Test yourself with some exercises on separable solutions with this FREE worksheet in Maple Learn: learn.maplesoft.com/d/COKQBLEMDIGTPODOJIPGMQHKIPBGAMIQOOIGJSKTDFIOELMPEPERDKJHLRIIEHGHMHKQGLLTNLCLOFGTOGONMMDJINDTGSALDFPR
@weonlygoupfromhere7369
2 жыл бұрын
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
@Spectator007
Жыл бұрын
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.
@TomRocksMaths
Жыл бұрын
Glad I could help!
@wez7279
2 жыл бұрын
Was literally going to recap this topic today after finishing my first year, perfect timing!
@sunandinighosh6037
2 жыл бұрын
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!!
@bos567564
2 жыл бұрын
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!
@jcleary3134
3 ай бұрын
I was reading the textbook for an hour+, and this video just saved me. Thank you sir.
@M.athematech
2 жыл бұрын
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).
@TomRocksMaths
2 жыл бұрын
I suppose I’m really appealing to uniqueness of the solution (my bad for failing to state this explicitly).
@cristianorlandoelpro416
Жыл бұрын
Mate, my textbook did a horrible job explaining this topic. I'm glad I came across your vid
@peterhall6656
2 жыл бұрын
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.
@BlackEyedGhost0
2 жыл бұрын
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.
@HuyNguyen-wj1ho
Жыл бұрын
What a great and clear lecture. Thank you very much Dr. Tom. Waiting for your next lecture.😊
@giosanchez2714
2 жыл бұрын
Excited for this one!
@nicholasifeajika1827
2 жыл бұрын
Great explanation. Easy to understand
@jakobandrews2096
3 ай бұрын
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
@aniketeuler6443
2 жыл бұрын
Pretty excited sir!
@ronanmccluskey900
2 жыл бұрын
Why does D=1 when u(1,1)=e??
@TomRocksMaths
2 жыл бұрын
I’m appealing to the unique solution property (without proving it - my bad).
@felipesernabarbosa2796
8 ай бұрын
D = exp(1 - 3c/2), I believe.@@TomRocksMaths
@priscillaflores3082
Жыл бұрын
Great explanation
@Au-fx4pv
Жыл бұрын
Thanks for helping me!!!
@arjunsinha4015
2 жыл бұрын
Nice video sir
@user-mb6gv6ez3e
9 ай бұрын
Thank you sir
@two697
2 жыл бұрын
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)
@TomRocksMaths
2 жыл бұрын
We rely on being able to show the PDE has a unique solution, which can be done for most of the examples seen here.
@MrFtriana
2 жыл бұрын
You must check that this solution satisfies the boundary conditions. If two different solutions of a given PDE satisfies the same boundary conditions, it can be assumed that they are the same.
@travischism
2 жыл бұрын
if we label f(x) == ln(F(x)) and g(x) == ln(G(x)) then u(x,y) == f(x) + g(x) == ln(f(x)) +ln(G(x)) == ln(F(x)•G(x)) and now the solution U(x,y) == exp(u(x,y)) == F(x)•G(x)
@camachojankowilderbeismar6167
2 жыл бұрын
Hello
@MisterTutor2010
7 ай бұрын
Logan Paul does PDEs? :)
@raneena5079
2 жыл бұрын
I feel really weird just assuming that it's separable with no justification :/
@TomRocksMaths
2 жыл бұрын
It’s a standard technique to try and if it happens to work, then we can appeal to the uniqueness of solutions to claim it is the only solution (and in some sense we made a lucky/good first guess).
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