Man you are really amazing! My visit here was to know why we relate the fourier series with the solution of the PDE Specifically when we are trying to find the coefficients of the solution. Thanks a lot
VERY interesting comment about a great combination. Before I became an academic, I was a DJ for 10 years. I used to correspond with Markus (well, the people at Markus' record label, who would send me records every now and then) when he was living in AZ. Boy - hasn't he gone on to do great things!
There are two solutions for your right ear: either unplug the headphones a little bit until the sound is equalised, or simply take off your headphones and put them in front of you at max volume. :)
@speckofdust21 There are no recordings of the other lectures (that is, they weren't recorded at all) but I hope these will be of some use. There may be some more coming next semester when I begin filming again. Best wishes.
Just wanted to thank you for a very clearly explained video. It is well organized an thoughtful. Your lecture was bounded and focused. Great work, keep it up. I for one certainly appreciated it.
Cheers for putting this up. I hope the stuff comes out in the exam today ... 11 hours to go "yawn", 3 a.m. already. Anyway, cheers again for a great semester.
@yeequettoff For the first BC (boundary condition), u(0,t) = 0, the constant for cosine equals zero. For the second BC, u(pi,t) = 0, you find that the eigenvalues must be n, where n = 1, 2... within sine. We omit the n=0 since sin(0*x) = 0, always, which is trivial. Therefore, instead of getting cosines with the previous BC's, we get an infinite series of sines. Solve for constants using orthogonality of sines, and there you go!
@gabriellando What's between the brackets is zero if and only if \lambda is zero, but if you look at the top of the page you will see that we are discussing the case \lambda > 0, so this leads to a contradiction. Hence what's between the brackets cannot be zero in this case.
@WiseHuman Thanks for the compliments. Thanks for posting some great questions. Yes, you can split the integral for piecewise continuous functions just as you suggest. I also agree with you about the funny length of the bar - one would hardly be able to make a bar of length pi. Although slightly "confected" it does simplify the calculations for this particular example.
minutemantv: I'm using a prime to denote differentiation with respect to the independent variable, where each of the different functions is a function of one variable.. As a result, It does not matter if the independent variable is $x$ or $t$ or something else, like $s$. Thanks for posting!.
@turtleman1234 I am not sure if you're aware, but there is a strong historical connection between maths at UNSW and Waterloo. Good luck with your studies.
Dr. Tisdell - Do you have lectures on solving wave equation and bessel functions? Thank you for making partial differential equations easier to understand.
This lecture maked me understand so much of my diff. eq. course that I take this semester :) Thank you so much! Are there any other uploaded lectures involving the wave equation solved with this method? If so, please upload it!! :-) Thanks again!
@yeequettoff I solved the problem that you posed in the previous lecture (but did not record it). I will certainly try to address this problem next time I teach this course.
Awesome lecture, way better than the one im havING next week. about lambda, can you disregard it being positive or negative directly by noticing neumann or dirichlet boundry conditions? Like this one we had neumann , and what happends if we have mixed? both get information from positive and negative lambda? :S
@fallenfossl From what i can see you don't need anything other than the fourier series to solve part e). I think it's just the convergence of the series as t approaches infinity. . . Granted i’m most likely wrong lol
At 28:38 Dr Tisdell says that we need to find whether lambda is 0 or negative again. Why does this need to be done? Hasn't it been established that lambda is negative?
@DrChrisTisdell sigh...would be great if you could upload lecture 23 as well. And thanks for all the vids, they're really helpful....wish all universities would implement this, things go by way too fast in the lectures
The reason is, we know from the start that t and x are independent variables, if we allow both sides to vary then the equation will not hold because left side would not equal the right side for some x and t.
This video is really nice, but pls you mentioned about the previous video with the boundary condition u(0,t) = u(L,t) = 0. Pls I really need to watch the video urgently but I can't find it. What is the name of the video? Thank you.
26:00 ^_^ Haha, a cute rod of length pi accompanied with a similarly endearing chuckle I think this video has helped to consolidate my knowledge effectively so thank you! Maths exam, come at me!
@temptamen : How is that sad? I don't understand. English is my second language as well, but I recognize it as the academic first language. The best and the brightest publish and teach in English, so how is it surprising or sad that your university can't compete.
This guy is a VERY GOOD TEACHER!!! I had to teach myself PDE's while in GS...and that was online....talk a/b a bitch! Wish this was available then!!! geez.... But what a great vid....makes me wanna start studying again!!!! LOL!
Can someone explain to me why F''/F=G'/4G are both equal to a constant, and the same one? Why does he say we only vary x and only vary t? Won't they both vary?
good video but want to ask that 1. how do we know that such solutions (where variables can be separated) exist for given PDE. 2. what are the limitations of method of separations of variables. I mean what type of PDEs can be solved using this method. anybody answer please?
This is math pedagogy at it's best. What a great teacher!
Man you are really amazing!
My visit here was to know why we relate the fourier series with the solution of the PDE
Specifically when we are trying to find the coefficients of the solution.
Thanks a lot
This is my first ever youtube comment and if I pass my exam tomorrow, it will be all thanks to your video. Thank you so much!
VERY interesting comment about a great combination. Before I became an academic, I was a DJ for 10 years. I used to correspond with Markus (well, the people at Markus' record label, who would send me records every now and then) when he was living in AZ. Boy - hasn't he gone on to do great things!
If you were a dj for 10 years did you do your degree in mid 30s then ?
Jayjay F: I studied at uni in the day time and DJed at night time. I was 28 when I got my first academic position.
@@DrChrisTisdell im 28 now not sure if i want to do a phd, can i email you for some advice?
Thanks Sir, its really help. Hope you're doing well right now!
great lecture! my right ear enjoyed it so much :)
mine also..only one ear
There are two solutions for your right ear:
either unplug the headphones a little bit until the sound is equalised, or simply take off your headphones and put them in front of you at max volume. :)
@speckofdust21 There are no recordings of the other lectures (that is, they weren't recorded at all) but I hope these will be of some use. There may be some more coming next semester when I begin filming again. Best wishes.
This video showed me what was barely taught to me in the span of six live lectures
Just wanted to thank you for a very clearly explained video. It is well organized an thoughtful. Your lecture was bounded and focused. Great work, keep it up. I for one certainly appreciated it.
neat stuff! amazing how one video you posted managed to clear my doubts that one entire semester of lectures did not. thanks for the great work!
Thanks Dr Tisdell had problems trying to solve Fickian diffusion equation. Shout from NUS here! :)
Cheers for putting this up. I hope the stuff comes out in the exam today ... 11 hours to go "yawn", 3 a.m. already. Anyway, cheers again for a great semester.
great video, it would have been impossible for me to understand PDEs without this video, Great work Sir.
@yeequettoff
For the first BC (boundary condition), u(0,t) = 0, the constant for cosine equals zero. For the second BC, u(pi,t) = 0, you find that the eigenvalues must be n, where n = 1, 2... within sine. We omit the n=0 since sin(0*x) = 0, always, which is trivial.
Therefore, instead of getting cosines with the previous BC's, we get an infinite series of sines. Solve for constants using orthogonality of sines, and there you go!
Amazing!!! You explain this so much better than my professor. Thank you so much for these videos
love it im studying in norway been thinking my lecturer is great but this method is super digestive thnx
Nice video, well documented steps and procedure... Totally worth the 40 minutes at 2am :D
@remonman Glad you enjoyed it and thanks for commenting.
That was some really nice presentation. For sure I am going watch some of your other videos too.
Dr. Chris... Great Thanks from Switzerland
@vandelpool44 - good idea - I will try to talk more about applications in future vids.
@gabriellando What's between the brackets is zero if and only if \lambda is zero, but if you look at the top of the page you will see that we are discussing the case \lambda > 0, so this leads to a contradiction. Hence what's between the brackets cannot be zero in this case.
@WiseHuman Thanks for the compliments. Thanks for posting some great questions. Yes, you can split the integral for piecewise continuous functions just as you suggest. I also agree with you about the funny length of the bar - one would hardly be able to make a bar of length pi. Although slightly "confected" it does simplify the calculations for this particular example.
Cheers from Denmark for a great lecture!
"Its a little bit cute" haha
I finally understand the heat equation now! My lecturer made no sense. You explained it very clearly. Thank you
This video save my life. Thanks Bro! you're a great person.
Very well explained and shown. This was honestly a great help. Thanks!
Such a good lecturer ...explained everything perfectly!!!
minutemantv: I'm using a prime to denote differentiation with respect to the independent variable, where each of the different functions is a function of one variable..
As a result, It does not matter if the independent variable is $x$ or $t$ or something else, like $s$.
Thanks for posting!.
@DrChrisTisdell awesome...thanks for the effort Dr Tisdell
good to see people like you...
Great lecture, extreeeeeemely helpful!
Best regards from Portugal!
@SimplifiedQuestion I don't have a video lecture of this, but I will try to upload one in the future as there definitely seems to be a demand!
Good to hear that these are of some use over there!
Always happy to help!
awesome :), learned a lot about pde's in just 40 mins
I love hearing his voice. It makes me happy :)
@delkhairio Nice to hear from a NTU student. I have visited that university a few times. The Jurong area is very nice and green.
Fantastic lectures! Keep up the good work.
@buddydog1956 I'm very glad that you liked this video - PDEs are qutie amazing.
@austprash Yes, there are quite a few mathematicians here at UNSW who have worked at UW!
At 39:45 shouldn't it be pi/2 on the y axis (f(pi/2)=pi/2) as opposed to just pi?
@turtleman1234 I am not sure if you're aware, but there is a strong historical connection between maths at UNSW and Waterloo. Good luck with your studies.
Couldn't stop my laughter at 26:00 . Great Lecture!
thanks a lot DR Chris Tisdell
Dr. Tisdell - Do you have lectures on solving wave equation and bessel functions? Thank you for making partial differential equations easier to understand.
@MsTiffanyVo Not yet, but hopefully next semester when I will teach Engineering Maths (again!). Best wishes.
This lecture maked me understand so much of my diff. eq. course that I take this semester :) Thank you so much! Are there any other uploaded lectures involving the wave equation solved with this method? If so, please upload it!! :-)
Thanks again!
@yeequettoff I solved the problem that you posed in the previous lecture (but did not record it). I will certainly try to address this problem next time I teach this course.
My right ear enjoyed this.
Soooo helpful! Thanks,Chris
good leccture man!!! this will help when im doing PDES"
@ravil4 You're welcome!
my prof spent only 15mins going through this. and his handwriting was crap. Thumbs up to this guy!
best lecturer eva
@doctorsleepy Good to hear this is useful and best of luck with your exams!
so excellent video ..thks sir ..i did not find the separation of variable of non homogeneous?
It is really helpful. Thank You for uploading. ^^
Hey Chris, did u have a video for part 4)e) of this past paper (June 2009), can't really figure that part out...yet!!
donkeyboyz: good idea! I will try to incorporate this into future lectures at some stage.
At the end of the video, we have two functions for f(x) depending on the range. Do we then have 2 an and 2 a0? What do we do then do we add them?
You would separate it into two integrals with limits that match the respective ranges of each “piece” of the function.
I have posted some material on ODEs which appear on my personal channel an also on the UNSW Elearning channel. Hope this is helpful.
Awesome lecture
Awesome lecture, way better than the one im havING next week. about lambda, can you disregard it being positive or negative directly by noticing neumann or dirichlet boundry conditions? Like this one we had neumann , and what happends if we have mixed? both get information from positive and negative lambda? :S
Thank you (from Waterloo, again!) =)
Great videos.Love it!!!
You're welcome, D. It nearly killed me but we got it posted in time for the exam. Enjoy!
@fallenfossl From what i can see you don't need anything other than the fourier series to solve part e). I think it's just the convergence of the series as t approaches infinity. . . Granted i’m most likely wrong lol
At 28:38 Dr Tisdell says that we need to find whether lambda is 0 or negative again. Why does this need to be done? Hasn't it been established that lambda is negative?
@TooheysFrew Thanks and see you 'round campus!
@DrChrisTisdell sigh...would be great if you could upload lecture 23 as well.
And thanks for all the vids, they're really helpful....wish all universities would implement this, things go by way too fast in the lectures
My pleasure!
there is no any download option.. how can i download it??
The reason is, we know from the start that t and x are independent variables, if we allow both sides to vary then the equation will not hold because left side would not equal the right side for some x and t.
@pemulung Best wishes for your studies!
that was very helpful, many thanks
Nice video , do you have notes
@speckofdust21 Yes - it is the only one. Good luck with your studies.
@farooqaziz86 You're welcome!
This video is really nice, but pls you mentioned about the previous video with the boundary condition u(0,t) = u(L,t) = 0. Pls I really need to watch the video urgently but I can't find it. What is the name of the video? Thank you.
26:00 ^_^ Haha, a cute rod of length pi accompanied with a similarly endearing chuckle
I think this video has helped to consolidate my knowledge effectively so thank you! Maths exam, come at me!
@temptamen : How is that sad? I don't understand. English is my second language as well, but I recognize it as the academic first language. The best and the brightest publish and teach in English, so how is it surprising or sad that your university can't compete.
I barely even remember the last time i laughed in math class. I think it was probably when i saw my score... But today i laugh again :)
This guy is a VERY GOOD TEACHER!!! I had to teach myself PDE's while in GS...and that was online....talk a/b a bitch! Wish this was available then!!! geez.... But what a great vid....makes me wanna start studying again!!!! LOL!
Is Lecture 23 on youtube?
No worries!
Muito bom! Realmente gostei, obrigado!
Is this the only lecture on PDEs? Can;t find lectures 16 - 23 or anything after this.... and i really need help with this =(
why does F'(L)= sinpi =0 suddenly mean Fn(x)=cosnx ?
Can someone explain to me why F''/F=G'/4G are both equal to a constant, and the same one? Why does he say we only vary x and only vary t? Won't they both vary?
You're welcome!
C
A BIG thank you
good video but want to ask that
1. how do we know that such solutions (where variables can be separated) exist for given PDE.
2. what are the limitations of method of separations of variables. I mean what type of PDEs can be solved using this method.
anybody answer please?
Thank you for the vid.
@happily1986 NUS is another great university! I've been there too (but not for a while).
From Nanyang Tech University, thanks!!
shouldn't the first solution you found be in terms of sine and not cos Fn(x) = sin(nx)
Ut(x, t) - auxx(t, x) =bu??
@temptamen exactly what im think right now!
You can do it!
why didn't I find this video before?