Introduction to Ordinary Differential Equations (MAY514)
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General
| School |
School of Science |
|---|---|
| Academic Unit |
Department of Mathematics |
| Level of Studies |
Undergraduate |
| Course Code |
ΜΑΥ514 |
| Semester | 5 |
| Course Title |
Introduction to Ordinary Differential Equations |
| Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 5, Credits: 7.5) |
| Course Type |
General Background |
| Prerequisite Courses | - |
| Language of Instruction and Examinations |
Greek |
| 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 linear and non-linear ODE. The notion of existence of solutions and uniqueness of solutions for a linear and non-linear ODE. The notion of stability for a linear ODE, for a system of linear ODE's and for a vector linear ODE. (2) Comprehension: Study the existence and uniqueness of solutions of a ODE. Methods for finding the formula of the general solution of an linear ODE and studying their stability. Study systems of linear ODE's. (3) Applying: Study related real world problems. (4) Evaluating: Teaching secondary school courses. |
|---|---|
| General Competences |
Working independently and in groups. Production of free, creative and inductive thinking. Creative, analytic and synthetic thinking. |
Syllabus
Section 1. Introduction: Study specific, not necessarily linear, ODE's (Indicatively first order linear, Bernoulli, Riccati), Existence and uniqueness of solutions for first order, not necessarily linear, ODE's (Indicatively Peano Theorem).
Section 2. Study linear ODE's: Methods of calculating formulas of solutions (Method of undetermined coefficients, method of variation of parameters, power series solutions, Laplace transformation), Phase plane, Stability, Transforming a system of ODE's to a vector ODE.
Teaching and Learning Methods - Evaluation
| Delivery |
Face-to-face (Lectures) | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Use of Information and Communications Technology |
The platform “e-course” of the University of Ioannina | ||||||||||
| Teaching Methods |
| ||||||||||
| Student Performance Evaluation |
Written Final Examination (Theory and Exercises) 100% |
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:
- Χ. Φίλος, Μία Εισαγωγή στις Διαφορικές Εξισώσεις
- R. Agarwal, D. O’Regan, H. Agarwal, Introductory Lectures on Ordinary Differential Equations
- F. Ayres, Differential Equations