thank you so much for doing this. World needs more people making math accessible and teaching it in a way thats easy to follow instead of just throwing complicated formulas at students and expecting us to remember all of the components!!! YAY U ROCK
WOW! Can I just say that covering the distribution with a graph in case we couldn't see color was the most wholesome thing I've seen since all of our classes went online? Because it is.
+Andres haha, what happen, did you give up on Jhevon Smith? Btw, why does the textbook represent the heat eq. as C^2Uxx and he doesn't include the C^2...
Nah. I wanted to learn some PDE's on the side, lol. I've following in total like 12 classes so it's hard to keep with Jhevon sometimes since I also work. I believe the C is just a constant of proportionality that is derived from heat capacity and other topics from thermodynamics however in order to keep things simple he just removed the C so that we're not distracted by an additional term. I think the method of solving the heat equation should still be the same just with a constant added. It's the partials that are problem.. for me anyways. But you might want to research into it.
Oh yeah, this confirms it. It's just an empirical constant that relates the metal's thermal conductivity and density. ramanujan.math.trinity.edu/rdaileda/teach/s14/m3357/lectures/lecture_2_25_slides.pdf
Yo. Search up a book called Applied Partial Differential Equations with Fourier and Boundary Value problems, the first 12 pages gives a really good derivation of the heat equation, then it'll make way more sense. There is a constant that is within the heat equation if the rod is an ideal rod that has uniform density, uniform composition and thermal conductivity doesn't vary with temperature; otherwise the equation becomes much more complicated because they become functions of position instead of constants as in the one dimensional rod shown in these videos. I don't know, I found it to be a little interesting. You should be able to follow it easily.
Hi! I'm taking a course on PDEs this semester and was wondering if I could get my hands on the Mathematica code you used for the animations. Is that possible?
This is explained so well, and the order in which you are introducing topics is making the topic very easy to understand. I can't thank you enough these videos are literally saving my cgpa.
Thanks a lot! I was taking notes and I wrote the Laplace Equation down as ∂²u/∂x² - ∂²u/∂y² = 0 . When I was going over my notes I noticed the Laplace Equation looked the same as the Wave equation. I should have double checked the video. This makes sense now. Great videos! They are very helpful. Thank you.
Just cracked open my PDE book for spring semester by Strauss and already coming to you for clarification. My classes begin about a week from tomorrow but I wanted to get an early start because I got a B in my ODE class because I had little exposure. My ODE class was right after I finished calc 2.
In the case of periodic heating condition, I don't think the temperature of the right side of the rod will decrease to zero but will decrease to the equilibrium temperature of the rod after heating.
+胡维 I was thinking the same thing. I think just a little inaccuracy over looked by the man. For sure it shouldn't ever be cooler than the far left side.
with that final animation, why would the sinosodial (heat induction section) ever go below the rest of the function? I don't see how the temperature in that section of the rod ever going below the quasi- equilibrium section of the rod?
Thanks for the response. I actually like your way of teaching. It would be great if you can do it. There might be a lot of people interested since CFD is a big thing now.
Laplace eqn: No "wire frame" in the interior. Solution is completely determined by the boundary conditions. A "wire frame" would imply inhomogeneities (e.g. Poisson equation).
In my textbook for my PDE class, the wave equation is listed as Utt = C^2 Uxx. What is the significance of the constant squared/why do you choose to admit it?
ok sir the mathematic code it's very helping, can i know what software you use for lecture, because it's make me can imagine that and i want make some use it
In the last example, the rod with the end cut off, my intuition tells me that the end that is periodically heated should never be lower in temperature than any other part of the rod. Why does this happen in the model?
I recently started learning mathematica and I would like to plot the functions from this video. Can You post the coding if u got it saved or send a mathematica file? Regards Martin Nymark
I would say Finite element and finite volume. That is the most helpful for the kind of work I am doing. Its kinda hard to get a good video about them where they talk about intuition. I can do the math but I would like to understand it a bit more.
I'm wondering about the Wave Equation and the Laplace Equation. They appear to be essentially the same thing, only the variables are different. For the Laplace Equation if you add ∂²u/∂y² you get ∂²u/∂x² = ∂²u/∂y². I don't see how this describes anything different from the wave equation: ∂²u/∂t²=∂²u/∂x².
Hi. Do you see yourself doing some non linear partial differential equations in the future and their numerical solutions. I am doing fluid mechanics, it helps a lot to have an intuition. Good job by the way
At the very end of the video, the boundary condition is not "periodic". A periodic boundary condition is that one that "loops" two sides the rod. This is not the case in this example.
I just realised, the principle of superposition of waves, or theory of partial differential equations, is not much of an answer to the question: Why do waves pass through each other. Leonard Susskind reports that Q.M. is fundamentally different than classical Newtonian physics because it regards the space of states as a VECTOR SPACE. This gives a feeling of quantum woo in itself because it underlies the Bell' inequality violation prediction. But, real propertied matter also acts like a vector space, i.e. water waves. Is there a classical reason ? Presumably this would be the real answer as to why wave transmission continue on their merry way after interference.
Really great educational vids. Made me curious how the fuck did these fucking brilliant scientists and mathematicians came up with those fucking brilliant equations
Your video is great! Although, I kind of laughed when you used blue in your temp gradient for the Heat Equation. Scientifically speaking, blue is hotter than red (I'm sure you know this as well). But I get that your color choices were just to give us a better idea of the temperature gradient. :-)
thank you so much for doing this. World needs more people making math accessible and teaching it in a way thats easy to follow instead of just throwing complicated formulas at students and expecting us to remember all of the components!!! YAY U ROCK
WOW! Can I just say that covering the distribution with a graph in case we couldn't see color was the most wholesome thing I've seen since all of our classes went online? Because it is.
Your mathematica animations are brilliant and so helpful!!
i agree clear and concise!
This series is fantastic. It's exactly what I was looking for, and I am greatly appreciative.
Somewhere out on the ocean, two waves passing in the night lollol!
Your videoes are really well thought out. I was humbled by the fact that you could included additional animations for color blind people. Thanks.
+Andres haha, what happen, did you give up on Jhevon Smith? Btw, why does the textbook represent the heat eq. as C^2Uxx and he doesn't include the C^2...
Nah. I wanted to learn some PDE's on the side, lol. I've following in total like 12 classes so it's hard to keep with Jhevon sometimes since I also work. I believe the C is just a constant of proportionality that is derived from heat capacity and other topics from thermodynamics however in order to keep things simple he just removed the C so that we're not distracted by an additional term. I think the method of solving the heat equation should still be the same just with a constant added. It's the partials that are problem.. for me anyways. But you might want to research into it.
Oh yeah, this confirms it. It's just an empirical constant that relates the metal's thermal conductivity and density.
ramanujan.math.trinity.edu/rdaileda/teach/s14/m3357/lectures/lecture_2_25_slides.pdf
Yo. Search up a book called Applied Partial Differential Equations with Fourier and Boundary Value problems, the first 12 pages gives a really good derivation of the heat equation, then it'll make way more sense. There is a constant that is within the heat equation if the rod is an ideal rod that has uniform density, uniform composition and thermal conductivity doesn't vary with temperature; otherwise the equation becomes much more complicated because they become functions of position instead of constants as in the one dimensional rod shown in these videos. I don't know, I found it to be a little interesting. You should be able to follow it easily.
You are very mindful of accessibilty, which is fantastic to see.
Hi! I'm taking a course on PDEs this semester and was wondering if I could get my hands on the Mathematica code you used for the animations. Is that possible?
This is explained so well, and the order in which you are introducing topics is making the topic very easy to understand. I can't thank you enough these videos are literally saving my cgpa.
Beautiful examples through great animations. Thank you!
Thanks a lot! I was taking notes and I wrote the Laplace Equation down as ∂²u/∂x² - ∂²u/∂y² = 0 . When I was going over my notes I noticed the Laplace Equation looked the same as the Wave equation. I should have double checked the video. This makes sense now. Great videos! They are very helpful. Thank you.
Just cracked open my PDE book for spring semester by Strauss and already coming to you for clarification. My classes begin about a week from tomorrow but I wanted to get an early start because I got a B in my ODE class because I had little exposure. My ODE class was right after I finished calc 2.
I found this indeed very useful as a 3rd year mechanical engineering student and i hope i could be as useful as such at spreading knowledge.
Thanks, this helped me understand this topic more than my lecturer could!
Excellent use of Mathematica to visualize concepts. Grants nice intuition.
nice to give some context before the formal derivations that I suspect will come later in the series, good stuff!
In the case of periodic heating condition, I don't think the temperature of the right side of the rod will decrease to zero but will decrease to the equilibrium temperature of the rod after heating.
+胡维 I was thinking the same thing. I think just a little inaccuracy over looked by the man. For sure it shouldn't ever be cooler than the far left side.
These videos are amazing. You make difficult concepts easy.
Your videos are very clear and so helpful. Thank you!!
very helpful, underrated channel
Thank you for igniting the interest in doing cfd coding.
partial differential equations for dummies. Thank you very much. This video helped me on so many levels.
Can you please tell how did you create the animations and graphs? I m very interested in learning that. Thank you
Absolute fantastic explanations and animations! Thank you so much!
In the last example, I think the heated end of the rod will not go lower than the rest of the rod.
Thanks
I read down and realised You already answered my question. Thanks for the videos.
In your second graph of demonstrating the Heat equation, the equilibrium is not its original temperature?
In the final animation, does the temperature of the blowtorch end go below the temperature of the left side of the rod as it fluctuate?
So helpful! Amazing thank you, Sir. I like you illustrations and word clarity.
with that final animation, why would the sinosodial (heat induction section) ever go below the rest of the function? I don't see how the temperature in that section of the rod ever going below the quasi- equilibrium section of the rod?
Another great video: thanks I was looking for practical applications of PDEs! What software do you use to do the blackboarding?
Thanks for the response. I actually like your way of teaching. It would be great if you can do it. There might be a lot of people interested since CFD is a big thing now.
Laplace eqn: No "wire frame" in the interior. Solution is completely determined by the boundary conditions. A "wire frame" would imply inhomogeneities (e.g. Poisson equation).
In my textbook for my PDE class, the wave equation is listed as Utt = C^2 Uxx. What is the significance of the constant squared/why do you choose to admit it?
Thank you so much, this is an example of quality teaching! I will learn a lot thanks to you.
Cool illustrations! 😊
ok sir the mathematic code it's very helping, can i know what software you use for lecture, because it's make me can imagine that and i want make some use it
Wonderful video. The hope of students in colleges.
In the last example, the rod with the end cut off, my intuition tells me that the end that is periodically heated should never be lower in temperature than any other part of the rod. Why does this happen in the model?
Thank you so much, the figures and animations are so useful 👍👍
Here is a video of a vibrating string where you can see the harmonics if anyone was interested
ruclips.net/video/ttgLyWFINJI/видео.html
I fucking love you, your voice, your videos and the fact that now I have hope for my exam
Hi, what program are you using for these simulations? (I need because I have to simulate 1D heat transfer)
Mathematica.
what is the program that you use to do this graphics ?
I recently started learning mathematica and I would like to plot the functions from this video. Can You post the coding if u got it saved or send a mathematica file?
Regards
Martin Nymark
Beyond awesome. thank you so much.
I would say Finite element and finite volume. That is the most helpful for the kind of work I am doing. Its kinda hard to get a good video about them where they talk about intuition. I can do the math but I would like to understand it a bit more.
Where can I get the animations of the heat equation?
sir your videos are really very helpful...thank you sir...
One of best ...understandable lecture
I'm wondering about the Wave Equation and the Laplace Equation. They appear to be essentially the same thing, only the variables are different. For the Laplace Equation if you add ∂²u/∂y² you get ∂²u/∂x² = ∂²u/∂y². I don't see how this describes anything different from the wave equation: ∂²u/∂t²=∂²u/∂x².
Hi. Do you see yourself doing some non linear partial differential equations in the future and their numerical solutions. I am doing fluid mechanics, it helps a lot to have an intuition. Good job by the way
At the very end of the video, the boundary condition is not "periodic". A periodic boundary condition is that one that "loops" two sides the rod. This is not the case in this example.
how you simplify dy"/dx" +a(t) dy/dx =dy/dt using method of characteristics?? Pl. help me
I just realised, the principle of superposition of waves, or theory of partial differential equations, is not much of an answer to the question: Why do waves pass through each other.
Leonard Susskind reports that Q.M. is fundamentally different than classical Newtonian physics because it regards the space of states as a VECTOR SPACE. This gives a feeling of quantum woo in itself because it underlies the Bell' inequality violation prediction.
But, real propertied matter also acts like a vector space, i.e. water waves. Is there a classical reason ? Presumably this would be the real answer as to why wave transmission continue on their merry way after interference.
Can you please share a demo on solving linear system of hyperbolic equations?
It would be great if you could share the Mathematica code as well
Thanks you. It was very very useful.
super good explanation!
you are so great ! why don't u upload videos now ?
sir can you give me link or something about scrip in Matlab, for you explain in this video
In the example 1:36 boots waves mus go at the same speed. Otherwhise, the wave equation was false.
Great content!
You form a saddle point curve in Laplace's Equation.
Thanks for these videos!
This is very interesting.
why Utt not Ut??
I'm watching these videos in anticipation of what it is to come next semester...
Great job. Thank you
Great videos. Thanks!
guess, the last animation wasn't correct, but indeed its a awesome video
Brilliant, thank you very much.
thx so much. this channel is great!!!!
AWESOME video
quite helpful, thank you verymuch
Awesome ,,,,,,,,, Super Awesome
thank you so much
Keep up
Thanks for uploading
Really great educational vids. Made me curious how the fuck did these fucking brilliant scientists and mathematicians came up with those fucking brilliant equations
good video. thanks
thanks sir very gd effort
Thank you
Thank you so much for that,
"so you can imagine somewhere out in the ocean, two waves passing in the night" - commutant
gracias very good vids
Thanks. It is really helpful.
Thanks
thanks mate.
"so you can imagine somewhere out on the ocean two waves passing in the night"
very romantic :)
Indeed it is
good video
why would you down vote this? "i came here looking for a pasta recipe and all i found was deferential equations. SMH fake media"
Jacob Sebastian called cooking noodles
lovely
"in our example, YOU will be temperature"- :O holy s*** !!!!!!
Something's are common scense
Your video is great! Although, I kind of laughed when you used blue in your temp gradient for the Heat Equation. Scientifically speaking, blue is hotter than red (I'm sure you know this as well). But I get that your color choices were just to give us a better idea of the temperature gradient. :-)
two waves passing in the night lol way to go
"alright, there's my blowtorch"
Euler discover it first.