1.  During the quiz you may use your textbook, my 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 4, be able to:

-- Set up finite element equations using piecewise quadratic
   approximations to the true solution.

-- Use the error bounds for finite element computations:
     If I reduce h by a factor of 2, how would you expect
        the error to change?
     How might I decide which triangles to refine 
        in an adaptive mesh computation?

-- Use the vertices of a triangle to evaluate basis
   functions that are nonzero within the triangle.

-- Assemble a stiffness matrix.

-- Use the barycentric integration rule to compute a 
   contribution to a matrix entry.

-- Evaluate an error indicator R_K.

-- Verify that a given vector is the eigenvector of a
   given matrix and compute the corresponding eigenvalue.

-- Verify that a given function is the eigenfunction of a
   given differential operator and compute the corresponding 
   eigenvalue.

-- Express the solution u to a differential equation Au=f
   as a linear combination of eigenfunctions.
   (So, given the eigenfunctions phi_j of A, 
   write u = alpha_1 phi_1 + alpha_2 phi_2 + ...
   and solve for the parameters alpha by using the
   function f.)

-- Express a given function in a given orthonormal basis.

-- Use monotonicity to compute upper and lower bounds
   on eigenvalues, given eigenvalues for inscribed and
   circumscribed regions.