1. During the quiz you may use your textbook, my notes, scribed notes, and your own notes. 2. No calculators or other electronic devices are permitted. 3. Please make sure your cell phones are quiet during class and off during quizzes. For Quiz 6, be able to: -- Do the unquizzes in the ODE notes -- Use Taylor series to determine the accuracy of a numerical method for ODEs. -- Determine whether a numerical method for ODEs is stable. -- Verify some of the properties of Fourier transforms when d=1. -- Use the Fourier transform to solve a pure IVP parabolic equation. -- Explain why the heat equation is well posed but the backward heat equation is not. -- Explain the smoothness property of solutions to the heat equation (IVP and IBVP). -- Solve an IBVP for a parabolic equation using eigenfunctions. -- Write a parabolic problem in weak form. -- Use the maximum principle. -- Discretize a parabolic PDE using finite differences in space, with Euler, Backward Euler, or Crank-Nicolson in time; determine whether the discretization is stable; and write Matlab code to compute the solution.