Very well explained but you kinda got it wrong with the Fourier Transforms. The forward fourier tansform is with an - in the exponential and the backwards one is with the +.
No, that's just one convention :) Other conventions are available. So long as a consistent transform/inverse pair are used along with theorems (e.g. derivative theorems) that are consistent with the definition, all is well :)
Need to redo this video with the proper definition of a fourier transform. All this is doing is making me more confused with how to solve the heat equation and also more confused to understand where the fundamental solutions of this PDE come from. Yes, because of the boundary conditions for the heat equation; this way to define the fourier transform will still agree with the fourier derivative theorem. But still, I came here for help and all I got was a new form or way in which the fourier transform was to be defined as.
Your video is very clearly explained ! I've understood the main principe of FT for PDE'S thank you so much !
thanks! :) absolutely clear as always
excelent work, short and complete
Awesome video! Thank you!
Tomorrow is my test and you man have saved me!! Thank You.
Props to you! Great step through step explanation. Thanks, man
Thank you!
Thank you :)
Well done!But how to visualize it?
is it possible to use the first shifting theorem on this example ?
thanks a lot🎉
excellent
Very well explained but you kinda got it wrong with the Fourier Transforms. The forward fourier tansform is with an - in the exponential and the backwards one is with the +.
No, that's just one convention :) Other conventions are available. So long as a consistent transform/inverse pair are used along with theorems (e.g. derivative theorems) that are consistent with the definition, all is well :)
Sir, could you explain me why are you not using -ve i (iota) in the definition of Fourier Transform and +ve i in the inversion formula......?
Otherwise you are just creating a new way to define a fourier transform
Need to redo this video with the proper definition of a fourier transform. All this is doing is making me more confused with how to solve the heat equation and also more confused to understand where the fundamental solutions of this PDE come from. Yes, because of the boundary conditions for the heat equation; this way to define the fourier transform will still agree with the fourier derivative theorem. But still, I came here for help and all I got was a new form or way in which the fourier transform was to be defined as.