Introduction to Integral Equations in Visual Computing
Lecturer:
Dr. Bernhard Burgeth
Office Hours: Tuesday: 15:0016:00.
Summer term 2008
Lectures (2h) with exercises and assignments (2h);
6 ECTS points
Lectures: Thursday, 1012 c.t., Building E13,
Lecture Hall 001
First lecture: Thursday, April 17th, 2008
Tutorials: Monday, 1618 c.t., Building E13,
Seminar Room 014, see below
First tutorial: Monday, April 21st, 2008
Results of the written exam are available on a list attached to the black board
at the entrance of the floor of the MIA group in building E1 1.
Each participant has been informed about his individual results by email.
Opportunity for exam inspection:
Tuesday, August 19th, 14:00  15:00, Room 3.06, Bld. E1 1
Opportunity for oral exam: First Info!
Prerequisites –
Synopsis –
Tutorials –
Exams –
Material for Assignments –
Literature
This course is suitable for students of mathematics , physics or computer
science who completed their undergraduate studies in mathematics.
Knowledge of functional analysis or image processing is
helpful but not required. The lectures will be given in English.
Hence passive knowledge of English is necessary.
The lectures are given in English.
Integral equations are an important tool to model evolution
processes from physics, engineering, and biology.
As the name already indicates an integral equation involves
integrals of an unknown function u one
wishes to solve for.
In the lectures we will concentrate on
linear Fredholm and Volterra integral equations of the second type.
After theoretical considerations concerning existence and uniqueness
of solutions we will discuss numerical aspects of these equations.
Usually the treatment of equations of the first type is
more involved. Hence we convey in this introductory course
only the basic facts about this type of equations.
Among the numerous applications of integral equations
we restrict ourselves to two fields:
 integrodifferential equations in image processing, and
 computer tomography, a medical image acquisition technique.
After Appointment.
The tutorials include assignments that provide important
additional mathematical insights.
The tutorials are conducted by the lecturer.
The first exam has taken place in the lecture hall 001,
bldg. E1 4 on July 17th, 2008 from 10:15 to 11:45.
Each student qualified to participate in the first exam will have an
opportunity for an oral exam at September 30th, 2008.
The better grade counts.
Further details will follow.
Participants of the course can download the assignments.
Homework:
Classroom assignments:
There are numerous books on Integral Equations. We will not
follow a specific one, but most topics are treated in one
of the following samples:
 Heinz Engl:
Integralgleichungen,
Springer, Wien, 1997.
 W. Hackbusch:
Integralgleichungen, Theorie und Numerik,
Teubner, Stuttgart, 1989.
 R. Kress:
Linear Integral Equations,
SpringerVerlag, Berlin, 1989.
These and further books can be found in the computer science library.
