Your videos are so much informative and lucid❤.I was struggling in understanding the ODE's and watched several youtube videos but couldnt get it done...Your videos made me understand all the concepts.Thank you so much..I'm the guy who never comments to the youtube😅 but you made me do it...Can you make the video on animation of spring mass system showcasing the real spring contraction and relaxation
I very glad to hear your feedback and know it was helpful! ^^' I did make a video in the past about animating (simple animation) the mass-spring system if you checked it out already, where we can see the elongation of the spring (ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-nT16-yQrnFk.html) Now for the real spring contraction and relaxation is an interessting topic I will through it! Thank you for your suggestion!
Hello everyone, as promised here is the notebook that contains most of the details of the video! If you have any questions feel free ^^ github.com/Younes-Toumi/RU-vid-Channel/tree/main/Notebook%20Courses/Differential%20Equations
Could anyone explain why is it necessary to use a copy of array u in the scheme equation? I know that it gives slightly different results if we just rewrite u array in each loop, thanks
Hello! We use a separate copy of the array `u` because it represents the temperature distribution at a specific time, `t`. When we discretize our equation in time and space, we get: u[t+1, i] = (dt * a / dx^2) * (u[t, i-1] - 2 * u[t, i] + u[t, i+1]) + u[t, i] In this equation, `u[t, ...]` represents the temperature distribution at time `t`. By updating `u` using a while loop, we ensure that the computation of the distribution at all nodes is accurate for time `t`. If we don't use a copy of `u`, we end up computing the solution at `t+1` using a mixture of data from both `t` and `t+1`. For example, without a copy, `u` is updated dynamically, and when computing each node [i], the left node [i-1] is used from time `t+1` while the right node [i+1] is still from time `t`. This leads to: u[t+1, i] = (dt * a / dx^2) * (u[t+1, i-1] - 2 * u[t, i] + u[t, i+1]) + u[t, i] This does not conform to the established numerical scheme. I hope this clarifies why it's necessary to use a copy of the array `u` in the scheme equation. Let me know if you have any other questions! :)
Hello! Thank you for your comment :) I am not familiar with HTML, however I can maybe share with you what I know maybe it will help you out. In its root, an STL file is made out of coordinates, You group three coordinate-points together to get a triangle, and you get an STL file by combining triangle together. If you are able to convert an X, Y and Z coordinate, it would be theoritically entirely possible. Maybe these links will help you out: 1. tonybox.net/posts/simple-stl-viewer/ 2. stackoverflow.com/questions/12880980/need-js-and-html-example-for-displaying-stl-3d-objects-in-a-web-page
I actually tend to think this as well! When we say "the flap of a butterfly" at a micriscopical level, it is really just the movement of atoms and particles colliding with each other 🤔
Thank you for your feeback!! 👏 I've been falling off with video production lately, but I am still marking down video ideas. Your comment gives me motivation to start again!
@@YounesLab Keep doing what you're doing, mashaAllah you've go a good strategy, InshaAllah your channel would be a good source of passive income for you and you would never have to be a wage slave for anyone.
Thank you for your support @Idk-mc2dd !! I very much appreciate it, I've been lacking good topics to treat but I just found one I am sure will be of great use when it comes to modeling Differential Equation Systems!
@saodatqurbonqulova1527, If you want to solve a system symbolically, the Sympy Library will be your best (and only) option, since odeint uses a numerical scheme. I would suggest you going to check the SymPy documentation on how to solve differential Equations here: docs.sympy.org/latest/guides/solving/solve-ode.html From what I can say, you can achieve it using the dsolve function, here is a small code snippet: from sympy import symbols, Function, Eq, dsolve # Define symbols and functions t = symbols('t') # Independent variable x, y = symbols('x y', cls=Function) # Dependent variables # Define the system of differential equations # Example: dx/dt = y, dy/dt = -x eq1 = Eq(x(t).diff(t), y(t)) eq2 = Eq(y(t).diff(t), -x(t)) # Solve the system of differential equations solution = dsolve((eq1, eq2)) # Print the general solution sol_eq1 = solution[0] sol_eq2 = solution[1]
Be sure to run the regular python file (not the .ipynb) and at the end of the file is there is the `update(...)´ function, I am running the code on python 3.12. If you still are getting troubles getting the animation you can save it as a gif at the end before showing the plot doing: animation.save("animation.GIF")
If you are getting an "IndentationError: unexpected indent" this means there is a problem with the indentation (tabbing) of the line, make sure to delete the tabs and manually re do it.
Dude thanks for this video!! I just have a question, I am currently trying to model the electrical activity of the heart by ordinary differential equations(for a school project )but the heart is a really complicated system, which is why I would need atleast need a system of nonlinear ODE i think? If you are interested im this project, would u be willing to help? Please answer even if u are uninterested so that i know, and again thanks for this detailed video 👊🏼
Thank you for your Feedback! Your Project seems very Interessting I'd appreciate if you can give more details via mail: younes.abdeldjalil.commercial@gmail.com (my Official Commercial E-Mail)
Hello, could you make a video about the electrostatic field of a flat and finite capacitor with parallel plates to analyze especially the edge effect? thank
Hola, ¿podrías hacer un video sobre el campo electrostático de un condensador plano y finito con placas paralelas para analizar especialmente el efecto borde?
thank you for your great work. before finding your channel i was thinking maybe I was dumb not understanding underlying concepts for "easy" things, though I had spent years trying to just know how math works for some calculus. but now i am confident that i can understand math and teach my kids.
How would you do a variable limits integral in D dimensions instead of that integral in a rectangular D-dimensional region? wouul you create numbers following a given distribution?
Exactly! To handle variable limits in D-dimensional integrals using Monte Carlo, employ importance sampling. Generate points based on probability distributions reflecting the integrand's behavior along each dimension, concentrating samples where the function has higher values for more accurate integration estimates.
I used a python math animation engine called "manim" for both text and visuals, it takes a bit time to set up and learn, but once you get the hang of it, it becomes -relatively- easier. And thank you for your feedback!
