True, 'axis' refers to a single object, where 'axes' refer to multiple ones within one figure. Thank you for pointing this one out! :)

This might be happening in a near future hopefully 😁

@@YounesLab will it be a separate course or integrated modules within an existing course?

It will likely be a seperate course. However, I might include a small recap (summary) and integrate a small portion as a module in my Python existing course (to give an overall tool kit for engineers) Being a seperate course, it will have some prerequisites such as a deep understanding of Python when it comes to computational physics, calculus, and so on. More about it soon! 😄

Thank you for your support 👏

21:32 time

Indeed! I made a little typo mistake there abd it should be x, y, and z. Thank you for for letting me know! I will correct it in the github as well

In order to update text within your animation, you have to set the blit mode to false `blit=False` and then specify within the update function a line that update the title for example: fig, axis = plt.subplots() animated_bridge, = axis.plot([], [], color='blue') # ',' is used because axis.plot returns an array axis.set_xlim([0, L]) axis.set_ylim([-10, 10]) axis.set_title(f"Frame: {0} / {len(time_points)}") # Initial title def update(frame): print(frame) animated_bridge.set_data(space_points, u[frame]) # Updating the data across [frame] axis.set_title(f"Frame: {frame} / {len(time_points)}") return animated_bridge

I am glad to hear it! :)

Ah, I see you're a man of culture as well. Thank you kind sir

This really is an underrated advice that people often overlook! Sleep really is the foundation of everything. There is a quote I heard once saying "sacrificing the night-life for the morning-life" meaning to improuve you have to be willing to give up on the (bad) night behavior 🤔 Thank you for sharing! :)

Pretty much 🤔 depending on how brave you are you can also do it with vegetables

The formulas represent an approximation of derivative via a method called "the finite difference method" often called FDM, this method represent a simple but powerfull technique for solving differential equation related problems (especially flow/heat problems) If you want to learn more about it I suggest you to watch another video I made (part 1) kzbin.info/www/bejne/kKbbco2unNqpY5I

Thank you for your feedback ^^ Personally I am not that familiar with cuda (though this surely is motivating me to make a video about it 🤔) However there are several techniques you can use drastically improuve the speed (method I discoreved after making the video) * writing the main calculations as a function, then using numba's jit to optimize the computation (by chacing it, ...) * Important note: since the result of each iteration is more or less dependent on the one before, parallezing will most likely not work, however one trick you can use is to vectorize the code by, instead of writing it in form of a loop, you replace it by some sort of linear system of equations A*T = b, which will be way faster since it uses linear algebra to find the solution (using numpy)

If you elaborate, I can have a look at it ^^'

Great suggestion thank you ^^' ! I will plan on doing this video about the wave equation it will be an interessting subject (in a couple of weeks)

@@YounesLab thanks

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 (kzbin.info/www/bejne/pIWUZ2CvhtehfM0) Now for the real spring contraction and relaxation is an interessting topic I will through it! Thank you for your suggestion!

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! :)

Glad to read your comment! I wanted to propose something other than the conventional "Hangman / geuss the number" type of project 😄

I am glad to hear it thank you 🙏 I often believe that if you understand the principles behind things it makes it very intuitive and plausible

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 🤔

I am pleased to know it! Thank you for your feedback @liliklbm3607 😄

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.

Jazaka Aallah khayran @optiondrone5468 ! I do hope so as well, Thank you very much 😄

@@YounesLab ayak akhi, Allah Hu salmak

A pleasure to hear it! My salute to Croatians! 😄

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]