Computational integro-differential algebra
Clemens Raab and Georg Regensburger
In this course, we will mainly learn about algebraic algorithms for linear ordinary differential equations (ODE). The focus will be on the symbolic treatment of corresponding initial value problems and boundary value problems. In particular, we will learn how to
- compute with integro-differential operators,
- compute the Green’s operator of a linear ODE, and
- how to decompose boundary value problems into simpler ones.
The necessary foundations from differential algebra, symbolic integration, and non-commutative algebras will also be provided.
Students should be familiar with basic algebraic notions such as rings, fields, polynomials, vector spaces, and determinants. Also basic knowledge from ordinary differential equations and calculus is needed.
Grading will be based on small individual projects, which are to be presented after the end of the course.
Related topics for master theses are available in the frame of our research project.
Weekly lectures: Thursdays, 13:45 – 15:15, MT 130 (Science Park 1)