Engineering Sciences (XE) 2009

Let A and B be two similar square matrices of order two. If 1 and -2 are the eigenvalues of A, then the Trace of B is

The root of ax + b = 0 (a,b constants), can be found by the Newton-Raphson method with a minimum of

The solution u(x,t) of the one-dimensional heat equation, ∂u/∂t = α2∂2u/∂x2, x ∈ R with a Gaussian initial condition,

Let C be the boundary of the square given by 0 ≤ x ≤ 1, 0 ≤ y ≤ 1. Then ∮C (xdy − ydx) equals

Let the eigenvalues of a square matrix A of order two be 1 and 2. The corresponding eigenvectors are [0.6, 0.8] and [0.8, -0.6], respectively. Then, the element A(2,2) is

Let y1(x) and y2(x) be two linearly independent solutions of d2y/dx2 + 6 dy/dx + q(x)y = 0, x ∈ (1,3), where q(x) is a continuous function in (1,3). If the Wronskian of y1(x) and y2(x) at x = 1, denoted by W(y1, y2)(1), is 1, then W(y1, y2)(2) is