(4 points) Use the Fourier integral transformations to solve the heat equation д2u du 0 < x u(x, 0) = 0, 100, a(0,t) (Please use "alpha" for the variable α.) n(x, t) = Jo (4 points) U...
(4 points) Use the Fourier integral transformations to solve the heat equation д2u du 0 < x u(x, 0) = 0, 100, a(0,t) (Please use "alpha" for the variable α.) n(x, t) = Jo
4. Solve the initial, boundary value problem by the Fourier integral method te = kurz, 0<x<oo, t>0, us(0,t) = 0, u(x, t) bounded as T-100 0S$ 0, >4 f(x)-( 4 u(z,0)=f(x), 4. Solve the initial, boundary value problem by the Fourier integral method te = kurz, 04 f(x)-( 4 u(z,0)=f(x),
Problem 6 [30 points Use Fourier transform to solve the heat equation U = Ura -o0<x< t> 0 subject to the initial condition -1, 1 u(x,0) = -1 < x < 0 0 < x <1 x € (-00, -1) U (1,00)
4. Solve the initial, boundary value problem by the Fourier integral method. u (0,t)0, u(r,t) bounded as-00 4. Solve the initial, boundary value problem by the Fourier integral method. u (0,t)0, u(r,t) bounded as-00
Solve heat equation in a rectangle du = k ( ou + dou), 0<x<t, 0<y< 1, t> 0 u(x, 0, 1) = 0, uy(x,1,1) = 0, with boundary conditions u(O, y,t) = 0, u(r, y, t) = 0, and initial condition u(x, y,0) = (y – į v?) sin(2x).
1. Solve fully the heat equation problem: Ut = 5ucx u(0,t) = u(1, t) = 0 u(x,0) = x – 23 (Provide all the details of separation of variables as well as the needed Fourier expansions.)
Solve the heat equation 4,0 < x < 3,1 > 0 kou det u(0, 1) = 0, u(3,t) = 0,1 > 0 S2, 0<x< } u(x,0) = { 10, { <x<3 are the eigenfunctions You will need to apply separation of variables to obtain a family of product solutions un(x, t) = x (x)Ty(t) where X of a Sturm-Liouville problem with eigenvalues an (as in Section 12.1). Using the explicit expressions for un(x, t) gives (8,0) = ŠA, n=0 Then...
Fourier transform: 3. Consider the equation a(x, 0) = f(x) u(x,t) lim 0 Using a Fourier transform, solve this equation. Evaluate your solution in the case when f(x)-δ(x). 3. Consider the equation a(x, 0) = f(x) u(x,t) lim 0 Using a Fourier transform, solve this equation. Evaluate your solution in the case when f(x)-δ(x).
2. [-/3 Points] DETAILS ZILLENGMATH6 13.3.002. du at 0<x<L, t> 0 subject to the given conditions. Assume a rod of length L. Solve the heat equation Lazu axz u(0, 1) = 0, u(L, t) = 0 u(x,0) = x(L - x) u(x, t) = + n = 1 eBook
1 & 5 Solve the following heat equations using Fourier series ux Ut, 0 <x <1,t>0, u (0,t) = 0 = u(1,t), u(x,0) = x/2 1/ 2/ Ux=Ut, 0<x< m ,t>0 ,u(0,t) = 0 = u( 1, t), u(x, O) = sinx- sin3x 3/ usxut, O <x < 1 ,t>0, u(0,t) = 0 = u,(1, t), u(x,0) = 1 -x2 Ux=Ut,O<x <m ,t>0, u(0, t) = 0 = u,( rt , t) , u(x, 0) = (sinxcosx)2 4/ 5/Solve the...