(This file is now complete.)

The quiz will cover the last piece of the ODE-BVP notes,
Part 1 of the Elliptic notes and the first 4 pages of 
Part 2 of the Elliptic notes.

For Quiz 3, be able to:

-- Construct a finite difference or finite element approximation
   to a given ODE-BVP.

-- Use the discrete maximum principle.

-- Use the error formulas to draw conclusions about how
   fast the error will decrease.

-- Compare and contrast finite difference and finite element
   methods for solving ODE-BVPs.  For example:

    -- Which requires less work to form and solve the
       linear system?

    -- Which should be used if we want to compute an
       approximation to u'?

    -- For each method, what can we do if we decide
       that we need to reduce the error? (reduce h?
       increase the order of approximation?)

-- Apply the Maximum Principle and the Minimum Principle
   to draw conclusions about the behavior of the solution 
   to an elliptic PDE.

-- Use Theorem 3.2.

-- Define uniqueness and stability of the solution of an elliptic
   PDE

-- Determine the solution to an elliptic PDE given its Green's function.

-- Derive the weak form of the problem from the strong.

-- Determine the regularity of a solution to an elliptic PDE.

-- Solve Unquiz 1 in Part 2 of the Elliptic notes.

-- Be able to form a finite difference approximation to
   an elliptic problem on a rectangular or L-shaped
   domain.  (In other words, extend Quiz 1 to a rectangular
   or L-shaped domain.)

-- Determine the sparsity pattern of the matrix in
   Unquiz 2 in Part 2 and understand how the matrix entries
   are formed.
   (Example: what is the domain of integration
    for the matrix entry A(6,7)?)

-- Be able to form a finite element approximation to
   an elliptic problem on a polygonal domain.  (In
   other words, extend Quiz 2 to a polygonal domain.)

-- Determine whether a given triangulation is admissible.