Solving the Mathematics Calculus Problem in 'Gifted'
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- Опубликовано: 9 дек 2023
- I'm continuing my 'Solving Mathematics in the Movies' series and today, we're looking at the film 'Gifted'!🚀
❗️ERROR❗️: 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 :)
Full solutions: payhip.com/b/HDABu
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❗️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 :)
I came to comment section to comment this same thing. but nice it's already done.
I still suggest the "line integral problem" from the "Cloak and Dagger" 1946 movie.
I'll take a look!
@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?
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."
Love that part 😂
@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!
Yesss I’ve been waiting for this video!! Clear explanations as always 😊 can’t wait for the next video
These kind of videos are so cool. I even discovered the film because of it, so thank you, i really enjoyed it
Just started watching your videos and I love them.
Aaah thank you so much!!
miss, i really love mathematics, nd your videos motivates me a lot
Thanks a lot for this video!! I really like this movie and your explanation is awesome 🎉🎉
Hi Ellie! How are you? Imust say that you explain so well that even a person like me understand... Thank you
Glad to see you’re solving a problem you couldn’t when you were young
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.
❤ Perfect solution
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!!
I'm new to the channel and it seems like you produce entertaining contents.
Very nice explanation of the gaussian integral!
Good Job Professor
Great video! Thank you!
ESPERE MUCHO TIEMPO DESDE QUE VI ESE ESCENA EN LA PELICULA...
MUCHAS GRACIAS POR EL VIDEO.
SALUDOS DESDE Perú
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
I love when you smile 😘🥹
This was a cozy one.
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
Wawa you here, nice dear been waiting!
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.
If you want a video explaining the concepts, I’d be happy to create a video on it!
@@EllieSleightholm Sure!
The actor for this continues to act as a child genius in Paige from Young Sheldon
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?
She looks just like you!
Now.... please continue calculus basic to high........love from india
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 🎉
Aww thank you so much!
This equation is related to standard deviation and standard deviation is important for statistics
I love this ❤
U got a new sub sis💖😁😄😃😀
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.
Any advice for university maths exams?
needed another "-" sign in the hint, too :D
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.
The standard deviation is not defined to be negative. You are wrong
I know the original integral diverges but it is still symmetrical so shouldn't it just be 0?
Omg Ellie I didn’t know you were a child movie star!!!! Crazy!!!!!
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.
3) Show manual calculation of square root of 2 to, say, 4 decimal places. Can use one or more methods.
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.
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. 😂
Stupid question… could we substitute xt=y?? It turns out to be a bit faster maybe. No idea if that’s correct though
Hello teacher Undergraduate mathematics 1. Can you recommend a book for the course?
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!
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”?
This is the problem I’m talking about ruclips.net/video/mGe0t4xVvX4/видео.htmlsi=V9AqQKUMpww9wxil (I think the last thing on the line that starts “dim” is an 8 but his handwriting is terrible)
Yessss its on my list! ☺️
@@EllieSleightholm Awesome! Look forward to it.
The problem is very simple with the hint that suggests a change of variables. There are other methods more clever to prove the result.
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.
there should be integral limits on both :) two separate variables are needed as you are squaring the integral - does that make sense?
@@EllieSleightholmtry one from a beautiful mind
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.”
Ellie you have a passion for mathematics, you can try solve riemann hypothesis 😊😊
Try jee advanced math question from 2016 paper .
already a video on it on my channel 😁🫡
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 😢
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
Math problem about Ettore Majorana fight scene between Majorana and Fermi the name of the movie i ragazzi di via panisperna)
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 ??
Pretty simple but kind of a cool trick; cartesians to polars and integrate .... many integrals often involve a neat substitution!
❤❤❤❤❤❤
What app do u use to do maths
Good notes on my ipad :)
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..
Could you pls explain why in 4:44 these are two different integrals and we can't just square it?
Thank u
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
Thank u !!@@_mark_3814
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
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.
What do you mean by wasn't good?
@@karag4487 She had expected stronger competition from her cohort that what she experienced.
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.
This is just a standard proof of the Gaussian Distribution that is shown in pretty much any Probability course in college
Hello , were u that great at math when you were at high school?
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
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?
@@_mark_3814 find the solution of y1=2 and y2=2 same roots by method of Variation of parameters
Gaussian integral
Where do you watch the movie? 😂
Next up P vs NP😅😅
Love from india 🧡🤍💚
lol you look like what the little girl in gifted would look like if she grew up
Get it smartie pants
I'd like to see you explain the math in beautiful mind
Working on it 🚀
Your age ??
Thats fkd up
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.
Yes anyone who has taken a multivariable calculus knows this example same in America
You look like her though 😮😮😮😮
ricks math equations
No one is gifted, we are all human
not gonna lie the girl in gifted looks a bit like 10 year old Ellie
Ngl Mary looks like Ellie's illegitimate daughter.
What's sigma here
Why does she look like the little girl in the scene😅
This channel isnot for me. I am not that smart. lol
Let me know what content you’d like to see! I’m thinking of teaching some mathematics on here 😁
Why do you write math you’re not American…
because people complain when I write 'maths'😂 can't seem to win!
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.
hope the change in title helps :)