Very clear explanation, thank you! It's kind of interesting why the conditions are referred to as initial when they are obviously boundary (the first one is Dirichlet BC and the second one - Neumann BC).
Thanks for the feedback. I typically refer to Dirichlet & Neumann boundary conditions when one has a fixed domain where one considers the differential equation. When the DE is posed on the full real line, then I typically use the terminology initial conditions :)
Thank you for this excellent video. Unfortunately, I get an error in both of these alternative lines: exp.subs(C1,0).subs(C2,1) exp.subs({C1: 0, C2: 1}) On a repeated run I get a different result each time: C1+1/16, C1+zoo, 1/16 .... After about 5 times I get the correct result. The rest works fine.
Hi! With C1 and C2 we have a general family of solutions, with one solution for each choice of values for C1 and C2. We set C1=0 and C2=1 just to illustrate one choice of values. Without additional initial conditions on the ODE, all the solutions in the parametrized family (C1 and C2) are equally good. Hope this helps :)
Great video: succinct and clear. Thank you!
You're welcome! Thanks for the nice comment :)
Very Clear Explanation, thanks a ton.
Very clear explanation, thank you! It's kind of interesting why the conditions are referred to as initial when they are obviously boundary (the first one is Dirichlet BC and the second one - Neumann BC).
Thanks for the feedback. I typically refer to Dirichlet & Neumann boundary conditions when one has a fixed domain where one considers the differential equation. When the DE is posed on the full real line, then I typically use the terminology initial conditions :)
This is the definition of precise and concise!
Thanks!
Thanx a lot for sharing this information. well prepared video and great playlist.
Thanks! Really appreciate it :)
7.54 The free symbols are not always in the same order. Is there a way to prevent this?
Thank you for preparing such useful tutorial for us
No problem :)
幫助很大，期中報告就靠這部了。
Thank you for this excellent video.
Unfortunately, I get an error in both of these alternative lines:
exp.subs(C1,0).subs(C2,1)
exp.subs({C1: 0, C2: 1})
On a repeated run I get a different result each time: C1+1/16, C1+zoo, 1/16 ....
After about 5 times I get the correct result.
The rest works fine.
Very nice video, congrats! And thanks for the explanation.
Thanks!
Thanks for the video! why did you set the constants to 0 and 1 how can you know what they are?
Hi! With C1 and C2 we have a general family of solutions, with one solution for each choice of values for C1 and C2. We set C1=0 and C2=1 just to illustrate one choice of values. Without additional initial conditions on the ODE, all the solutions in the parametrized family (C1 and C2) are equally good. Hope this helps :)
Awesome video! Thank you so much!
thank you so much :D
No problem :)
Awesome
Wow