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School of Science
Department of Mathematics
|Level of Studies||
|Independent Teaching Activities||
Lectures (Weekly Teaching Hours: 3, Credits: 6)
|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.|
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.
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|
|Student Performance Evaluation||
Students choose evaluation by one or both of the following:
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.
- Σ. Ντούγια, Ολοκληρωτικές Εξισώσεις
- C. Corduneanu, Principles of Differential and Integral Equations