The person who teaches PDEs on you tube on nonhomogeneous differential equations gave a lot of information in a short time. I did not think I would find anything on the heat equation with an exponentially depletable source input term and the radiation outflow boundary conditions. However I found what I was searching for. Wish there were resources like this 40 years ago.
I'm cramming, yes, but not for an exam. I was out of commission for the first two weeks of the semester, and my professor doesn't give extensions. Ever. So now I have to teach myself the first two weeks' material.
Oh no! Here's the link to my PDEs playlist: hopefully it should sufficiently cover the material you learn in class! ua-cam.com/video/O3ahEHAX-KU/v-deo.html Good luck!
Very nice review. Best I have seen. However I think you can go one step further, more complication, but if two or more dependent variables exist you can have coupled system of pdes.
1:21 In the immortal words of Trump: "Wrooong". I am watching your video a month before my term starts to prepare myself for my PDE module. To that end, thank you for making this!
At 7:24 I think instead of g it should have been the first derivative of f with respect to epsilon. g is being used represent the constant term 1 and y should be represented by the first derivative if f with respect to epsilon.
Great video! I have a question: how do I classify (parabolic, hyperbolic or elliptical) linear 2nd order PDEs in three dimensions, i.e. PDEs with three independent variables? I'm completely stumped...
I'm not too well-versed in classifying PDEs with more independent variables, but I believe you have to write the PDE in matrix form and determine the eigenvalues of the coefficient matrix. The eigenvalues will tell you whether the PDE is hyperbolic, parabolic, or elliptic. Here's a source that might help some more: www.personal.psu.edu/jhm/ME540/lectures/ClassificationExamples.pdf
Good video as usual, but I didn't understand the explanation as to why/ when a PDE is considered hyperbolic. I didn't understand how the variable substitution works after 6:40, I believe I am missing something that is not explicitly said.
Thank you! Basically, a PDE of the form in 6:40 is hyperbolic if the constant coefficients A, B, and C are such that B^2 - 4AC > 0. You can then make a variable substitution (basically replace x and y by eta and epsilon) to get the PDE in the more obvious hyperbolic form. I didn't illustrate the variable substitution, and you don't really need to know how it works beyond the details I gave; this is just to show why the PDE gets called hyperbolic in that instance (the equation resembles the equation of a hyperbola). Hope that helps!
What do you mean by variable substitutions and how are they done? Is there a video where you show an example of doing that to reduce the PDE into the hyperbolic/elliptic/parabolic forms?
By variable substitutions, I mean something like changing x to phi where phi = phi(x), and then writing the entire PDE in terms of phi instead of x. Also, I don't have any videos showing examples of this: is that something you would be interested in for the future?
@@FacultyofKhan Hello. Yes I would like such a video. In the meanwhile, could you provide a link to an example of such substitution? I've read through the wiki articles for each type of equation, but I would appreciate additional commentary
@@FacultyofKhan No, God NO. What? Last semester I watched your videos and requested the same. And this time I didn't even look at description assuming you hadn't heard me. Sorry man. You are ten times more useful with those notes. Because making notes takes most of my time AND they are still aren't as good as yours. THANK YOU very much.
I was trying to write an epsilon there. Epsilon and eta denote variables that have been changed from x and y to make a simpler PDE. What I'm saying there is that if you can reduce your original PDE to the form in 6:54 via variable substitutions, then your PDE is hyperbolic (this is equivalent to saying that B^2-4AC > 0). Hope that helps!
dam this dude is so good he even figured out why i cared about learning pdes
he's so good he figured it out 7 years before you did.
I dishonored my family and failed lots of exams. Your words set me on fire and burned me to the core.😢
The dishonor comes from giving up. That is true failure. Keep trying. You can do it.
nah, there is no dishonour after you get your final goal, after which all your previous dishonour will be forgotten
1:32 It is now 12AM. I should technically be studying for my organic chemistry final but this is a good way to procrastinate.
Same :D
OMG same
i am in vaccation and i am bored to play video games
@@SHADOWLEGENDDRAWS ye. grind math for years.
@@UnforsakenXII need it for studying heat diffusion equations in physics
Your intro is so good that I will watch your preface series first then come back for everything to be crystal clear going on.
The person who teaches PDEs on you tube on nonhomogeneous differential equations gave a lot of information in a short time.
I did not think I would find anything on the heat equation with an exponentially depletable source input term and the radiation outflow boundary conditions. However I found what I was searching for. Wish there were resources like this 40 years ago.
I'm cramming, yes, but not for an exam. I was out of commission for the first two weeks of the semester, and my professor doesn't give extensions. Ever. So now I have to teach myself the first two weeks' material.
Oh no! Here's the link to my PDEs playlist: hopefully it should sufficiently cover the material you learn in class!
ua-cam.com/video/O3ahEHAX-KU/v-deo.html
Good luck!
How the fuck does ur prof not give extensions?
Why should I care!!?? 😂 It's exactly why I started watching this video! To cram everything I can for my test...!🙄
Very nice review. Best I have seen. However I think you can go one step further, more complication, but if two or more dependent variables exist you can have coupled system of pdes.
PDE's are also in mathematical finance, the Black-Scholes equation. This is also a reason why we should care.
1:19 nailed it
the best pde lecture ever.
1:21 In the immortal words of Trump: "Wrooong". I am watching your video a month before my term starts to prepare myself for my PDE module. To that end, thank you for making this!
thanks for the playlist! I havent started this in school yet but we r starting it this year and i wanna get a headstart over summer hehe
Wow...you covered a lot in 10 min.....thanx!
My new years goal was to learn Einstein's field equation. Im finally ready. Feels good.
1:22 bro you are savage...
excellent explanation..specially the funny part in the middle..keep doing great work..thanks..
Well explained 🙏⭐
Gee was on point about my interest in PDEs
At 7:24 I think instead of g it should have been the first derivative of f with respect to epsilon. g is being used represent the constant term 1 and y should be represented by the first derivative if f with respect to epsilon.
1:22 me except I've found the playlist way too late and have got probably not even a couple of days
1:19 very accurate 😭
what exactly is a variable substitution? thank you for this video! it was very helpful!
Great video! I have a question: how do I classify (parabolic, hyperbolic or elliptical) linear 2nd order PDEs in three dimensions, i.e. PDEs with three independent variables? I'm completely stumped...
I'm not too well-versed in classifying PDEs with more independent variables, but I believe you have to write the PDE in matrix form and determine the eigenvalues of the coefficient matrix. The eigenvalues will tell you whether the PDE is hyperbolic, parabolic, or elliptic. Here's a source that might help some more:
www.personal.psu.edu/jhm/ME540/lectures/ClassificationExamples.pdf
Thank you very much, I think I understand the idea now, that's a good source! Keep up the good work!
May I ask what system are you using to make these presentations? Some writing tablet plugged into the computer?
ua-cam.com/video/z6N8OnYQqco/v-deo.html
Good video as usual, but I didn't understand the explanation as to why/ when a PDE is considered hyperbolic. I didn't understand how the variable substitution works after 6:40, I believe I am missing something that is not explicitly said.
Thank you! Basically, a PDE of the form in 6:40 is hyperbolic if the constant coefficients A, B, and C are such that B^2 - 4AC > 0. You can then make a variable substitution (basically replace x and y by eta and epsilon) to get the PDE in the more obvious hyperbolic form. I didn't illustrate the variable substitution, and you don't really need to know how it works beyond the details I gave; this is just to show why the PDE gets called hyperbolic in that instance (the equation resembles the equation of a hyperbola). Hope that helps!
What do you mean by variable substitutions and how are they done? Is there a video where you show an example of doing that to reduce the PDE into the hyperbolic/elliptic/parabolic forms?
By variable substitutions, I mean something like changing x to phi where phi = phi(x), and then writing the entire PDE in terms of phi instead of x. Also, I don't have any videos showing examples of this: is that something you would be interested in for the future?
@@FacultyofKhan Hello. Yes I would like such a video. In the meanwhile, could you provide a link to an example of such substitution? I've read through the wiki articles for each type of equation, but I would appreciate additional commentary
i wish they would credit the person who did the video in the description
Well, I'm the one who did it, so no need to credit!
@@FacultyofKhan oh i thought this was mulitude of people working on vidoes. Didnt know you're a one man army!
@@davidho1258 He is the whole faculty.
Wdym welcome back if this series just started😭
1:20
🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣
SAVAGE
God bless you!
"you have an exam coming up and you're doing some last minute cramming." uhhh yes definitely not me
4:40 Isn't the correct term for this autonomous?
Thanks you sir
Is it Sal Khan or somebody else?
The style is so similar
I have the same question XD
Damn :'3
Nope. Voice and handwriting are completely different
Its definitely not Sal.
If you could just share your file you write in these videos. In description it would help ALOT.
There should be a link to the lecture notes in the video description!
@@FacultyofKhan No, God NO. What? Last semester I watched your videos and requested the same. And this time I didn't even look at description assuming you hadn't heard me. Sorry man. You are ten times more useful with those notes. Because making notes takes most of my time AND they are still aren't as good as yours.
THANK YOU very much.
@@FacultyofKhan Which writing app do you use though and do you record your voiceover after you write to allow those speed writing bits?
I got lost when we hit the Parabolic, Hyperbolic, or Elliptic section. :-(
how did you know about my tommorow's exam....???
which video is the next please?
See this playlist: ua-cam.com/video/O3ahEHAX-KU/v-deo.html
Where is PDEs
Who is PDEs
No, I will do you one better, Why PDEs
I have no exam I’m just trying to get ahead in class.
Show off
❤️❤️
1:29 damn😅😅
lol you know I have an exam coming up
Could someone pleas explain where did the Sigma (or an E) came from 6:54
I was trying to write an epsilon there. Epsilon and eta denote variables that have been changed from x and y to make a simpler PDE. What I'm saying there is that if you can reduce your original PDE to the form in 6:54 via variable substitutions, then your PDE is hyperbolic (this is equivalent to saying that B^2-4AC > 0). Hope that helps!
Aaa ok now it makes sense :) Thank You very much
panicking in 2021, exam tomorrow ! help !
The first minute and a half was too real to process
ua-cam.com/video/z6N8OnYQqco/v-deo.html
Ha ha ha that wasn't funny at all