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Home page for the course
|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 infinite-dimensional 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, North-Holland,
(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. 127-141 (1984) (copies will be supplied)|
|10.||Miscellaneous additional applications||Note: Some of these are finite-dimensional, and may be presented before
topics 1-8 above.
Parametric Surfaces Using Interval Arithmetic", The Visual
Computer, International Journal of Computer Graphics, 10 (7), pp. 363-371 (1984).