Oxford Calculus: Separable Solutions to PDEs

University of Oxford mathematician Dr Tom Crawford explains how to solve PDEs using the method of "separable solutions". Links to worksheets and app download below.

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The technique of solving PDEs using separable solutions is introduced and then used to solve two examples. In both cases the technique of "separation of variables" is required.










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[weonlygoupfromhere]

I love how you teach complex topics simpler than a good chunk of professors. They just explain it but don't give you an in-depth and step by step explanation

[Spectator]

If I took my Fourier analysis class a quarter earlier this video wouldn't have been posted. Now I get MGK as my math tutor. You make me really enjoy my uni class even though you are sadly not my professor.

[wez]

Was literally going to recap this topic today after finishing my first year, perfect timing!

[sunandinighosh]

Yesterday I was trying to understand the solution of Schrodinger's equation for my physics exam and couldn't understand the method...thankfully today you uploaded this video. What a coincidence!!

[bos]

Hi Tom. I'm from South Africa. I just wanted to thank you for your channel. I wasn't very good at maths at school. In fact, I really struggled with it, especially with geometry .Since leaving school, I have started learning maths again. It has become a sort of hobby of mine. Maths is in my opinion the most interesting subject I have ever learnt after philosophy (that will always be my first joy, because I believe it is even more fundamental than maths, although you might disagree with me haha) 😀. Your channel gives me hope that I can learn and will improve. So thanks a lot, and keep making videos for us your maths fans!

[jcleary]

I was reading the textbook for an hour+, and this video just saved me. Thank you sir.

[cristianorlandoelpro]

Mate, my textbook did a horrible job explaining this topic. I'm glad I came across your vid

[BlackEyedGhost]

Had to go back and review linear differential equations before I could remember how to do this. Thanks for the practice problems. Apparently I needed the practice.

[peterhall]

Separability ultimately has its physical justification in the assumed independence of the functional relations. This is quite believable in all the major PDEs which arose form looking at physical phenomena. Just look at how Maxwell derived his velocity distribution law to appreciate the independence angle.

[M.athematech]

Hi Tom, like John I am also from South Africa, but I was very good at maths at school and went on to complete my PhD at 24. I wasn't very good at begging people to give me money to do maths research though and started an IT company instead. But anyway, D = 1 doesn't follow from u(1, 1) = e. The most one can say is that D and C are related by D = e^(1-3C/2).

[HuyNguyen-wjho]

What a great and clear lecture. Thank you very much Dr. Tom. Waiting for your next lecture.😊

[jakobandrews]

When you say u(1, 1) = e, wouldn't D=1/e and C=4/3 also work? I feel there is an infinite number of constants that work here

[two]

How do you know the only solution is in this form though? How do you know it isn't a linear combination of them? For example f(x)+g(y)

[raneena]

I feel really weird just assuming that it's separable with no justification :/