❗️NOTE❗️: At 6:41, the dx & dy equations should be: dx = (∂x/∂r)dr + (∂x/∂θ )dθ, dy = (∂y/∂r)dr + (∂y/∂θ )dθ, accidentally swapped them around in the calculations but the Jacobian remains correct :)
@mathalysisworld8 ай бұрын
I came to comment section to comment this same thing. but nice it's already done.
@ericerpelding23489 ай бұрын
I still suggest the "line integral problem" from the "Cloak and Dagger" 1946 movie.
@EllieSleightholm9 ай бұрын
I'll take a look!
@leif10758 ай бұрын
@EllieSleightholm just to clarify why is the absolute value necessary and a neatctrick..because if not the exponent is positive and the function diverges because it keeps growing right?
@ericerpelding23489 ай бұрын
Teacher: "Who wants to try three plus three?" Mary: "Three plus Three, really? What kind of school is this anyway?" Teacher: "Can you tell me what 57 multiplied by 135 is?" Mary: "Seven thousand and six hundred and ninety-five."
@EllieSleightholm9 ай бұрын
Love that part 😂
@leif10758 ай бұрын
@EllieSleightholm Why is it one of your favorite movies Ellie, if I may ask? And really hope you can respond to my other comment when you can. How can I be as gifted as this girl in real life or Ramanujan? Hope to hear from you!
@louiseefford9 ай бұрын
Yesss I’ve been waiting for this video!! Clear explanations as always 😊 can’t wait for the next video
@JorgeGuitar9 ай бұрын
These kind of videos are so cool. I even discovered the film because of it, so thank you, i really enjoyed it
@soobindoll95619 ай бұрын
Just started watching your videos and I love them.
@EllieSleightholm9 ай бұрын
Aaah thank you so much!!
@adamlopez23398 ай бұрын
at 11:38 when u did the u-sub, the "infinity" in the bound of integration should be a negative infinity, if i'm not mistaken. It doesn't affect the answer, though, since you went back to the "r" world. Great video, loved it!!
@Dviih9 ай бұрын
Glad to see you’re solving a problem you couldn’t when you were young
@tallwindowenvelope37459 ай бұрын
Very good explanation indeed! I believe you snuck in a slight inaccuracy in your calculations. When doing the u-substitution the limit for the new integral should be 0 -> MINUS infinity, but since you perform back-substitution afterwards and preserve the limits of r, the result remains correct.
@anedgedancer51478 ай бұрын
3:50 "i like that touch in the film, it was very nice." Me, just taking your word for it, "OKAY" lmao thanks for the breakdown
@muratoktem25044 ай бұрын
❤ Perfect solution
@taif15058 ай бұрын
miss, i really love mathematics, nd your videos motivates me a lot
@carlosalbertocuadros54699 ай бұрын
Good Job Professor
@mostshenanigans8 ай бұрын
I know the original integral diverges but it is still symmetrical so shouldn't it just be 0?
@lauradehart13979 ай бұрын
She looks just like you!
@pizza87259 ай бұрын
This equation is related to standard deviation and standard deviation is important for statistics
@กนกพรรณแสงแก้ว5 ай бұрын
I love when you smile 😘🥹
@AJ-et3vf6 ай бұрын
Great video! Thank you!
@orcaauragames30979 ай бұрын
Any advice for university maths exams?
@PhrontDoor5 ай бұрын
This was a cozy one.
@xayphanthourath94938 ай бұрын
To be honest I clearly have no idea what you are explaining, but i enjoy what you are teaching and as i always say to others Never Stop Learning Cause Life Never Stops Teaching
@Angel33Demon6668 ай бұрын
The actor for this continues to act as a child genius in Paige from Young Sheldon
@modok_ff9 ай бұрын
I was waiting for this, although couldn't understand much as this level of calculus is not in our syllabus. I hope I learn this in college though.
@EllieSleightholm9 ай бұрын
If you want a video explaining the concepts, I’d be happy to create a video on it!
@modok_ff9 ай бұрын
@@EllieSleightholm Sure!
@luisakehau13989 ай бұрын
That was a nice video for a sunday morning, just waking up and seeing a well explained video about gifted. I really enjoyed that movie, I'm really hoping to see it with my daughter someday hahaha 🎉
@EllieSleightholm9 ай бұрын
Aww thank you so much!
@mariaeduardamafrasartori43799 ай бұрын
Thanks a lot for this video!! I really like this movie and your explanation is awesome 🎉🎉
@mdinventions17639 ай бұрын
U got a new sub sis💖😁😄😃😀
@coshy27489 ай бұрын
I suggest you view a South Korean movie called In Your Prime (2022). You can prepare a video on some problems. Two candidates are 1) Prove you cannot find the area of a specified triangle (in the mivie) as the triangle does not exist. I used Pythaogas formula in my proof. 2) Prove Euler's Identity - relationship between e, pi, I, 1, 0.
@coshy27489 ай бұрын
3) Show manual calculation of square root of 2 to, say, 4 decimal places. Can use one or more methods.
@coshy27489 ай бұрын
Another movie is Marry Me (2022). A circle with perimeter 8*pi is inscribed in an ellipse whose width is twice its height. Find the area of the ellipse.
@coshy27489 ай бұрын
I found a video answering this question in Marry Me. He used a formula for area of an ellipse. You can show a calculation without use of a formula. 😂
@lauracracogna48149 ай бұрын
Hi Ellie! How are you? Imust say that you explain so well that even a person like me understand... Thank you
@ELMASNA1239 ай бұрын
ESPERE MUCHO TIEMPO DESDE QUE VI ESE ESCENA EN LA PELICULA... MUCHAS GRACIAS POR EL VIDEO. SALUDOS DESDE Perú
@wolfiegames15729 ай бұрын
Very nice explanation of the gaussian integral!
@ФилипФилмар21 күн бұрын
What note-taking program are you using in this video?
@mikeshlyak70709 ай бұрын
Ive never learned the matrix method or partial derivatives. So i was forced to use geometry. Going from cartisian to polar, I said the radius acts like x on the cartisian and is linear so x is related to r. No matter what theta is, the radius,r, moves from the origin and extends out linearly also in the polar world, so x=r and dx=dr. For y, in cartisian is also linear, but polar it will be curving. I used arc length s=r*theta. And take any 2 sectors on a polar graph, the radius doesnt change, but theta does. So dS=r *dtheta which is related to dy because the angle is what turns the radius on a polar graph. So, dy=dS=rdtheta. Geometrically/graphically, picture a rectangle on cartisian, its dementions would be dx*dy as it get smaller. In the polar world, i see a curved 'rectangle' in polar form. So as r2 approaches r1 at the base of the rectangle, you can see the dx=dr transformation and is independent of the angle theta. For y, or S, r1 needs theta to move to another point, so theta is changing, same reasoning for r2 to move. As s2 approaches s1, the angle and r get smaller, but the only way to rotate is due to theta, and the radius does not depend on theta at all to do this. So we can see dS=rdthetha as the 2 sectors get closer. Then apply the identity for x squared and y squared =r squares for a circle. So at the end i get r(e^-r^2)drdthetha. The inner integral goes from 0 to infinity(the smallest radius of a circle becomes a point at 0) and the outer integral from 0 to 2pi for 1 complete revolution for theta. I got the I=sqrt(pi) No clue what a jacobian is 😢
@epicchocolate18669 ай бұрын
The matrix is the Jacobian matrix which is essentially a scaling factor. What you are doing, is converting to polar coordinates to simplify, but the mathematical theorems require thag you scale the integral by |J(T)| where T is the transformation from polar coordinates to rectangular coordinates
@Sravanvlogs078 ай бұрын
Now.... please continue calculus basic to high........love from india
@wernerheisenberg38258 ай бұрын
I didn't understand how you filled in the limits after substitution, why does theta goes from 0 to 2pi and r from 0 to infinity. Also didn't get how the double integral is solved? you just wrote 2pi for integral o to 2pi d(theta) ig. but how is it just simply multiplied ?? don't we have to first solve the inner integral first and then the outer one? I guess, it doesn't change the result since r and theta are independent so it is just like multiplying a constant but am I correct about what I said about solving double integrals ??
@hlumelohlumelo42549 ай бұрын
I almost gave up on mathematics now that I saw your calculation I am inspired, I don't know if you have ever watched ramanujan movie, can please solve ramanujans' problem?
@rafazieba99823 ай бұрын
There needs to be an argument why we can merge and split those multiplications of integrals into a double integral and back. In a general case you can't do that.
@michalina15909 ай бұрын
I'm new to the channel and it seems like you produce entertaining contents.
@SaadmanSaif9 ай бұрын
The line where you expressed the integral I^2 with separate variables, you wrote one without limit. Is that correct? I actually didn't understand why two separate variables was taken in the first place.
@EllieSleightholm9 ай бұрын
there should be integral limits on both :) two separate variables are needed as you are squaring the integral - does that make sense?
@user-lu6yg3vk9z9 ай бұрын
@@EllieSleightholmtry one from a beautiful mind
@davidelarussa18859 ай бұрын
Stupid question… could we substitute xt=y?? It turns out to be a bit faster maybe. No idea if that’s correct though
@vaibhavkarche12939 ай бұрын
Try jee advanced math question from 2016 paper .
@EllieSleightholm9 ай бұрын
already a video on it on my channel 😁🫡
@ericerpelding23487 ай бұрын
Regarding this problem, solving the Gaussian Integral, Lord Kelvin wrote: “A mathematician is one to whom that is as obvious as that twice two makes four is to you.”
@seanhunter1119 ай бұрын
Great vids. Can you do the blackboard problem in “ a beautiful mind” that John Nash says “for some of you, this problem will take many months to solve, for some of you, it will take the term of your natural lives”?
@seanhunter1119 ай бұрын
This is the problem I’m talking about kzbin.info/www/bejne/o3jIYadqrbupjpYsi=V9AqQKUMpww9wxil (I think the last thing on the line that starts “dim” is an 8 but his handwriting is terrible)
@EllieSleightholm9 ай бұрын
Yessss its on my list! ☺️
@seanhunter1119 ай бұрын
@@EllieSleightholm Awesome! Look forward to it.
@hisnameisdavid50829 ай бұрын
Omg Ellie I didn’t know you were a child movie star!!!! Crazy!!!!!
@neilgerace3559 ай бұрын
The integrand has σ² in it, which should dial in a |σ| in the answer even if you don't know anything about the normal distribution.
@epicchocolate18669 ай бұрын
The standard deviation is not defined to be negative. You are wrong
@randydiffenderfer77939 ай бұрын
needed another "-" sign in the hint, too :D
@AdrienLegendre9 ай бұрын
The problem is very simple with the hint that suggests a change of variables. There are other methods more clever to prove the result.
@taresy6789pp9 ай бұрын
Ellie you have a passion for mathematics, you can try solve riemann hypothesis 😊😊
@angelamusiemangela9 ай бұрын
Buongiorno ,ma scusa alla fine ,in tutti questi anni hai scoperto , l' America di Cristoforo Colombo, andamento della caravelle ,tutti e tre i vettori ,(x+x)=; ( 2x+x)=;(3x+x);; sono indifferenziate quindi impossibili da calcolare ,ma quiiiiii! Abbiamo il genio delle bionde a quanto pare ,! Complimenti ,! Ecco il diagramma risolto dell'inizio del metodo di Cramer! Il principio dei numeri Reali nel , Piano Cartesiano. Brava Signora!
@jamesjohn25379 ай бұрын
Wawa you here, nice dear been waiting!
@yassin51839 ай бұрын
Could you pls explain why in 4:44 these are two different integrals and we can't just square it? Thank u
@_mark_38149 ай бұрын
Taking an area under a curve doesn’t change with the variable you use to represent the function as long as you integrate with respect to that variable. It is useful to change one to a y so you can do the polar substitution
@yassin51839 ай бұрын
Thank u !!@@_mark_3814
@armanavagyan18769 ай бұрын
Math problem about Ettore Majorana fight scene between Majorana and Fermi the name of the movie i ragazzi di via panisperna)
@talatbulut14739 ай бұрын
Hello teacher Undergraduate mathematics 1. Can you recommend a book for the course?
@letitiabeausoleil40259 ай бұрын
Hiya Ellie. My mom said Camb wasn't as good as the reputation made out. She did a physics PhD in the Cavendish in the 90's before heading to law school. We both see promising signs that someone righted the ship for them. You are one of those signs. You think mathematically and that should be the goal of the Tripos.
@karag44879 ай бұрын
What do you mean by wasn't good?
@letitiabeausoleil40259 ай бұрын
@@karag4487 She had expected stronger competition from her cohort that what she experienced.
@Sheikh_Nishad_Hyder19489 ай бұрын
Pliz clear by doubt Why Wronskien didn't work in same roots that is roots are real and equal ordinary differential equations with constant coefficient Method of variation of parameters
@_mark_38149 ай бұрын
The wronskian tells you if you have a fundamental set of solutions what do you mean doesn’t work? Do you mean you could not find a fundamental set?
@Sheikh_Nishad_Hyder19489 ай бұрын
@@_mark_3814 find the solution of y1=2 and y2=2 same roots by method of Variation of parameters
@mastershooter649 ай бұрын
lol you look like what the little girl in gifted would look like if she grew up
@tanusharma18389 ай бұрын
can you able to give me the exact correct reason about the "Ramanujan summation series" that is How 1+2+3+4+5+..............................+to infinity = -1/12 by the way i am from India. I think you know very well about Sir shrinivasa Ramanujan
@kunal_kumar-9 ай бұрын
I vote for fermat's last theorem that was proved by Andrew wiles.. This problem has its own history of 350 years I think it was probably a billion dollar problem.. I think you should make video on that..
@Will-Ch5 ай бұрын
I love this ❤
@RozarSmacco9 ай бұрын
No professional mathematician would ever leave out that negative sign in the exponent twice(!) in one problem. As Lord Kelvin said a mathematician is someone who can solve the Gaussian integral as easily as normies know 1+1= 2.
@Abhishektwit8 ай бұрын
Love from india 🧡🤍💚
@alecrego48798 ай бұрын
This is just a standard proof of the Gaussian Distribution that is shown in pretty much any Probability course in college
@ssaalktbi29709 ай бұрын
Hello , were u that great at math when you were at high school?
@HaroldSchranz9 ай бұрын
Pretty simple but kind of a cool trick; cartesians to polars and integrate .... many integrals often involve a neat substitution!
@宻9 ай бұрын
What app do u use to do maths
@EllieSleightholm9 ай бұрын
Good notes on my ipad :)
@EMEngi4ALL9 ай бұрын
Gaussian integral
@زينالعابدينماجدمحمد9 ай бұрын
❤❤❤❤❤❤
@hayday78999 ай бұрын
Where do you watch the movie? 😂
@andrewsmatilda999 ай бұрын
Get it smartie pants
@theencryptedpartition46339 ай бұрын
Next up P vs NP😅😅
@ILYA1991RUS_Socratus9 күн бұрын
)
@Melissa-fi1vq9 ай бұрын
I'd like to see you explain the math in beautiful mind
@EllieSleightholm9 ай бұрын
Working on it 🚀
@shivashishsharma24629 ай бұрын
Your age ??
@DyverD19318 ай бұрын
Thats fkd up
@TheSabian3218 ай бұрын
Ngl Mary looks like Ellie's illegitimate daughter.
@shubhamdas35868 ай бұрын
not gonna lie the girl in gifted looks a bit like 10 year old Ellie
@gauravsrivastava32529 ай бұрын
We have solved this kind of problem in India in first year of UG. And its not even tough for Indian mathematicians. Its actually quite easy cause it is closely related to a standard gaussian integral. If you are not going to judge me for that, I had already solved this in my mind.
@_mark_38149 ай бұрын
Yes anyone who has taken a multivariable calculus knows this example same in America
@abather118 ай бұрын
You look like her though 😮😮😮😮
@sohamadak68118 ай бұрын
What's sigma here
@marios_-nk4qg8 ай бұрын
Why does she look like the little girl in the scene😅
@danielhooper5028 ай бұрын
No one is gifted, we are all human
@razio61399 ай бұрын
ricks math equations
@farhanshaqib87469 ай бұрын
Why do you write math you’re not American…
@EllieSleightholm9 ай бұрын
because people complain when I write 'maths'😂 can't seem to win!
@hansanaik38359 ай бұрын
They say 'math' only in the US and Canada and in both these countries, people do not know that 'maths' is also the short form of mathematics.
@EllieSleightholm9 ай бұрын
hope the change in title helps :)
@fakharjafri35059 ай бұрын
This channel isnot for me. I am not that smart. lol
@EllieSleightholm9 ай бұрын
Let me know what content you’d like to see! I’m thinking of teaching some mathematics on here 😁