Math 641-600 Test 2 Review
The structure of the test will be the same as that used for Test
1. The test covers these sections from the text: 3.3-3.6, 4.1, 4.2,
4.3.1, 4.3.2, 4.5.1, 4.5.2, 5.1. In addition, it will cover the notes
on the 1D
Sobolev Theorem and on the pointwise
convergence of Fourier Series. You will be asked to state a few
definitions, possibly including terms introduced in class -
accumulation point, resolvent set, spectrum -, and to do problems
similar to
assigned or
suggested homework problems and examples done in class. In
addition, you will be asked to give a proof or sketch a proof for a
major theorem from the list below.
- Be able to show that the operator-norm limit of compact operators
is compact.
- Any part of the spectral theory for compact, self-adjoint
operators. See your class notes for 10/26/05 and 10/28/05.
- The contraction mapping theorem
- Any part of the spectral theory for compact, self-adjoint
operators. See your class note for 10/26/05 and 10/28/05.
- Be able to sketch the proof of the pointwise convergence of
Fourier series,at least for piecewise continuous functions
- Be able to sketch the proof of the 1D Sobolev Theorem
Updated 12/9/05 (fjn).