I know you probably get this a lot, but I just have to say, your videos are supremely excellent. You don't just provide a formula with no context to solve the problem, but you introduce concepts and methods to really understand the math intuitively. Very rare to find an explanation like yours, and for that, I thank you and tremendously admire your approach. You have inspired a fellow math lover!
Great explanation. My notes were so unclear about this and didn't even derive it, but now I understand the equation intuitively and exactly why it holds :).
Good explanation of the transport equation. A prerequisite to know before hand would be the concept of the directional derivative. Good to revise that, then come to this video again
Let me just say I attend a pretty well-known college and these videos have been instrumental in my understanding 9 years after publication. Bravo to you.
The way you get the result so naturally is super-fascinating! Thanks a lot. Didn't really get that in class, and now finally got (maybe I deserve some sleep now, finally)
Why is it "x - ct =constant" and not "x + ct = constant"? If we are looking at the lines on the x-t plane, isn't it just "ax + bt = constant" for a and b be some other constants. I don't see how "c" fits in the line argument.
Okay I figured it out after 4 years. For those who are confused. It is because at t = 0, the wave travels at speed c, but x = x_0 + ct. And that's it, it's the standard equation in physics.
I was about to ask the same question then remembered that is is one of the forms of the multi-variant chain rule. If you have a basic calc book look up the chain rule towards the end. The chain rule is the sum of the partials multiplied by the ordinary derivative. I hope that helps if you are still trying to figure that out.
If t=time, u=amplitude, what is x? All I can figure is that it's where the peak is along some scale, but since it's not time, what is the scale? I'll guess distance from some arbitrary object, like electron distance from voltage source.
Thank you so much for the insight into how the transport equation can be determined through the directional derivative!! We're doing something similar where c is a function, but your explanation was really insightful into the equations derivation (a detail unfortunately skimmed over by our lecturer). Subbed!
I am unclear where ux comes from--this is the partial of u with respect to x--but you are differentiating with respect to t--i have replayed several times and dont get it. Can you give me a hint? thanks
Its very elegant! I was wondering though if you could point to the details of the subtlety you alluded to, that involved replacing x by ct+x0 but then using u_x0 and u_x interchangeably..Intuitively its clear about u_x and u_x0 but I would like to see the formal reasoning somewhere.. (I am looking at PDEs and such after a long gap)
In case it was necessary to normalize vector (c,1) how would it be done? May You tell some example where it would be necessary and explain how it would be done. Thank You.
I didnt study multi-variable calculus, so could you help clarify why the directional derivative is zero, why is normalising the function and obtaining a unit vector the deravative important if the derivative is not equal to zero and how did you obtain the formula for obtaining the directional derivative? Thanks
The directional derivative can be given by the dot product of the gradient vector and the unit vector in the direction that we want to take the derivative in.
Interestingly light and static waves (and some other types of waves) move at the speed of light which as you might know the speed of light is represented with the letter c and c is a constant speed of (299,792,458 m/s) so I think while not a full on Easter egg it is pretty cool to note.
"c" is in general used to denote the velocity of a wave based on context; i.e. in a relativistic problem it is used to denote 2.998 x 10^8 m/s, in a sound problem the speed of sound (which I don't have off the top of my head) propagating through air, and in stuff like this the speed of physical waves propagating through the medium
For the chain rule: www.khanacademy.org/math/multivariable-calculus/multivariable-derivatives/multivariable-chain-rule/v/multivariable-chain-rule Your videos are really helpful thank you very much !
I know you probably get this a lot, but I just have to say, your videos are supremely excellent. You don't just provide a formula with no context to solve the problem, but you introduce concepts and methods to really understand the math intuitively. Very rare to find an explanation like yours, and for that, I thank you and tremendously admire your approach. You have inspired a fellow math lover!
Whoa that description of characteristics at 4:20 is really great. Made me understand them more in 30 seconds than in 2 weeks of class. Great video!
literally was going to say the exact same thing. That was so well done and clear.
You're really really really an awesome teacher!
I give you so much thankful mind!
I am going to listen all of your lectures.
Thank you so much again.
Wow, you do a very thorough clear neat approach that I just love. Plus your voice is just pleasant to listen to.
Great explanation. My notes were so unclear about this and didn't even derive it, but now I understand the equation intuitively and exactly why it holds :).
Good explanation of the transport equation. A prerequisite to know before hand would be the concept of the directional derivative. Good to revise that, then come to this video again
Let me just say I attend a pretty well-known college and these videos have been instrumental in my understanding 9 years after publication. Bravo to you.
The way you get the result so naturally is super-fascinating! Thanks a lot. Didn't really get that in class, and now finally got (maybe I deserve some sleep now, finally)
How did I miss this channel? I understood this characteristic lines now from a video which is more than a decade old. Its great.
Why is it "x - ct =constant" and not "x + ct = constant"? If we are looking at the lines on the x-t plane, isn't it just "ax + bt = constant" for a and b be some other constants. I don't see how "c" fits in the line argument.
Okay I figured it out after 4 years. For those who are confused. It is because at t = 0, the wave travels at speed c, but x = x_0 + ct. And that's it, it's the standard equation in physics.
Thanks
I was about to ask the same question then remembered that is is one of the forms of the multi-variant chain rule. If you have a basic calc book look up the chain rule towards the end. The chain rule is the sum of the partials multiplied by the ordinary derivative. I hope that helps if you are still trying to figure that out.
The best illustrative video teaching the concept of characteristic lines with a transport equation. Thank you very much.
I like you illustrations with the graphs!
How did you explain it in so simpler way..
Its amazing
Thanks 👍
Lectures are done by Logan, Applied Mathematics
You are really a genius derive it in this way all the people can understand totally.
If t=time, u=amplitude, what is x? All I can figure is that it's where the peak is along some scale, but since it's not time, what is the scale? I'll guess distance from some arbitrary object, like electron distance from voltage source.
Thanks so much for the great explanation. Very informative videos and a great way to show the physics behind the PDEs.
Oh my god, this is the only good explanation I found on this topic, I'm so thankful! Helped me lots.
Thank you so much for the insight into how the transport equation can be determined through the directional derivative!! We're doing something similar where c is a function, but your explanation was really insightful into the equations derivation (a detail unfortunately skimmed over by our lecturer).
Subbed!
I am unclear where ux comes from--this is the partial of u with respect to x--but you are differentiating with respect to t--i have replayed several times and dont get it. Can you give me a hint? thanks
www.khanacademy.org/math/multivariable-calculus/multivariable-derivatives/multivariable-chain-rule/v/multivariable-chain-rule
@@alonsechan8178 thank you, It helped me.
thank you for that representation of characteristic curve. i didn't understand this using my last month's lectures.
any recommendation on a book where i can follow along these lectures? i would like to do some homework based on these lectures :)
thanks you. Even more clear than our lecturer!
Fantastic video...I finally understand the meaning behind partial differential equations!!
Wow !!! Thank you for accomplishing what my paid Uni couldn’t!
great work, well done
Its very elegant! I was wondering though if you could point to the details of the subtlety you alluded to, that involved replacing x by ct+x0 but then using u_x0 and u_x interchangeably..Intuitively its clear about u_x and u_x0 but I would like to see the formal reasoning somewhere.. (I am looking at PDEs and such after a long gap)
In case it was necessary to normalize vector (c,1) how would it be done? May You tell some example where it would be necessary and explain how it would be done. Thank You.
Thank you for your amazing videos! I am especially appreciative that you provide proofs for theorems!
Thank you teacher :) Very helpful!
Finally I get my favourite tuter
Thank you so much, easily the best explanation I've seen on this topic
Thank you, best explanation of characteristics I've seen.
What happens when the wave hits a boundary? Characteristic lines must change at that point, right?
How do we know the lines have formula X-Ct? Why not X + Ct?
this is so good! btw, anyone confused about directional derivative should check out khan academy's videos on that, and all this becomes super clear
u r my hero, all the best to you.
how does U become to Ux near the end of the video?
www.khanacademy.org/math/multivariable-calculus/multivariable-derivatives/multivariable-chain-rule/v/multivariable-chain-rule
Alon Sechan Thank you!!
Thank you for this video
so great--clear explication plus brilliant drawing--thanks
This is a great video and Thank you so much Sir.
Sir, can you please recommend some good books for partial differential Equations...
Why is the directional derivative zero?
Which software do u use to write with pentab
Is it the same as D'Alembert solution in some textbooks?
What device do you use for this? Is it a Wacom tablet or something similar?
how did you establish x-ct=cont?
u r very helpful, sir, GBU
YOU SAVE ME FROM THE HELL OF FKING PDE!!!
I didnt study multi-variable calculus, so could you help clarify why the directional derivative is zero, why is normalising the function and obtaining a unit vector the deravative important if the derivative is not equal to zero and how did you obtain the formula for obtaining the directional derivative?
Thanks
The directional derivative can be given by the dot product of the gradient vector and the unit vector in the direction that we want to take the derivative in.
you are life saver , I really mean it. many thankssssssss
Amazing interpretation, thank you!
Awesome lecture!!!
best videos ever thank you so much
very clear! great!
This is very helpful, thank you!
good to understand to everyone sir thankyou
Your 2 is surprisingly similar to a partial-derivative sign
Beautiful...thank you very, very much...
Interestingly light and static waves (and some other types of waves) move at the speed of light which as you might know the speed of light is represented with the letter c and c is a constant speed of (299,792,458 m/s) so I think while not a full on Easter egg it is pretty cool to note.
"c" is in general used to denote the velocity of a wave based on context; i.e. in a relativistic problem it is used to denote 2.998 x 10^8 m/s, in a sound problem the speed of sound (which I don't have off the top of my head) propagating through air, and in stuff like this the speed of physical waves propagating through the medium
Gold!
Damn you're good thanks for this
what kind of math is this?? so confusing the derivation.
Wow!!!..Thanks a lot.
perfect video, cheers
you're fucking amazing! a true life saver
i need to pay my 9k to you and not these other lecturers
3 videos before? But I thought this was the third??
Thanks a lot!
Thanku sir
Supercool, thanks a lot.
Thx to Strauss ch1
HELPFUL
ingenious
I would say most of the difficulty in advanced math is still the algebra
thanks;)
are you casually explained? you sound just like him
So PDE's are just difficult to explain. FUCK, I'm failing!!!
For the chain rule: www.khanacademy.org/math/multivariable-calculus/multivariable-derivatives/multivariable-chain-rule/v/multivariable-chain-rule
Your videos are really helpful thank you very much !
jävla så bra då!
Kewl
oops my bad--needed a refresh on multivariate chain rule--please delete my posts. great videos. thanks
seems the more advanced mathematics gets it becomes quite a battle of deciphering the notation
not at all your doing a splended job
not at all