![Main Results][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=postimage.png&userId=2442585 [2]: https://www.wolframcloud.com/obj/8f37394e-0b63-49b1-903c-a265cfa83989 ..read more

Reading a scientific article, I came across the following integral $$ \int_0^1 dx \int\dfrac{d^2k}{16\pi^3} \psi(x,k)^2 $$ So, I had a huge question: how to use Mathematica to do integral $ \int d^2k $? Can anyone help me with this? Thanks ..read more

Hello, I am trying to solve Fick's 2nd law of diffusion in Mathematica. The initial and boundary conditions are shown in the image attached. The only difference is that the concentration at t = 0 s is defined by a function of x. I have attached the Mathematica code below and the errors I get while solving the problem. Thank you ![enter image description here][1] ![enter image description here][2] (*Define the PDE*) pde = D[F[x, t], t] == 0.000051*D[F[x, t], {x, 2}] (*Define the initial and boundary conditions*) ic = F[x, 0] == Co bc = {F[0, t] == 0, F[x, t] == Co (*Solve the PDE*) sol = NDSolv ..read more

&[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/bf679a34-1ed9-41d3-b35f-8a6b351d2383 ..read more

![enter image description here][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=dsf34dfgadf43sad.jpg&userId=11733 [2]: https://www.wolframcloud.com/obj/72ac236c-888b-43ce-a10b-59aad3935f91 ..read more

Hello, I need to calculate the Stokes' determinant in Mathematica, such as ![enter image description here][1] What should I do in Mathematica? I can't image the right code in Mathematica. [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2024-04-21152648.png&userId=2471588 ..read more

![enter image description here][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=3530main.png&userId=20103 [2]: https://www.wolframcloud.com/obj/98f6f67b-7526-4748-bb2e-b73ed562e65a ..read more

Hi hope you are all doing well, I am trying to prove that the two graphs I got are the same so I want to put both results in the same graph (distribution and the last one) apparently there are clearly not the same because of the values of the x axes, If any of you knows how to put them both on the same graph and how to solve the problem of the last graph that would help me a lot, Thank you all in advance. &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/189c59d2-ec63-4955-a1f9-c18a4361b69b ..read more

&[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/891f285d-43fb-4ecd-aaed-80270881a858 ..read more

Hello, In my book, there is an exercise: > f(x,y) is continuous over a closed region of D={(x,y)|x^2+y^2<=y,x>=0}, and f(x,y)=Sqrt[1-x^2-y^2]-8/Pi*Integrate[f(x,y),dy,dx] In Mathematica Solve[f[x, y] == Sqrt[1 - x^2 - y^2] - 8/Pi*Integrate[ f[x, y], {x, 0, 1/2}, {y, -Sqrt[1/4 - x^2] + 1/2, Sqrt[1/4 - x^2] + 1/2}], f[x, y]] // Simplify produces {{f[x, y] -> 1/2 Sqrt[1 - x^2 - y^2]}} But the right answer should be Sqrt[1-x^2-y^2]+8/9/Pi-2/3 So, what the reason for Mathematica to produce that answer ..read more