Assignment 3, due Thu, Nov. 16.

Problem 1: Use Solving ODEs using the Laplace Transform in Matlab
Problem 2(a): I will use the matrix A=[1 -1;2 4] as an example here: Use [V,D] = eig(sym([1 -1; 2 4])) to find eigenvalues and eigenvectors: The columns of V are the eigenvectors, the diagonal elements of D are the eigenvalues.
Problem 2(b): Use [y1,y2] = dsolve('Dy1 = 1*y1+(-1)*y2', 'Dy2 = 2*y1+4*y2', 't') as explained in Using Matlab for Systems of ODEs.
Problem 2(c): Define the inline function f as f = inline('[1 -1;2 4]*y','t','y') and use Plotting a Phase Portrait of an Autonomous System.