Hints for Assignment 3
Problem 1:
Use my instructions for the Laplace transform (rather than the instructions in the Matlab supplement).

Use the command setcurve (see explanation) to plot f(t) and y(t) in a different style.

Problem 2:
Use a command like A=sym([5,6;7,8]) to define the matrices (otherwise eig will give numerical, not symbolic results). Use [eigvect,eigval]=eig(A) to find eigenvalues, eigenvectors. To find ``generalized eigenvectors'': w=A\b gives a solution of the linear system with matrix A and right hand side vector b (even if A is a singular matrix).

For vectfield, ode45: you can define the inline function like g=inline('[5,6;7,8]*y','t','y').

For each starting point compute and plot trajectories both forward and backward in time, as explained on the page for autonomous systems.

Problem 3:
Use my instructions for autonomous systems (rather than the instructions in the Matlab supplement). As explained there, compute trajectories starting at a point both forward and backward in time. For the vector field, use the command vectfieldn which draws arrows with the same length. This makes it easier to see the direction of the vector field. You must first save the commands vectfield.m and vectfieldn.m in your home directory.

Plot the separatrix in a different style, e.g., using setcurve (see explanation).