Oxford Calculus: Solving Simple PDEs

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).

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.

You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths.

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[henrymarkson]

Slowly but surely, Tom is working his way through to the Navier Stokes equation.

[nathanielj]

I'd also like to say that this is an exceptionally clear and approachable lecture on the topic. Very nice!

[Isomnophilia]

Done this in university close to 20 years ago, this is explained so clearly that i am being glimpses of the past!

[iteerrex]

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

[damienthorne]

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. 😁

[AruzhanOmirseit]

Thank you a lot for this amazing explanation! You simplified and broke the topic down to more manageable bite size pieces!!! Thank you

[fahrenheit]

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.

[soph.m.p]

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.

[taresypp]

try solving the Riemann hypothesis tom

[jackingham]

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!

[sadmanislam]

Great Video. @Tom Rocks Maths would it be possible to do a collab with @Stand-up Maths?

[peterwall]

Professor Tom, given eyesight of 20/20, how close to someone would two objects have to be, to distinguish them at 1” apart?

[HuyNguyen-wjho]

It would be really helpful if you fix the unaccessible practice work sheet at Maple😅. Btw your video is really 😃.

[peterwall]

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

[blackid]

Please explain about Sumudu Decomposition Method for solve PDEs sir🙏🏼, i can't found explained about sumudu method in YouTube 🥲

[duncankoepke]

Would you consider talking about the heat equation?

[carlosneves]

did not know Billy Idol did maths. Nice video btw!

[enigma]

Heya Tom...How did the football go? That's an epic chalk stick.

[abhijitmahata]

Hello, I am from India.Can you suggest any book for ordinary and partial differential to learn theory part.

[pazzy]

when you scrub through to the end to see if he takes his shirt off