Integral Equations (MAE613)

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School of Science

Academic Unit

Department of Mathematics

Level of Studies


Course Code




Course Title

Integral Equations

Independent Teaching Activities

Lectures (Weekly Teaching Hours: 3, Credits: 6)

Course Type

Special Background

Prerequisite Courses -
Language of Instruction and Examinations


Is the Course Offered to Erasmus Students

Yes (in English)

Course Website (URL) See eCourse, the Learning Management System maintained by the University of Ioannina.

Learning Outcomes

Learning outcomes

The course aims to an introduction to the area of Integral Equations. Students are expected to obtain basic knowledge on standard types of integral equations, learn how to solve certain linear integral equations, also study existence and uniqueness of solutions by the use of fixed point theorems.

General Competences
  • Working independently
  • Team work
  • Production of free, creative and inductive thinking
  • Production of analytic and synthetic thinking


An introduction with historical notes. Classification of Integral Equations. Problems leading to integral equations. Laplace transformations and their use to solving integral equations. Other integral transformations. Volterra integral equations: Neumann series, successive approximations, Laplace transformation and the convolution kernel. Fredholm integral equations: Symmetric kernels, separated kernels, Fredholm Alternative, classical Fredholm theory. Green functions for second order boundary value problems. Existence and uniqueness of solutions: Banach spaces, contractions and applications to integral equations. Existence of solutions by Schauder's theorem.

Teaching and Learning Methods - Evaluation


Lectures. Presentations in class.

Use of Information and Communications Technology Use of the platform “E-course” of the University of Ioannina
Teaching Methods
Activity Semester Workload
Lectures/Presentations 39
Assignments 33
Individual study 78
Course total 150
Student Performance Evaluation

Students choose evaluation by one or both of the following:

  • Class presentation - Essays - Assingments
  • Final Written Examination

In case that a student participates to both, the final grade is the maximum of the two grades. Evaluation criteria and all steps of the evaluation procedure are accessible to students through the platform “E-course” of the University of Ioannina.

Attached Bibliography

See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:

  • Σ. Ντούγια, Ολοκληρωτικές Εξισώσεις
  • C. Corduneanu, Principles of Differential and Integral Equations