An introduction to partial differential equations. PDE playlist: ruclips.net/user/view_play_list... Part 7 topics: -- intuition for one dimensional wave equation
You are quite possibly the clearest (in terms of voice, handwriting, AND presentation), most logical, and most helpful teacher I have ever had by far! With your videos I hope to survive at least a portion of my PDE class, because let's face it, everyone's curriculum is too varied for one person to cater to. But this video alone has made a huge difference so please, feel free to add ANYTHING at all in the near future, I'm positive it will be helpful in one way or another!
Intuition is just awesome, and it is so undervalued. Its what separates the "geniuses" from the "stragglers", and it only requires some discipline or a helping hand to achieve.
Very intuitive justification with a beautiful marriage between physics 1 and pre calculus. Really warms my heart seeing a tough subject tackled like this!
This is very clear 'hand-wavy' explanation. With no prior experience of the subject of PDEs I like it. See the lecture from Yale: "Maxwell's Equations and Electromagnetic Waves" - it goes the same informal way.
Wow nice derivation I've never seen that one. Yes a little quick and simplified but makes a very good way of remembering the wave equation anyhow, or at least "justifying" it without a full derivation one would probably not understand fully on the first go anyhow.
These are wonderful, wonderful videos, and your explanations of PDE's is just great. The intuition you give for what they mean and how to solve them really is delicious. I eagerly await more videos in the series (here's hoping that more are coming T~T)
Hi commutant, great videos i have some questions regarding the heat equation. In my class we start off by finding the steady state solution and transient however finding new boundary conditions for the resulting DE has me stumped! any help would be great
My intuition is comparing the wave equation to the heat equation. The heat concavity profile is fixed with respect to x and simply diffuses in time. The wave concavity profile is moving with respect to x and so you have two separate concavity profiles, one in time and one in distance.
Oh and by the way, if you have another website or something with additional teaching materials I would be extremely grateful to hear about it! Or for that manner ANY other help with PDEs that you can recommend would be fantastic! Hell, I'll even buy another textbook if you think it presents the material well because the one that I'm using in class just can't get the topics across to me, and we've only had it for a week...
The second derivative with respect to position tells you how much the derivative of the function (aka the slope) is changing with respect to x (position). For example, if you look at the string around its lowest position and walk along the string, you can see that the slope is getting more and more positive as you move to the right. In fact, the rate at which the derivative (the slope) of x is changing, has its maximum at the bottom of the string. Let's say that the string can be described by the function sin(x) (we freeze the time, so the time is constant). The first derivative, cos(x), describes the slope of the curve. The second derivative, -sin(x), describes how the slope of the curve is changing. You can draw sin(x) on top of -sin(x) or simply think about it and you'll realize that the second derivative with respect to x, -sin(x), has its maximum wherever the function itself (the string) has its minimum. If you scroll up and look at his picture, you can see that for example when the string is at its lowest point (when sin(x) has its minimum), intuition tells us that the force should have its maximum value. The second derivative also has its maximum here, so that's why intuitively it makes sense that the force is related to the second spatial derivative (second derivative with respect to x).
Came here after reading malalasekera book on "intro to cfd". If anyone has understood the book chaper two's equilibrium and marching problems, please make video to explain it. Thanks. Your video is helpful to some extent commuter
Hi there, great video, thanks for it. However, there is a mistake in the interpretation of the sign of the constant of proportionality 'k', you say that bc the force vectors are directed towards the x, then k must be positive; it's actually the contrary, if you think of the x axis like "a mass attracting points of the rope", analogous to gravity fields, attraction forces are negative by convention, that's why you square k, to guarantee that it will be positive
WOW! Dude you simplified the crap out of the wave equation. I wish my PDE teacher was that good. Unfortunately, she knows how to do the math and she knows the science behind it, but she doesn't explain crap for any equation she gives us. Now, if you can do a heat equation sometime, start your own website and charge $2 / video, you would make your self some money. Almost no one tutors PDEs, I believe because PDEs are pretty brutal.
Well I am curious about something. I have a final next week. My teacher doesn't teach for crap and I am struggling to get my homework done for this week and be prepared for my final. Would you be interesting in tutoring and helping out with 3 problems? I am more than willing to pay you. If interested I would you through paypal.
Oh wow- lots of angry college students it seems.... Thanks for making these- sometimes with all the hairy equations in university lectures, all I hoped to see is some intuition. Exactly what I got! Thank you!
Hey there! I am stuck on like 3 math problems. Is there anyway you could help me out over my hurdles? I don't mind paying you money to get your help. Atleast I will understand the material for my finals. If you can help, Could you take PayPal? Mike
Too many assumptions. Here is a shorter way: wave is shifting a shape f(x) on speed v, therefore f(x - vt) is a moving wave. taking partial derivative on f for x and for t with the chain rule: f_xx = f''(u) and f_tt = v^2*f'(u)=v^2*f_xx, where u =x-vt We get wave function immediately with only one assumption f(u)= f(x-vt).
You are quite possibly the clearest (in terms of voice, handwriting, AND presentation), most logical, and most helpful teacher I have ever had by far! With your videos I hope to survive at least a portion of my PDE class, because let's face it, everyone's curriculum is too varied for one person to cater to. But this video alone has made a huge difference so please, feel free to add ANYTHING at all in the near future, I'm positive it will be helpful in one way or another!
Intuition is just awesome, and it is so undervalued. Its what separates the "geniuses" from the "stragglers", and it only requires some discipline or a helping hand to achieve.
Jose Ortiz im trying noy to b a straggler, thata why i watch commutant
That's why many high math books are unreadable .Stragglers love chaos .They don't have enough mind power or intellectual resource for harmonicity .
8 year old comment .
False
Amazingly clear explanation that connects the dots that are not always plainly apparent on first look.
The way your teaching and your voice just have magic. Thank you.
Very intuitive justification with a beautiful marriage between physics 1 and pre calculus. Really warms my heart seeing a tough subject tackled like this!
Thanks for producing this video, it’s helped me make more sense of the wave equation. I like to visualise everything, not just understand the maths.
This is the most confident I have felt about PDE's yet.
This is very clear 'hand-wavy' explanation. With no prior experience of the subject of PDEs I like it. See the lecture from Yale: "Maxwell's Equations and Electromagnetic Waves" - it goes the same informal way.
Wow nice derivation I've never seen that one. Yes a little quick and simplified but makes a very good way of remembering the wave equation anyhow, or at least "justifying" it without a full derivation one would probably not understand fully on the first go anyhow.
Thanks, this brings together physics and math in an "aha!" way!
These are wonderful, wonderful videos, and your explanations of PDE's is just great. The intuition you give for what they mean and how to solve them really is delicious. I eagerly await more videos in the series (here's hoping that more are coming T~T)
Excellent explanation!!
I understood the wave equation by this video.
Very good.
this was a fantastic explanation!
Wow what a coincidence! Well thank you so very much for all of your help, not to mention your speedy replies!
Well you just solved all my doubts of differential equtions hope it works for my GATE paper ..
:) Thanks a lot ..
you help me become a better student and a better teacher thank you
Nice video. Looking forward to the next part! :)
amazing video’s my man
Hi commutant, great videos i have some questions regarding the heat equation. In my class we start off by finding the steady state solution and transient however finding new boundary conditions for the resulting DE has me stumped! any help would be great
My intuition is comparing the wave equation to the heat equation. The heat concavity profile is fixed with respect to x and simply diffuses in time. The wave concavity profile is moving with respect to x and so you have two separate concavity profiles, one in time and one in distance.
Oh and by the way, if you have another website or something with additional teaching materials I would be extremely grateful to hear about it! Or for that manner ANY other help with PDEs that you can recommend would be fantastic! Hell, I'll even buy another textbook if you think it presents the material well because the one that I'm using in class just can't get the topics across to me, and we've only had it for a week...
Nice clear explanation ...
Fantastic explanation! Just one question: How did you deduce that the concavity is the second spatial derivative of u?
im guessing it's from calculus? cuz plugging in a point into a second derivative of a function tells you if it's concave up/down around that point
The second derivative with respect to position tells you how much the derivative of the function (aka the slope) is changing with respect to x (position). For example, if you look at the string around its lowest position and walk along the string, you can see that the slope is getting more and more positive as you move to the right. In fact, the rate at which the derivative (the slope) of x is changing, has its maximum at the bottom of the string.
Let's say that the string can be described by the function sin(x) (we freeze the time, so the time is constant). The first derivative, cos(x), describes the slope of the curve. The second derivative, -sin(x), describes how the slope of the curve is changing. You can draw sin(x) on top of -sin(x) or simply think about it and you'll realize that the second derivative with respect to x, -sin(x), has its maximum wherever the function itself (the string) has its minimum. If you scroll up and look at his picture, you can see that for example when the string is at its lowest point (when sin(x) has its minimum), intuition tells us that the force should have its maximum value. The second derivative also has its maximum here, so that's why intuitively it makes sense that the force is related to the second spatial derivative (second derivative with respect to x).
Came here after reading malalasekera book on "intro to cfd". If anyone has understood the book chaper two's equilibrium and marching problems, please make video to explain it. Thanks.
Your video is helpful to some extent commuter
This video is everything i wished it would be x
We are using "A First Course In Partial Differential Equations with Complex Variables and Transform Methods" by H. F. Weinberger
@commutant Ah, I should have seen that. Thank you sir.
Hi there, great video, thanks for it. However, there is a mistake in the interpretation of the sign of the constant of proportionality 'k', you say that bc the force vectors are directed towards the x, then k must be positive; it's actually the contrary, if you think of the x axis like "a mass attracting points of the rope", analogous to gravity fields, attraction forces are negative by convention, that's why you square k, to guarantee that it will be positive
WOW! Dude you simplified the crap out of the wave equation. I wish my PDE teacher was that good. Unfortunately, she knows how to do the math and she knows the science behind it, but she doesn't explain crap for any equation she gives us. Now, if you can do a heat equation sometime, start your own website and charge $2 / video, you would make your self some money. Almost no one tutors PDEs, I believe because PDEs are pretty brutal.
How did you conclude that uxx has the units of 1/L...
Please upload thenext video as soon as possible.
They are awesome, and I have an exam in 5 days.
what is characteristic line actually..
thank u !
Wowwwww great tnx 🌺😍
thank u...:-)
god this is so cool
I do not get the relation of the force (magnitude+direction) wrt the wave displacement. it is highly unintuituve for me
maybe it would work for a standing wave
where is the next part???????????
hey friend can you explain the mighty wave equation ie. e^ikx.
Well I am curious about something. I have a final next week. My teacher doesn't teach for crap and I am struggling to get my homework done for this week and be prepared for my final. Would you be interesting in tutoring and helping out with 3 problems? I am more than willing to pay you. If interested I would you through paypal.
dear sir thank you for all you have done, you are an honorable man, but I would like you to know that I don't like hats.
Oh wow- lots of angry college students it seems.... Thanks for making these- sometimes with all the hairy equations in university lectures, all I hoped to see is some intuition. Exactly what I got! Thank you!
Can u explain me what is intuition
Hey there! I am stuck on like 3 math problems. Is there anyway you could help me out over my hurdles? I don't mind paying you money to get your help. Atleast I will understand the material for my finals. If you can help, Could you take PayPal?
Mike
Too many assumptions. Here is a shorter way: wave is shifting a shape f(x) on speed v, therefore f(x - vt) is a moving wave. taking partial derivative on f for x and for t with the chain rule: f_xx = f''(u) and f_tt = v^2*f'(u)=v^2*f_xx, where u =x-vt We get wave function immediately with only one assumption f(u)= f(x-vt).
Hello!