The Heat Equation + Special Announcement! | Infinite Series
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- เผยแพร่เมื่อ 20 ก.ย. 2024
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What is the heat equation? And find out who the two new hosts of Infinite Series are!
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Previous Episode
Hilbert's 15th Problem: Schubert Calculus | Infinite Series
• Hilbert's 15th Problem...
Imagine a giant -- endless, infinite -- sheet of metal. For mathematical convenience, let’s overlay a grid. Now, imagine you light a very tiny and very powerful match directly underneath the origin, the point (0,0). This super special match instantaneously creates infinite heat at the origin, and zero heat everywhere else. Immediately remove the match and watch the heat diffuse along the surface, radiating out from the origin.
Links to Resources:
Distribution of Heat Graph
• 2D Heat Equation Anima...
Normal Distribution Graph
www.statisticsh...
3D Plot Heat Graph
www.mathworks....
Written and Hosted by Kelsey Houston-Edwards
Produced by Rusty Ward
Graphics by Ray Lux
Assistant Editing and Sound Design by Mike Petrow
Made by Kornhaber Brown (www.kornhaberbrown.com)
Thanks to Matthew O'Connor and Yana Chernobilsky who are supporting us on Patreon at the Identity level!
And thanks to Nicholas Rose and Mauricio Pacheco who are supporting us at the Lemma level!
"Before I say goodbye to you all"
*_Never says goodbye_*
What Inferno Cop said plus why would you care about the adoration of other people? That's sad
never gonna say goodbye
never gonna tell a lie
and hurt you
a rickroll
Thank you all for making this such an amazing experience! Y'all are awesome!
Send me all your fun math things (especially if they're about the heat equation) on Twitter at @kelseyahe. I'm excited to join you all in the comment section here, and see what wild and beautiful mathematics Tai and Gabe are going to show us. -- Kelsey
Hi Gabe! Glad to see you back! Your fans missed you.
Nooooooooooooo! You will be sorely missed.
PBS Infinite Series thaks for all your effort and time !
Goog luck and make great things happen!
What is your dissertation about specifically?
Gabe!
Glad to see you too back again!
yeah. love that dude.
I always wonder what happened to him after space time.
I thought he was the Jon Stewart of the physics world.
He's back!
I will miss you . You were an AMAZING host!
Thanks, Kelsey! Best of luck on your dissertation. I hope to eventually see videos from Dr. Houston-Edwards!
The Heat Equation has many applications outside thermodynamics. In electronics, for example, the charge distribution on a sheet of graphite. I'd also like to hear more about the equivalent discrete version, for example, the voltage applied to a grid of resistors.
Welcome back Gabe, and hello Tai-Danae! Can't wait to see what you share with us!
Thanks BobC! Since the beginning, you've been so involved in the channel's community. I've really appreciated your thoughtful comments. -- Kelsey
Good luck with the research :-)
Sad to see kelsey go, but gabe's good i liked him on spacetime
Me 2
I didn't though, matt is much better. kelsey is coool, but sad she is gone.
Yeah - he said he was going to the Nation Science Foundation, I thought. He made PBS SpaceTime what it is - got right to the heart of the matter quickly ... not an hour-long hype-filled documentary. Matt is great, but more fluff than Gabe. Kelsey never told us about her tattoo, did she?
I don't hate Matt but his presentations are boring IMO, Gabe's episodes back in Space Time are much more exciting.
GABE!! Man I missed you. It is crazy how the first PBS video I watched was your last. I'm so glad you are back.
Words cannot describe my happiness when I saw Gabe! Although I'm a mathematician, PBS Space Time is my favorite show of all time ^^
@Sam Knob Get your ears cleaned out.
Sam Knob TH-cam has the speed setting
Sam Knob i like how he speaks fast. Makes me wanna rewatch and rethink about the stuff he talked. And when i understands it, it's very satisfying.
Sam Knob everyone's preference is different, no one is blaming you for not liking Gabe...I just stated why I like Gabe more than Matt...because he makes things more interesting to watch...for me anyways.
Best of luck with your dissertation.
NOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
I'm gonna have to wait a day or two to watch this I'm genuinely sad.
OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
you sir just won the internet
you don't know what you have till it is gone
how did he win the Nobel prize
You'll be missed. Good luck with your work!
Thank you for your wonderful work on Infinite Series, Kelsey! Your personable comment sections at the end of each video in particular will be missed. You've made this show feel like an intimate get-together where we share the wonderful world of mathematics with each other. I wish you the best with your dissertation!
It was especially nice coming in here as someone who isn't a mathematician but who loves and appreciates mathematics. Her explanations would make things intuitive in a way that I could get and that I could get even more out of once I re-watched them after having learned more.
This will be.... Hard. We won't forget you, ever. Hope to hear from you soon.
Good luck, I wish you the best! We'll miss you!
I hope the new hosts watch most or all of the old episodes, to see how to do things right. For me I found this series to be a perfect balance of starting with the basics but not dumbing things down. I felt neither confused nor felt like my time was wasted
I agree, who knows what we'll do without her.
Thank you for all of the amazing videos!
Congratulations on your future! Your work really helped to launch the show.
Kelsey, it was so nice meeting you at the Joint Mathematics Meeting in Atlanta this past January. I'm very impressed (and grateful) that you managed to juggle being a PhD student and working on this outstanding youtube channel for so long! I totally understand your need to really focus now and finish your research. I do hope you return to making youtube educational content, as you have a real talent for it. Best of luck with the dissertation!
Regarding the new hosts, I'm excited that we'll have a mathematician and a physicist involved on this channel, and look forward to seeing where things go from here. I'm hoping at least one of you are familiar with Geometric Algebra (GA) and its associated multivector calculus (a.k.a. Clifford analysis), and would perhaps consider making an episode on it. GA is some truly beautiful mathematics with a fascinating history. If you're interested, you can check out the GA crash course I made on my channel.
We'll miss you! Great run!
Ok, you are, in my opinion, the best host in all of the PBS channels. The whole video, I was sad and remembering how I was sad when the same thing happened at PBS SpaceTime. Then you introduced Gabe. :)
I'm still very sad that I can't see you anymore, but at least I can watch other video's hosted by Gabe.
I'm gonna go cry now.
Good luck with your dissertation! Thank you soo much for starting this channel! Glad to see Gabe back!!! Can't wait for the new episodes!!!
That video came right in time for me! I'm currently studing Fourier series as a solution to the heat equation! Nice explanation!
Thank you very much for hosting this show, I hope that all go well with your dissertation and that maybe you could come back in the future! Live long and prosper!
I hate when mathematicians use delta instead of nabla squared, you don't distinguish the laplacian from the diference that way :c
I was a bit confused looking at it initially as a non-mathematician and non-physicist. I was like "where's the limit notation. Don't you need it on the left to make it work?" One of those things where it'd be nice if things were standardized across fields, I guess.
Mathematicians wouldn't use a large delta to denote a difference though, at least not in the same context where we would be talking about laplacians. A little delta, a d or even a more explicit notation of the difference (eg. |x_1 - x_2| ) would be more applicable.
In physics, the lowercase delta is an infinitesimal change, whereas a capitol delta is a finite difference. I.e. the lowercase is the limit of the uppercase as it goes to 0 [units].
In Riemannian geometry, nabla squared is actually something different from the Laplacian; technically, nabla squared is even misleading in the flat context of Rn since you are really taking the divergence of the gradient, not applying the gradient twice. So mathematicians generally take nabla squared to mean taking the gradient twice, which gives you the Hessian. We use delta to represent the trace of the Hessian, i.e. the Laplacian. I agree that the delta notation is unfortunate (it's far overused in different contexts, and in fact in spin geometry gets kind of annoying), but nabla squared is not really a better option. Then again, I like the delta more than the giant box used for the d'Alembertian operator in physics.
I think most mathematicians hate the nabla^2 notation because it is misleading as to how the Laplacian is constructed. The capital Delta symbol though hints at its function, which as Kelsey explained, is to compare the value at a point with those surrounding it on average, i.e. a change. The mathematicians I know prefer to write the Laplacian in its expanded form which is div(grad(...)) which better identifies its purpose and construction.
I'm a highschooler who was looking for this video for a project requiring that an object stay at a constant temperature. Sometimes doing research on your own is so much more fun than learning from others!
Calculus would been better to explain heat equation
Good luck to your research
You have been a wonderful host
Good luck with your dissertation, and good luck to the new hosts. So glad this series is continuing on :)
We hope u come back someday..
Good luck with your dissertation!!!
I have a PhD in Physics and I LOVE the way you explain this equation. With this reasoning it is easy to see why a solution of the heat equation can not oscillate in time. In this graph where the solution shows a "valley" and a "hill", at the moment that the values in the valley and the hill reach the equilibrium value, the solution stops evolving. Best luck with your dissertation! :-)
Good luck on your dissertation! Writting the Dissertation is the moment when all the ideas come together and you find that by end the end of writting process you'll be more knowledgeable on your topic than at the beginning. Just writting organize ideas in a weird way.
Gabe's back? Whoa. He should totally do cameos on Space Time. For old times' sake. :)
Sorry to see you go. You were a great host! Thanks for sharing knowledge so well!
Thank you Kelsey! GOOD SHOW ! I will review all episodes.
Best of luck on your dissertation!
Thanks for taking the time to make these videos, they've been excellent!
PBS Infinite SpaceTime Series.
We will miss you, thanks for being an awesome host! :( I look forward to meeting the new people, it will be fun!
Please don't go! We love you.
And suddenly Infinite Series cemented itself as my favourite ongoing PBS series.
Ok. I will miss you, I almost cry until I hear that it was about your dissertation. You will do great. You should have taken a sabbatical ;) Jokes aside, thanks for your dedication.
Thanks for making the show, sorry we won't be seeing you anymore. Good luck and God speed.
I hate to see you go but the dissertation, comes first. Go forth and Prove!
Thank you Kelsey.. be proud that you've been a wonderful teacher here! Will catch you here sometime later!
Yo Gabe is back. I love you Gabe. Now comes some beautiful stuff.
Good luck with your dissertation, Kelsey! I really enjoyed you as the host of Infinite Series, and I wish you all the best :)
Hopefully, you will come back Kelsey and make beautiful videos together with Tai and Gabe.
Dang, I wish you made this video 5 years ago when Fourier Analysis, and specifically this Heat Equation, were kicking my butt. Thanks for the explanation!
"Special Announcement!"
"Must be good! :D"
D:
That set-both-sides-of-a-partial-differential-equation-equal-to-a-constant-to-figure-out-what-the-exactly-heck-is-going-on trick was really helpful, I'm going to apply that in my studies from now on!
He's baaack
I'm going to miss you but that was a great surprise
Sorry to see you go. As a complete math neophyte, I enjoyed watching your videos to see how much I could comprehend. I found sometimes I could get between 50-75% just based on your careful and thoughtful explanations. Thanks for opening my mind to the world of higher math!
SAD! We love you
Gabe is back! Cool, good to see him again. Good luck with your dissertation Kelsey.
Aaah Gabe is back!
Ahhhhh I'm really sad you're leaving, but I'm still excited to see what the new hosts have to bring. Best of luck on your dissertation!
Please come back after your dissertation
Thanks for starting this awesome PBS series and the best wishes for your next project, from us all :)
My screen thanks you for not burning it
Sad to be gone tho
Will miss you dearly, thanks for everything and great luck on your dissertation.
I'm glad to see an old friendly face to fill the show.
I really enjoyed your videos. I knew that even if the title of the video didn't immediately interest me it would still be a good idea to watch it. Going to miss having you as host.
It's nice to see Gabe again, I like the physics videos he did.
I also got a good feeling about the new host :)
I think we were left in good hands.
thanks for getting me into 'Infinite Series', I hope you come back after the dissertation.
The heat equation is something I've done a lot of research on myself as well, mostly for numerical approximations in the realm of game design. It especially becomes interesting once you take into account other variables, but the idealised model is very interesting to start with, and surprisingly practical. However, one should take into account that typically we're dealing with a 4-dimensional problem, as heat diffuses within space. Additionally, there's numerical solutions involving particles, rather than (fixed) grids; Langrangian vs. Eulerian. That being said, do you personally work (a lot) with numerical solutions or are you only interested in non-numerical ones? Anyway, good luck with your dissertation.
I am a geophysicist and really appreciate the breakdown in mathematics. I can only imagine how challenging your work in heat diffusion is. Screw good, luck YOU are smart enough to make very important breakthroughs. You got this.
Yes, more physics in math! I cant wait to hear some cool theoretical physics stuff :D
I'm Glad, Gabe's back !!
Would love to see him interact with Matt on Collab videos.
GABE IS BACK WOOOO
Sad to see kelsey go tho.
Happy to see Gabe is back, loved his fast talking videos.Makes you always wonder how many lines he just had before the show.
We'll miss you
Thank you for your time, research, and writing :)
Will miss your videos :'(
Good luck to you and kick butt on your research!
Oh shit it's Gabe
Thank you Kelsey, you were an excellent host. I loved Gabe on Spacetime. Welcome new hosts.
heat equation???!!! *University "PTSD" intensifies*
PThd
Thanks for the video and good luck with your research. Just a comment about the graphic around 7:10 meant to illustrate the slope of a line (e.g., to show what dy/dt < 0 means). The graphic seems to show 3 different (unlabelled) functions, one with positive slope, one with slope=0 and one with negative slope. The audio says the slope at x=1/4 is positive, at x=1/2 is zero and 3/4 is negative. e.g., there is a disconnect between the audio, which describes a changing function, and the video, which shows 3 different functions (e.g., when the audio is talking about the point x=1/2, the video highlights the point x=1/2 on all 3 graphs, which makes no sense). Anyhow, just pointing this out as someone could go back and fix the graphic to make this video more coherent. Thanks.
NOOOOOOOOOO!
Translation: You have been fantastic; you will be missed here.
Good luck on doing whatever you are going to do. We all, Infinite Series fans, will miss you.
Gabe's back, HA!
He's back! :D
Good luck with your dissertation, hope you can join us again when it's finished. Would've liked an additional episode to transition with the new hosts, but I can think of several reasons why that might have been difficult.
Welcome back Gabe!
This channel should be proud to have one of the few clean and constructive comments sections on youtube.
GABE LIVES ON
Good luck with your dissertation!
And welcome, new hosts!
GABE?!
GAAABBBEEEEEE WE MISSED YOU WELCOME BACK DUDE!!!!!
Can't wait to see you in the cool maths department!
You're leaving big shoes to fill.
I'm not going to lie, Gabe coming back softens the blow of Kelsey leaving a bit. I got into SpaceTime after he left, so it's great to see new content from him! Good luck with your dissertation Kelsey!
welcome back gabe :)
Good Luck Kelsey! thank you for all the wonderful videos! a big welcome to the new hosts!
NO! DON'TGO! :C
Ruben mfbkdh de la semaine dernière à un moment de
Msggfgfgfgfdbfffgug
We're going to miss you so much! And welcome to the new hosts! It's going to be great and has been great so far :)
its nice to see gabe back to pbs!!!! Good luck with your research though
What is interesting about the heat equation is that it is not only important in mathematics and central to physics, but also quite important in finance.
I remember seeing a video a few years ago with a lecture about options pricing (from MIT, if memory serves me right). Here the lecturer told an interesting tale: Fisher Black and Myron Scholes were trying to come up with a model that could give the correct price for a financial option, but they ended up with this differential equation they could not find the solution for. When they were unable to, and other people in their own departments could not help them, they asked in another department (I do not remember if this was mathematics or physics). They immediately got the answer: "Oh, this is the heat equation, here is the solution", and they could progress with their work.
Later they won the Nobel price for their work. The model they came up with is now known as Black-Scholes model.
Gabe, this time speak a bit slowlier, please ... Sometimes it was quite difficult to follow your remarks at PBS ST
It's not really a big deal, if you have a pause button, you dont' have to watch videos like TV, being afraid to take a piss just in case you miss something. I see so many people complaining about his speech rate, but hey, come on. Writing on PBS ST is very good and Gabe's pronunciation is not bad at all.If you're not a native speaker, like me, just watch more videos and movies, it will benefit you enormously in the long run.
Putting that aside, however good the writing on PBS ST, you still need to watch their videos a few times before they really sink in. Sometimes I have to pause even their videos with Matt. They try to make it accessible, but it's freaking physics, dude, you have to put some effort :)
You tube videos have a speed control which can help. Click the gear icon at the bottom of the video and you can slow it down if you like.
It was never a problem for me, and I'm not even a native speaker. He talks fast, but also very clear, so it's actually a feature not a bug.
Thank you for all of your amazing work. It’s been an awesome ride! Best of luck on your research.
I’m excited to see where the new writers will take the show. They have a legacy to uphold!
Nooooooo!!!! Don't go
Good luck with your research! It was a fun ride, godspeed.
These comments are going by so fast nobody will know I parse HTML with regexes.
ProductionPresents - I noticed because of the unicorns screaming.
Well, bon travels, and thanks for hosting. A couple of spectacular replacements though!
NOOOOO! 😢😭
Hi, new hosts! I'm so excited to see your next episode!
Good luck with your dissertation, Kelsey! We'll miss you! (wow, that's a lot of exclamation points...)
No more hottie mathematician. Sad face.
so I'm not the only one who thinks she's total eye candy? 0.0
She's eye candy alright, but she has a great voice too, and great topics for me to keep watching. I hope the new hosts can match her.
nooooooooooooooo.com/
ye. real hottie. and smart. 😍 😔
Are you all visually impaired? She's a 5.5/10 at best.
I'll miss you but im excited Gabe is back. Good luck on your dissertation!
Thank you, and I hope your dissertation knocks their socks off.