You know, I am somewhat of a mathematician myself.
>>16844213Of course that fag doesn't use dot notation for time derivatives.
>>16844254For me? It's the topological notation.
>>16844265I'd like to see the wave equation written out like that.
>>16844254
So true, here’s a trillion dollars for that incredible insight.
every time i see the limit notation it really makes me wonder how much of mathematics is just experimentation with logical reasoning even if it doesn't make sense initially.
>>16844213so much this
>>16844213It's a very good formula. One of the best formulas
>>16844213all of that just to grab one of the coefficients of the f(x+h) expansion.
>>16844213elon's such a fag lolalthough at least he's more sovlful and funny than the other billiontards
>>16844626A lot for sure. Some giga-autist sorts the details out later, after the creative chadmatician shits out the cool new maths.
>>16844254newton lost
>>16844265There's a solution begging for a problem.
>>16845073Kek
>>16844265Source?
>>16844213Are fractions the closest thing mankind has to God?
>>168483133000 years too late, Pythagoras-pretender
>>16844213What's wrong with this
>>16848373Elong desperately wants to be seen as a science visionary despite just wanting the $ and tries to do it by feigning plebeian fascination with a formula where even "minus" is labeled.
>>16844314[eqn] \left(\lim_{h \to 0} \frac{f'\left(x_1,x_2,x_3,t+h\right)-f'\left(x_1,x_2,x_3,t\right)}{h}\right)^2 =c^2 \left( \sum_{i=1}^{3} \lim_{h \to 0} \frac{f'\left(\left(x_1,x_2,x_3\right)+h\mathbf{e}_i,t\right)-f'\left(x_1,x_2,x_3,t\right)}{h} \right) [/eqn]Here you go, the 3D wave equation written out in terms of the definition of the partial derivative.What do you think?
>>16849955wait a second, f' on the left hand side refers to the first time derivative, but f' on the right hand side refers to the first spatial derivative. and the left side is squared for no reason. this is all wrong.
>>16848383He's just sharing a meme and adding a caption though
>>16849955>>16849973[eqn] \lim_{h \to 0} \frac{f_t\left(x_1,x_2,x_3,t+h\right)-f_t\left(x_1,x_2,x_3,t\right)}{h} =c^2 \left( \sum_{i=1}^{3} \lim_{h \to 0} \frac{f_{x_i}\left(\left(x_1,x_2,x_3\right)+h\mathbf{e}_i,t\right)-f_{x_i}\left(x_1,x_2,x_3,t\right)}{h} \right) [/eqn]You're right. I fixed it now.
>>16844213The guy who posted it "for those who like calculus" is even dumber. Seriously, the definition of derivative is the best you got for calculus enjoyers? How fucking dumb is twitter these days
>>16850089>>16844314yeah this looks right but it's easier to frame this as a finite difference problem: [eqn]\frac{df}{fx} = lim_{\Delta x ->0} \frac{f(x+\Delta x) - f(x)}{\Delta x}[/eqn]now do this again but from the other side and you get the centered finite difference for the second derivative: [eqn]\frac{d^2f}{dx^2} = lim_{\Delta x ->0} \frac{ \frac{ f(x+\Delta x) - f(x)}{\Delta x} - \frac{ f(x) - f(x-\Delta x)}{\Delta x} }{\Delta x} \\ \frac{d^2f}{dx^2} = lim_{\Delta x ->0} \frac{f(x+\Delta x) - 2 f(x) + f(x-\Delta x)}{\Delta x^2}[/eqn]so the wave equation becomes: [eqn]\frac{\partial^2u}{\partial t^2} = c^2 \sum_{i=1}^3 \frac{\partial^2u}{\partial x_i^2} \\ lim_{\Delta t ->0} \frac{u(x_1, x_2, x_3, t+\Delta t) - 2 u(x_1, x_2, x_3, t) + u(x_1, x_2, x_3, t-\Delta t)}{\Delta t^2} = c^2 lim_{\Delta x ->0} \left( \sum_{i=1}^3 \frac{u(x_i+\Delta x, t) - 2 u(x_1, x_2, x_3, t) + u(x_i-\Delta x, t)}{\Delta x^2} \right)[/eqn]at this point you can rearrange and solve for [math]u(x_1, x_2, x_3, t+\Delta t)[/math], plug in some boundary and initial conditions and some small values for the infinitesimals and you have a numerical method.
>>16850186typo in the first equation left hand side is [math]\frac{d f}{d x}[/math]
>>16850086it's a meme for people who like the idea of math but don't actually do mathby sharing it, elon is outing himself as someone who likes the idea of math, but doesn't actually do math
>>16850186>>16850089Actually, it's been awhile since I saw the centered finite difference,but the wave equation does looks great extended.
>>16844213You're telling me this nigga got a physics degree?
>>16844213E=mc2 + AI
>>16848136looks like a ChatGPT output but Brown's "Topology and Groupoids" uses that exact notation (i.e. [math]\mathcal{N}_X(x)[/math] to refer to the neighborhood of the point x in X)
>>16850603This
>>16850603kek
>>16844265
>>16844213Is Elon Garrison an Indian?
