Es ist eine neuere Version 2024W dieser LV im Curriculum Master's programme Computational Mathematics 2024W vorhanden.
Workload
Education level
Study areas
Responsible person
Hours per week
Coordinating university
6 ECTS
M1 - Master's programme 1. year
Mathematics
Ronny Ramlau
4 hpw
Johannes Kepler University Linz
Detailed information
Original study plan
Master's programme Industrial Mathematics 2003W
Objectives
Obtaining a basic understanding of linear integral equations of the second kind.
Subject
This course deals with analytic and numerical aspects of linear integral equations, with an emphasis on Fredholm- and Volterra equations of the second kind. For this we consider the so-called Fredholm theory, the theorems of Riesz, and the spectral decomposition of compact linear operators. Furthermore, we familiarize ourselves with different numerical solution methods for these equations. In the second part of the course we learn about the Sturm-Liouville theory for initial- and boundary-value problems of the second kind with variable coefficients. These problems can again be treated via integral equations, which in turn leads us to the theory of Green functions and operators for their solution.
Criteria for evaluation
Oral exam after appointment at the end of the course
Methods
Blackboard presentation
Language
German or English
Study material
R. Kress: Linear Integral Equations, Springer, Berlin, 1989.
