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Integralgleichungen / Integral Equations (Summer Semester 2012)

  • Lecturer: PD Dr. Frank Hettlich
  • Classes: Lecture (0156900), Problem class (0157000)
  • Weekly hours: 4+2
  • Audience: Mathematics (6.-10. semester)

This is a class for students of any mathematics programm. Topics include integral equations of the second kind and their solution theory, the so-called Riesz-Fredholm theory. Furthermore a topic will be the Fourier transform and convolution equations.

A prerequesite to understand the material of this class are the basic lectures of the Bachelor in Mathematics. Necessary results from functional analysis will be discussed in the lecture. In fact, this class can be seen as an expansion and application of the concepts and methods of functional analysis.

Optionally, the lecture will be given in English

Lecture: Monday 9:45-11:15 Z1 Begin: 16.4.2012, End: 18.7.2012
Thursday 9:45-11:15 Z1
Problem class: Monday 15:45-17:15 Z1 Begin: 16.4.2012, End: 16.7.2012

On the content of the lecture

Besides the differential equations also integral equations are important mathematical concepts in physical, technical or medical applications. The formulation of boundary value problems by integral equations are often of theoretical interest (existence and uniqueness of solutions) as well as a basis of efficient numerical solution schemes. The lecture and the exercise session will give an introduction to a functional analytic approach to linear integral equations. We will discuss fundamental typs like Volterra equations, Fredholm equations and convolution equations.

problem sheets

Additionally there will be problem sheets and an exercise session, where we work on the problems. Afterwards also suggestions of solutions to the problems will be offered.

Problem sheetThemen
Problem sheet 1 ODE <-> IEQ
Problem sheet 2 completion, resolvent
Problem sheet 3 compact sets, compact operators
Problem sheet 4 compact operators, Riesz number
Problem sheet 5 dual systems
Problem sheet 6 Fredholm's alternative
Problem sheet 7 Hilbert spaces, proejection theorem
Problem sheet 8 adjoint operators, spectrum
Problem sheet 9 eigenvalues, eigenfunctions
Problem sheet 10 the neumann problem
Problem sheet 11 Fourier transformation
Problem sheet 12 convolution operators

There are solutions to the problems available in German. Please consider the German version of this page

Skriptum (pdf-Dateien)

Presumably, a lecture note will be available here by the end of the semester.


H. Engel Integralgleichungen Springer, 1997
H. Hochstadt Integral Equations Wiley, 1973
W. Hackbusch Integralgleichungen Teubner, 1989
K. Joergens, Lineare Integraloperatoren Teubner, 1971
R. Kress Linear Integral equations Springer, 1989
W. McLean Strongly Elliptic Systems and Boundary Integral Equations Cambridge University Press, 1999