Note: Some of the material referenced below is copyrighted, and hence is not generally available by clicking on it. Please email me, rbk@louisiana.edu, and I will email you either a Postscript or a PDF copy of the appropriate excerpts, according to the ``fair use" provision of the copyright law.
Topic no.  Description  Explanation / References / Projects 
1.  Review of the first semester and outlook for this semseter. 

2.  Review of (or introduction to) underlying functional analysis concepts (This topic may take several class periods.)  Parts of chapters 1 through 12 of R. E. Moore, An Introduction to Numerical Functional Analysis, Halsted Press (1985) 
3.  Contraction mappings and fixed point iterations in function spaces  Chapter 15 of R. E. Moore 
4.  Frechét derivatives  Chapter 16 of R. E. Moore 
5.  Newton's method in Banach spaces  Chapter 17 of R. E. Moore 
6  Example of a simple iteration method in an infinitedimensional space  Chapter 8 of Ole Stauning's Ph.D. dissertation 
7.  Introduction to Green's functions  See the web page at http://www.boulder.nist.gov/div853/greenfn/tutorial.html 
8..  A review of more sophisticated methods for elliptic boundary value problems  M. Plum, "Inclusion Methods for Elliptic Boundary Value Problems,"
in Topics in Validated Computations, ed. J. Herzberger, NorthHolland,
1994.
(Copies to be supplied.) 
9.  More on the solution of integral equations  L. B. Rall, "Application of Interval Integration to the Solution of Integral Equations," J. Integral Equations 6, pp. 127141 (1984) (copies will be supplied) 
10.  Miscellaneous additional applications  Note: Some of these are finitedimensional, and may be presented before
topics 18 above.
Parametric Surfaces Using Interval Arithmetic", The Visual Computer, International Journal of Computer Graphics, 10 (7), pp. 363371 (1984). 