Course: Integral Equations

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Course title Integral Equations
Course code KMA/IR
Organizational form of instruction Lecture + Exercise
Level of course Master
Year of study not specified
Semester Winter
Number of ECTS credits 4
Language of instruction Czech
Status of course Compulsory, Compulsory-optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
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. Hilbert-Schmidt 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.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Science General Physics and Mathematical Physics (2014) Physics courses 1 Winter
Faculty of Science Applied Mathematics (2014) Mathematics courses 1 Winter