Computer Analysis

Tue, 14:30-16:00, HS 17 (first meeting) and K 012D (rest of the semester). The final exam is a take home exam. The assignment can be downloaded here. If you want to participate, submit your solutions by email to Veronika Pillwein no later than Friday, July 15, 2022.

The lecture will be held in English.

• Update: in Task 5 it was missing that there is no P-finite differential equation that is satisfied by exp(exp(x)) - there is of course a linear differential equation satisfied by exp(exp(x)). Thanks for pointing this out!

The goal of the course is to understand the underlying principles of algorithms typically used in computer algebra systems for computing closed forms of integrals, or for solving differential equations. Participants are expected to be acquainted with the basic notions from analysis (differentiation, integration, power series expansions, etc.) and linear algebra (finite dimensional vector spaces, solving linear systems of equations, etc.). It might be an advantage, although it is not a formal requirement, to do the courses computer algebra and/or algorithmic combinatorics (or computer algebra for concrete mathematics) before this course.

Related literature:

• Bronstein: Symbolic Integration I, Transcendental Functions
• von zur Gathen, Gerhard: Modern Computer Algebra
• Geddes, Czapor, Labahn: Algorithms for Computer Algebra
• Winkler: Polynomial Algorithms in Computer Algebra

Veronika Pillwein