Fundamentals of Numerical Analysis and Symbolic Computation: Symbolic Integration

Lecturer: Dr. Clemens Raab

Lecture no.: 326.003

ECTS: 3.00, hours: 2.0

Time and place: Tue 10:15-11:45, room S2 054

First lecture: 7 March 2017

Abstract: Doing numeric computations, integration is easy (in the sense of numeric stability) and differentiation is hard (unstable). Computing with symbolic expressions, however, the situation is reversed: based on the product rule and the chain rule it is easy to obtain a symbolic expression for the derivative of a given function, whereas computing an expression for the integral usually requires more complicated algorithms. After explaining basic ways to represent functions in algebraic terms capturing their differential properties, the course will be centered around modern extensions of Risch's algorithm. These algorithms can deal with a large class of integrands involving special functions for symbolic computation of integrals. In addition to computing closed form antiderivatives, they can also find linear relations for parameter integrals.