Lecturer(s)


Holeček Pavel, Mgr. Ph.D.

Rohleder Martin, Mgr.

Rachůnková Irena, prof. RNDr. DrSc.

Course content

1. Classification of integral equations. 2. Fredholm linear homogeneous and nonhomogeneous integral equations. 3. Relationship with linear algebraic systems. 4. Relationship with linear boundary value problems for differential equations. 5. Integral equations with degenerated kernel. 6. Fredholm operator. Fredholm perturbation of the identity operator. 7. Fredholm theorems. 8. Integral equations with small kernel. Resolvent. 9. Method of iterated kernels. 10. Integral equations with symmetric kernel. 11. HilbertSchmidt operator and its properties.

Learning activities and teaching methods

Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming)
 Attendace
 39 hours per semester
 Homework for Teaching
 20 hours per semester
 Preparation for the Exam
 60 hours per semester

Learning outcomes

Understand basic elements of the theory of linear integral equations and methods of their solving.
Comprehension Differentiate between various types of integral equations, describe and prove their properties and determine their solutions.

Prerequisites

Knowledge of basis of the theory of Differential Equations and Linear Functional Analysis.

Assessment methods and criteria

Oral exam, Student performance
Credit: active participation in seminars. Exam: to know and to understand the subject and to be able to apply it on standard examples.

Recommended literature


A. J. Jerri. (1999). Introduction to Integral Equations with Applications. Willey&Sons.

P. Drábek. (1991). Integrální rovnice. MVŠT, sešit XXXI, SNTL Praha.
