Problem 2. Let u(x,y)=re-- denote the temperature distribution over the square [-2, 2] [-2,2]. a)...

   

Transcribed Image Text:

Problem 2. Let u(x,y)=re-²-² denote the temperature distribution over the square [-2, 2] × [-2,2]. a) Run the following MatLab code on you computer and determine the points with maximum and minimum temperature [x, y]-meshgrid (-2:0.2:2); u=x.*exp(-x.^2-y.^2); surf (x,y,u);view (2); axis equal; shading interp; colormap jet b) Solve the system Vu=0 and verify the solution with part a). c) The following MatLab code shows the gradient of u and the contours (level curves) of you [x, y] =meshgrid (-2:0.2:2); u=x.*exp(-x.^2-y.^2); [ux, uy]-gradient (u); 1 contour (x, y,u); hold on quiver (x, y, ux, uy) Find the equations of the curves that orthogonal to the vector field Vu (the equations of level curves). d) Find curves y = f(x) such that the derivative of u along the curves satisfies the following condition du dz =-2ru Problem 2. Let u(x,y)=re-²-² denote the temperature distribution over the square [-2, 2] × [-2,2]. a) Run the following MatLab code on you computer and determine the points with maximum and minimum temperature [x, y]-meshgrid (-2:0.2:2); u=x.*exp(-x.^2-y.^2); surf (x,y,u);view (2); axis equal; shading interp; colormap jet b) Solve the system Vu=0 and verify the solution with part a). c) The following MatLab code shows the gradient of u and the contours (level curves) of you [x, y] =meshgrid (-2:0.2:2); u=x.*exp(-x.^2-y.^2); [ux, uy]-gradient (u); 1 contour (x, y,u); hold on quiver (x, y, ux, uy) Find the equations of the curves that orthogonal to the vector field Vu (the equations of level curves). d) Find curves y = f(x) such that the derivative of u along the curves satisfies the following condition du dz =-2ru

Answer rating: 100% (QA)

aThe maximum temperature is at 00 because this is the ... View the full answer