Final version.

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 8, be able to:



-- Discretize a parabolic PDE using 
     finite differences in space
     Euler, Backward Euler, or Crank-Nicolson in time.
  determine whether the discretization is stable,
  and write Matlab code to compute the solution.

-- Discretize a parabolic PDE using
     finite elements in space.
     Euler, Backward Euler, or Crank-Nicolson in time.
  determine whether the discretization is stable,
  and write Matlab code to compute the solution.

-- Evaluate a lumped mass matrix and explain why it
   is useful.

-- Solve the IBVP for the wave equation using eigenfunctions.

-- Determine the cone of influence for a point (x,t) for the
   wave equation.

-- Determine the inflow and outflow boundaries for a given 
   1st order scalar hyperbolic equation.

-- Use the method of characteristics to solve a given 
   1st order scalar hyperbolic equation.

-- Solve a symmetric hyperbolic system ("Case 1").

-- Use finite difference formulas to solve hyperbolic problems,
   choosing appropriate step lengths.

-- Explain and apply the CFL stability condition.

-- Apply the Galerkin finite element method  to the wave equation

-- Problem 1 from Homework 4, Part 1.
   Could we solve the discrete problem using Cholesky or cg?