Why the reflected wave is not inverted? I think that the whole point of this method is to consider the odd initial condition case, which leads to 4 different waves. Two above the x-axis starting on the right and going in diiferent directions, and two waves on the left side below the x-axis. After some time one left and one right go through each other (canceling out at some moment), but always zero at zero(so the border condition ot the original task is satisfied). Then left wave become right but still below the x-axis, and this is the actual reflected wave.
Yeah, it is a good point. Waves could have three states in what you have had mentioned. But if they reflected in with same magnitude in oposit direction then, (x,t) will be zero! We need to prove the scenario 🤔
Dr. Peyam, I think the case with two walls shown at the end represents a standing wave. Neat, has application to a infinite potential well in quantum mechanics.
I’m really glad that you’ve started to more stuff related to your field of research. Any advice or books you recommend for someone who is starting grad school soon and is interested in analysis, PDEs, Fourier series, that sort of thing?
Love you dear. 😊😊😊 Really great. One question. Could you share us the book or the method that all of your videos you do? I will be gratefull if you would. 😊
Why the reflected wave is not inverted? I think that the whole point of this method is to consider the odd initial condition case, which leads to 4 different waves. Two above the x-axis starting on the right and going in diiferent directions, and two waves on the left side below the x-axis. After some time one left and one right go through each other (canceling out at some moment), but always zero at zero(so the border condition ot the original task is satisfied). Then left wave become right but still below the x-axis, and this is the actual reflected wave.
Yeah, it is a good point. Waves could have three states in what you have had mentioned. But if they reflected in with same magnitude in oposit direction then, (x,t) will be zero! We need to prove the scenario 🤔
Bruh how is this comment a month old
Dr. Peyam, you are the best!
Dr. Peyam, I think the case with two walls shown at the end represents a standing wave. Neat, has application to a infinite potential well in quantum mechanics.
I really love this video and the connection to the application! Thank you!
I’m really glad that you’ve started to more stuff related to your field of research. Any advice or books you recommend for someone who is starting grad school soon and is interested in analysis, PDEs, Fourier series, that sort of thing?
Evans PDE
And anything by Stein and Shakarchi
You are the reason my single last brain cell is still working at 2am studying for my exam. Thank you!
Brilliant approach. Thank you very much.
Great great lecture!!! But isn't (x - ct) for the right-moving wave?
Thank you! And you’re correct
Sorry, can you explain me why x-ct changes to ct-x at 14:15 ?
I love your videos!!
Thanks for the amazing content, Keep up the good job!
I was just searching for this today, what a coincidence
Thanks.
Awesome stuff
Character In the video It's great, I like it a lot $$
Now I wish I could have been able to solve my PDE in my biophysics project
Love you dear. 😊😊😊
Really great. One question. Could you share us the book or the method that all of your videos you do? I will be gratefull if you would. 😊
PDEs by Strauss, but I prefer the book by Evans
Thanks alot dear Dr Peyam
sir ..why we using here odd function?
To force the function to be 0 at 0
@@drpeyam
Thank you ..🌸
sir possibale explain more
If f is odd then f(0) = 0
thanm you🌸🌸