? It seems to me that any function I can think of, of dt can be integrated into W(a)-W(b), which ruins the whole point of integration producing unique results for unique functions. Is this a predictable and useless result, or am I just misunderstanding the premise?

[@drpeyam]

Can you give me an example of such function? I can only think of dW

[@xcalibur6482]

Woooooow!!

[@abaundwal]

Th... this is madness.

[@okaymckay]

This-is-Dr.Peyam-arta!!!

[@Uni-Coder]

It is about statistics, probability theory and Markov chains, I'm sure

[@Estoyentumente]

d is a constant, so Int. [sqrt (dx)] = 1) (2/3)sqrt(d)*x^(3/2), if you integrate in dx 2) sqrt(dx)*y, if you integrate in dy, where y is another variable Fé de errata (Edited): And if d is the variable, so 3) (2/3)*sqrt(x)*d^(3/2) if you integrate in Dexter's sister :v

[@hassansameh8960]

So... What's the answer?

[@drpeyam]

W(b) - W(a), where W is Brownian motion

[@ИльяФедоров-м6б]

1/dx pls

[@drpeyam]

I’ll think about it 😊

[@ninakarim9674]

Dr. Peyam I love you Please I want more and more videos about series conv n div

[@JorgetePanete]

can you do the integral of √(f'(x)+1)dx? used for the lengths of curves/lines from a to b

[@SimchaWaldman]

Equivalent to: Is a cucumber longer or greener? Answer: Greener! (I leave it to you to find the proof I found.)

[@blackpenredpen]

יהודה שמחה ולדמן did you send me that too? I don’t know the answe.

[@SimchaWaldman]

@@blackpenredpen Proof: The cucumber has of course a finite length L from edge to edge. But both its surface area and volume contain an infinite amount of "green lengths" - On its surface area: GL > L. In its volume: GL ≤ L.

[@jorgeeduardopereztasso6134]

omg this episode brought me so many memories of my Calculus 2 course in the first year of college

[@TheAzwxecrv]

What next, integrating some function of dx? (!!! ...) Soon high school calculus teachers all over the world r going to organize a conference to condemn Dr. Pym!

[@mehdisi9194]

If your videos continue the same way we will see probably the integral bessel function of dx in the future.😊

[@drpeyam]

Hahaha

[@romygomezjr]

Yeah, I think im getting high watching this haha great work Dr. P

[@savivirginia4501]

Your channel is superb man, subbed!!😊

[@drpeyam]

Thank you!!!

[@andreimiga8101]

Ok, I suck at maths. This video is a very rigurous proof of that.

[@mandanna5127]

you are crazy dude