**Symbolic Functional Analysis**

### Winter Semester 2005/2006

#### Markus.Rosenkranz@oeaw.ac.at

*Semester:* 5th

*Time:* Mondays 10:15 - 11:45

*Location:* HF9905

*First Lecture:* October 10
This lecture will give an overview of a highly exciting and
brand new field of symbolic computation that could be baptized
**Symbolic Functional Analysis**. Roughly speaking, it could
be characterized as the algorithmic analysis of operator
problems. As a whole, symbolic computation can be partitioned
into three levels: Starting out with algebraic algorithms for
numbers (traditional "computer algebra"), it proceeds to
algebraizing functions (often called "computer algebra"), which
is then continued by the symbolic treatment of operator problems
("symbolic functional analysis"). Of course, this hierachy is
solely meant in terms of its fundamental types: Number,
Number->Number and
(Number->Number)->(Number->Number); this does not imply
any grading in terms of difficulty.

After building up and clarifying the required algebraic tools,
we will turn to studying various kinds of **operator
algebras**. In this lecture, we will focus mainly on linear
boundary value problems, including a complete solution algorithm
for the ODE case.

The lecture notes for this course can be found here
as a Mathematica notebook. Additionally, there
is also a short summary of the chapter on Green's Polynomials in the form of
Mathematica slides.