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Oxford Calculus: Solving Simple PDEs
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- čas přidán 9. 06. 2021
- University of Oxford Mathematician Dr Tom Crawford explains how to solve some simple Partial Differential Equations (PDEs) by treating them like Ordinary Differential Equations (ODEs).
Practice solving some simple PDEs for yourself with this free worksheet in Maple Learn: learn.maplesof...
The first examples look at homogeneous first and second order PDEs where we integrate directly and replace 'integration constants' by 'integration functions'.
The third example looks at the inhomogeneous case and how we can use our methods for solving ODEs in the PDE context.
Check your working using the Maple Calculator App - available for free on Google Play and the App Store.
Android: play.google.co...
Apple: apps.apple.com...
Other videos in the Oxford Calculus series can be found here: • Oxford Calculus
Finding critical points for functions of several variables: • Oxford Calculus: Findi...
Classifying critical points using the method of the discriminant: • Oxford Calculus: Class...
Partial differentiation explained: • Oxford Calculus: Parti...
Second order linear differential equations: • Oxford Mathematics Ope...
Integrating factors explained: • Oxford Calculus: Integ...
Find out more about the Maple Calculator App and Maple Learn on the Maplesoft CZcams channel: / @maplesoft
Produced by Dr Tom Crawford at the University of Oxford. Tom is an Early-Career Teaching and Outreach Fellow at St Edmund Hall: www.seh.ox.ac....
For more maths content check out Tom's website tomrocksmaths....
You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths.
/ tomrocksmaths
/ tomrocksmaths
/ tomrocksmaths
Get your Tom Rocks Maths merchandise here:
beautifulequat...
Watch more from the 'Oxford Calculus' course here: czcams.com/play/PLMCRxGutHqflZoTY8JCm1GRzCdGXvZ3_S.html
Ty I can already understood the math 55 because of your explanation is very nice you can deliver it in a good math fan up students here satisfied.
try math in jee advanced it will test you skill on a great level
Would you be able to cover Green's functions by any chance? Love your content
Slowly but surely, Tom is working his way through to the Navier Stokes equation.
Yes. He really obsessed with it.
you know it.
@@pawankhanal8472who wouldn’t be?
I'd also like to say that this is an exceptionally clear and approachable lecture on the topic. Very nice!
Thanks - glad you found it helpful :)
Done this in university close to 20 years ago, this is explained so clearly that i am being glimpses of the past!
I'm a huge fan. I just found the channel by accident, I've taken ordinary differential equations and I'm studying relativity but I do feel like I grasp it quite enough so I love your tempo I love your pace and I'm going to subscribe!
I'm sorry I meant to say I don't ever feel like I grasp it enough. Stupid voice translation. 😁
Thank you a lot for this amazing explanation! You simplified and broke the topic down to more manageable bite size pieces!!! Thank you
You see, snakes can curve. Curves represent a mathematical change in gradient, linking in to differential calculus, and therefore it is perfectly reasonable that you have just witnessed a snake ad prior to a Partial Differential Equation video.
Nah I'm just as clueless as you are.
Farhan gets it.
Differential calculus is one of my favorite, coz of how amazingly useful it is.
By the way, Tom, if you dont play the electric guitar, you should start, coz you already look the part. lol
I've been trying to learn for a while, but unfortunately I seem to have little to no musical talent
I’m not sure if you’ve done it before, but I’d be interested to see you go through some step questions if you were interested. I love your videos.
On the list :)
@@TomRocksMaths Awesome! Thanks!
Really great content, my only question is how do you come up with the guess function with the u variable? Does this come from experience or are there standard procedures for applying a function as your "guess"?
I also didn't follow the part where:
u ~ e^mx => m^2 - 1 = 0 m = +- 1
Where did this part come from?
Many thanks!
This is a standard technique used to solve second order linear differential equations.
Thanks Tom great video
Glad you enjoyed it Josh!
try solving the Riemann hypothesis tom
This was cool, Thanks Tom :)
Glad you enjoyed it Nate!
Great Video. @Tom Rocks Maths would it be possible to do a collab with @Stand-up Maths?
We'll get round to it eventually...
Great video! :-)
Professor Tom, given eyesight of 20/20, how close to someone would two objects have to be, to distinguish them at 1” apart?
nice
Amazing sir
i can't believe this is free
And always will be :)
Your hair look really look nice 😃
Professor, what is a practical application of these PDE’s? I am a total laymen, I understand what your trying to do, but don’t understand the maths at all
Heat diffusion in a bar is modelled by the 1D heat equation which is a PDE. Also, reaction diffusion equations of most forms are also PDEs. Processing images (like denoising) can be done using continuous PDE based methods. There are so many applications of these- they’re actually everywhere. Hope this helps
THANKS SO MUCH!
happy to help :)
It would be really helpful if you fix the unaccessible practice work sheet at Maple😅. Btw your video is really 😃.
Thanks😇😇
You're very welcome :)
@@TomRocksMaths 😇😇
Here's link to an amazing Math video:
czcams.com/video/eSb_nnRO_tA/video.html
Great👍🏻👍🏻
Things I love to see
Would you consider talking about the heat equation?
It's on the list of topics, don't worry!
Please explain about Sumudu Decomposition Method for solve PDEs sir🙏🏼, i can't found explained about sumudu method in CZcams 🥲
This guy is an absolute freak😂😂😂😂
Heya Tom...How did the football go? That's an epic chalk stick.
Nyc
Hey
I'm not sure exactly which game this is referring too, but my team has wont he last 3 games I've played in :)
кажется у меня новый любимый канал )
did not know Billy Idol did maths. Nice video btw!
ha this is a new one, but I'll take it!
when you scrub through to the end to see if he takes his shirt off
Hiii
Hello,I am from India.Can you suggest any book for ordinary and partial differential to learn theory part.
I really like 'mathematical techniques' by Jordan & Smith
Thanks 🙂🙌🙌✨:-)
You're welcome :)
awesome didactic :)
Well said! Didactic is not a word used enough
Where would we use this math i.r.l
Is Maple App have any advantages over Wolfram Alpha?
You can use it on your phone and take photos of equations etc. which I find very helpful!
I see a trailer about snakes from FYFD.
Hey! Can you please solve an IGCSE or O level Math exam? I know it would be way too easy for you but just for us?
It's on the list so watch this space!
@@TomRocksMaths thank u!!
@@shrekwillalwaysfollowyou4592 well i was watching maths related and this appeared and idk i watched it at that time
The second equation is in fact the 1D wave equation in disguise (after a coordinate transformation).
Yes - good spot!
What do you think of the pokemon diamond and pearl remakes?
I can’t wait!! They were one of my favourite generations for sure.
@@TomRocksMaths i saw your podcast, and I noticed the tattoos. The 2000s were too awesome, the music, the Internet all of it. I remember playing the games as a kid, and the nostalgia comes in waves. Anyway! Awesome to see a pokemon enthusiast, mathematician !
Did I see “simple” in the title?
It is not easy to think about an easier equation. Perhaps (f_x)^2+1=0, f real valued, is easier for everybody knows it has no solutions at all.
As far as PDEs go, these are some of the simplest, but I agree the topic itself is anything but.
You look like Jordan Pickford;-)
ouch
His face : stupid
His brain: ye
I am From India I am very poor
Are you mad or what?
Tom are you gay?
Please don't use anything other thst the fact of WHY THE F**K . My 5 month old decided to have a better digital than this
got lost 10 seconds in
I suggest watching the video on 'partial differentiation' first: czcams.com/video/RVwcBGzQcT8/video.html
First
Hmm i see I understand it
(Doesn’t understand anything)
I'd suggest watching the video on 'partial differentiation' first: czcams.com/video/RVwcBGzQcT8/video.html
He looks so western and silly end my suffering i just want to pass and have to look at this
Skipped most, too little content extended into 15 minutes shame
Here's link to an amazing Math video:
czcams.com/video/YVqJn4rwP7M/video.html