Integral Equations (MAE613)

Undergraduate Courses Outlines - Department of Mathematics

General

School	School of Science
Academic Unit	Department of Mathematics
Level of Studies	Undergraduate
Course Code	MAE613
Semester	6
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	Greek
Is the Course Offered to Erasmus Students	Yes (in English)
Course Website (URL)	- Through the platform “E-course” of 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

Syllabus

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

Delivery	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

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