8 Eigenvalues used with ODE's Find two λ's and x's so that u елгх solves lu...
8. Find a Green's function for Lu u" +4u, 0< x<T, u(0) = u(#) = 0. 9. Find the general solution of ut+ cu f(x,t) 8. Find a Green's function for Lu u" +4u, 0
*Note: Please answer all parts, and explain all workings. Thank you! 3. Consider the follo 2 lu The boundary conditions are: u(0,y, t) - u(x, 0,t) - 0, ou (a, y, t) = (x, b, t) = 0 ay The initial conditions are: at t-0,11-4 (x,y)--Yo(x,y) . ot a) Assume u(x,y,t) - X(x)Y(y)T(t), derive the eigenvalue problems: a) Apply the boundary conditions and derive all the possible eigenvalues for λι, λ2 and corresponding eigen-functions, Xm,Yn b) for any combination of...
d1=8 d2=9 lu for Find the solution u(x,t) for the l-D wave equation-=- Qx2 25 at2 (a) oo < x < oo with initial conditions u(x,0)-A(x) , where A(x) Is presented in the diagram below, and zero initial velocity. For full marks u(x,t) needs to be expressed as an equation involving x and t, somewhat similar to f(x) on page 85 of the Notes Part 2. d2+5 di+10 di+15dı+20 (b) Check for the wave equation in (a) that if (x...
I need answers for question ( 7, 9, and 14 )? 294 Chapter 6. Eigenvalues and Eigenvectors Elimination produces A = LU. The eigenvalues of U are on its diagonal: they are the . The cigenvalues of L are on its diagonal: they are all . The eigenvalues of A are not the same as (a) If you know that x is an eigenvector, the way to find 2 is to (b) If you know that is an eigenvalue, the...
Velocity profiles in laminar boundary layers often are approximated by the equations Linear: -- U 8 lu Sin_ Sinusoidal: ร์".)-GT LU Parabolic Compare the shapes of these velocity profiles by plotting y/5 (on the ordinate) versus ulU (on the abscissa). Problem 2: Compute 6 /6 for the three profiles from problem 1 Problem 3: Compute θ/6 for the three profiles from problem 1. Velocity profiles in laminar boundary layers often are approximated by the equations Linear: -- U 8 lu...
1 (1 point) Find the eigenvalues of A, given that A 4 - 8 3 - 8 -4 4-5 0 -1 -1 1 and its eigenvectors are v1 = -1 ,V2 -2 and V3 1 -1 -1 0 The eigenvalues are and
Given the following vectors u and v, find a vector w in R4 so that {u, v, w} is linearly independent and a non- zero vector z in R4 so that {u, v, z} is linearly dependent: 1-3 8 -8 -2 u = V= 5 -4 10 0 w=0 1- z=0 0
Slove 2nd problem plz (1) Find the eigenvalues and corresponding eigenvectors of [o1 0 0 0 1 2 1 -2 HINT: Note that 13 + 2/2 - 1 - 2 can be regrouped as 1(12 - 1)+2(12-1). Then factor out the common (12 - 1). (2) Solve the equation Y" + 2y' - - 2y = 0) using the method of converting to a linear system of first-order ODE's. Show that the coefficient matrix is the 3 x 3 matrix...
5. Find an LU-factorization for the matrix 1 0 2. -I o3 U-6 6. 26721 11-2ら 1"0141 ? 1 3 4 5 3 0 2 5 -20-2-6--10 1 0 4 3 3-312
Problem 8. (15 points) Find eigenvalues and eigenvectors of the follwing matrix 3 -2 0 A= -1 3-2 0 -1 3 Problem 8. (15 points) Find eigenvalues and eigenvectors of the follwing matrix 3 -2 0 A= -1 3-2 0 -1 3