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the interval 0 < x < T 3.1.2. Find all separable eigensolutions to the heat equation...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x,t)...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x,t) represents the temperature. 9uxx = ut; 0<x< 6; t> 0; B.C.: Ux(0,t) = 0; Ux(6,t) = 0; t> 0; 1.C.: u(x,0) = 12 + Scos (x) – 4cos(21x); 0 < x < 6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (3 marks) (b) Determine whether the boundary conditions in this case is Dirichlet,...
Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t)...
Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = ut; 0<x< 6; t> 0; B.C.: ux(0,t) = 0; uz(6,t) = 0; t> 0; I. C.: u(x,0) = 12 + 5cos (x) – 4cos(27x); 0<x< 6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (3 marks) (b) Determine whether the boundary conditions in this case is Dirichlet, Neumann, or...
Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t)...
Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = Ut; 0<x< 6; t> 0; B.C.: 4x(0,t) = 0; uz(6,t) = 0; t> 0; 1. C.: 4(x,0) = 12 + Scos (6x) – 4cos(27x); 0<x< 6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (3 marks) (b) Determine whether the boundary conditions in this case is Dirichlet, Neumann, or...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x,...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = ut; 0<x< 6; t> 0; B.C.:u,(0,t) = 0; ux(6,t) = 0; t> 0; I. C.: u(x,0) = 12 + 5cos ( x) – 4cos(27x); 0<x< 6 (a) Whent 0, what would be the temperature at x = 3? (Use the initial condition.) (3 marks) (b) Determine whether the boundary conditions in this case is Dirichlet, Neumann, or mixed...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x,...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = ut 0<x< 6; t> 0; B.C.: 4x(0,t) = 0; uz (6,t) = 0; t> 0; 1.C. : u(x,0) = 12 + scos (x) – 4cos(2x); 0 < x < 6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (3 marks) (b) Determine whether the boundary conditions in this...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x,...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = Ut; 0<x< 6; t> 0; B.C. : Ux(0,t) = 0; Ux(6,t) = 0; t> 0; I. C.: u(x,0) = 12 + 5cos (x) – 4cos(21x); 0 < X < 6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (3 marks) (b) Determine whether the boundary conditions in this...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x,...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = ut; 0 < x < 6; t> 0; B.C.: ux(0,t) = 0; uz(6,t) = 0; t>0; I. C.: u(x,0) = 12 + 5cos (6x) – 4cos(21x); 0<x< 6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (b) Determine whether the boundary conditions in this case is Dirichlet, Neumann,...
Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t)...
Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = Uti 0<x< 6; t> 0; B.C.: ux(0,t) = 0; ux(6,t) = 0; t> 0; 1. C.: u(x, 0) = 12 + scos (6x) – 4cos(21x); 0<x< 6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (3 marks) (b) Determine whether the boundary conditions in this case is Dirichlet, Neumann,...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x,t)...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x,t) represents the temperature. 9uxx = upi 0<x< 6; t> 0; B.C.: uz(0,t) = 0; ux, t) = 0; t> 0; 1.C.:u(x,0) = 12 + 5cos 6 x) – 4cos(26x); 0<x<6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (3 marks) (b) Determine whether the boundary conditions in this case is Dirichlet, Neumann, or mixed...
1. Wave equation. Consider the wave equation on the finite interval (0, L) PDE BC where Neumann b...
1. Wave equation. Consider the wave equation on the finite interval (0, L) PDE BC where Neumann boundary conditions are specified Physically, with Neumann boundary conditions, u(r, t) could represent the height of a fluid that sloshes between two walls. (a) Find the general Fourier series solution by repeating the derivation from class now considering Neumann instead of Dirichlet boundary conditions. Your final solution should be (b) Consider the following general initial conditions u(x, 0)x) IC IC Derive formulas that...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x,t) represents the temperature. 9uxx = ut; 0<x< 6; t> 0; B.C.: Ux(0,t) = 0; Ux(6,t) = 0; t> 0; 1.C.: u(x,0) = 12 + Scos (x) – 4cos(21x); 0 < x < 6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (3 marks) (b) Determine whether the boundary conditions in this case is Dirichlet,...
Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = ut; 0<x< 6; t> 0; B.C.: ux(0,t) = 0; uz(6,t) = 0; t> 0; I. C.: u(x,0) = 12 + 5cos (x) – 4cos(27x); 0<x< 6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (3 marks) (b) Determine whether the boundary conditions in this case is Dirichlet, Neumann, or...
Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = Ut; 0<x< 6; t> 0; B.C.: 4x(0,t) = 0; uz(6,t) = 0; t> 0; 1. C.: 4(x,0) = 12 + Scos (6x) – 4cos(27x); 0<x< 6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (3 marks) (b) Determine whether the boundary conditions in this case is Dirichlet, Neumann, or...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = ut; 0<x< 6; t> 0; B.C.:u,(0,t) = 0; ux(6,t) = 0; t> 0; I. C.: u(x,0) = 12 + 5cos ( x) – 4cos(27x); 0<x< 6 (a) Whent 0, what would be the temperature at x = 3? (Use the initial condition.) (3 marks) (b) Determine whether the boundary conditions in this case is Dirichlet, Neumann, or mixed...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = ut 0<x< 6; t> 0; B.C.: 4x(0,t) = 0; uz (6,t) = 0; t> 0; 1.C. : u(x,0) = 12 + scos (x) – 4cos(2x); 0 < x < 6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (3 marks) (b) Determine whether the boundary conditions in this...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = Ut; 0<x< 6; t> 0; B.C. : Ux(0,t) = 0; Ux(6,t) = 0; t> 0; I. C.: u(x,0) = 12 + 5cos (x) – 4cos(21x); 0 < X < 6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (3 marks) (b) Determine whether the boundary conditions in this...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = ut; 0 < x < 6; t> 0; B.C.: ux(0,t) = 0; uz(6,t) = 0; t>0; I. C.: u(x,0) = 12 + 5cos (6x) – 4cos(21x); 0<x< 6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (b) Determine whether the boundary conditions in this case is Dirichlet, Neumann,...
Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = Uti 0<x< 6; t> 0; B.C.: ux(0,t) = 0; ux(6,t) = 0; t> 0; 1. C.: u(x, 0) = 12 + scos (6x) – 4cos(21x); 0<x< 6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (3 marks) (b) Determine whether the boundary conditions in this case is Dirichlet, Neumann,...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x,t) represents the temperature. 9uxx = upi 0<x< 6; t> 0; B.C.: uz(0,t) = 0; ux, t) = 0; t> 0; 1.C.:u(x,0) = 12 + 5cos 6 x) – 4cos(26x); 0<x<6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (3 marks) (b) Determine whether the boundary conditions in this case is Dirichlet, Neumann, or mixed...
1. Wave equation. Consider the wave equation on the finite interval (0, L) PDE BC where Neumann boundary conditions are specified Physically, with Neumann boundary conditions, u(r, t) could represent the height of a fluid that sloshes between two walls. (a) Find the general Fourier series solution by repeating the derivation from class now considering Neumann instead of Dirichlet boundary conditions. Your final solution should be (b) Consider the following general initial conditions u(x, 0)x) IC IC Derive formulas that...
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