Ordinary Differential Equations II (MAE716): Διαφορά μεταξύ των αναθεωρήσεων
(3 ενδιάμεσες αναθεωρήσεις από τον ίδιο χρήστη δεν εμφανίζεται) | |||
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=== Syllabus === | === Syllabus === | ||
Section 1. Functional differential equations: Reasons of existence of such equations, Existence and uniqueness of their solutions, Finding solutions, Stability, Linear and non-linear systems. Section 2. Integral equations: Reasons of existence of such equations, Fredholm equations, Volterra equations, Integral-difference equations, Abel problem, Non-linear integral equations. Section 3. Difference equations: Reasons of existence of such equations, Finding the formula of solutions for linear difference equations, Linearization, Systems of difference equations, Stability using the Lyapunov method. | |||
Section 1. Functional differential equations: Reasons of existence of such equations, Existence and uniqueness of their solutions, Finding solutions, Stability, Linear and non-linear systems. Section 2. Integral equations: Reasons of existence of such equations, Fredholm equations, Volterra equations, | |||
=== Teaching and Learning Methods - Evaluation === | === Teaching and Learning Methods - Evaluation === |
Τελευταία αναθεώρηση της 01:58, 16 Αυγούστου 2024
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General
School |
School of Science |
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Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE716 |
Semester |
7 |
Course Title |
Differential Equations I |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Language of Instruction (lectures): Greek
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Is the Course Offered to Erasmus Students |
Yes |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
Bloom's Taxonomy. (1) Remembering: The notion of functional differential equation, of integral equation, of integral-differential equation and of difference equation. The notion of solutions of such equations, of uniqueness of such solutions and of stability of such solutions. The notion of solutions of systems of difference equations. (2) Comprehension: Study of solutions of functional ODE's, of integral equations and of difference equations. Methods of finding such solutions and of studying their stability. Study of systems of such equations. (3) Applying: Study related real world problems. (4) Evaluating: Teaching secondary school courses. |
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General Competences |
Working independently and in groups. Production of free, creative and inductive thinking. Creative, analytic and synthetic thinking. |
Syllabus
Section 1. Functional differential equations: Reasons of existence of such equations, Existence and uniqueness of their solutions, Finding solutions, Stability, Linear and non-linear systems. Section 2. Integral equations: Reasons of existence of such equations, Fredholm equations, Volterra equations, Integral-difference equations, Abel problem, Non-linear integral equations. Section 3. Difference equations: Reasons of existence of such equations, Finding the formula of solutions for linear difference equations, Linearization, Systems of difference equations, Stability using the Lyapunov method.
Teaching and Learning Methods - Evaluation
Delivery |
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Use of Information and Communications Technology |
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Teaching Methods |
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Student Performance Evaluation |
Language of evaluation: Greek and English. Methods of evaluation:
In any case, all students can participate in written exams at the end of the semester, during the exams period. The aforementioned information along with all the required details are available through the course's website. The information is explained in detail at the beginning of the semester, as well as, throughout the semester, during the lectures. Reminders are also posted at the beginning of the semester and throughout the semester, through the course's website. Upon request, all the information is provided using email or social networks. |
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:
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