Ordinary Differential Equations I (MAE614)

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General

School	School of Science
Academic Unit	Department of Mathematics
Level of Studies	Undergraduate
Course Code	MAE614
Semester	6
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 Language of Instruction (activities other than lectures): Greek and English Language of Examinations: Greek and English
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

Remembering: The notion of nonlinear ordinary differential equations. The notion of initial and boundary value problems. The notion of systems of ordinary differential equations. The notion of solutions and stability for systems of ordinary differential equations. Comprehension: Studying nonlinear ordinary differential equations. Studying initial and boundary value problems. Studying systems of ordinary differential equations. Studying solutions and stability for systems of ordinary differential equations. Applying: Studying natural phenomena using the aforementioned notions. Evaluating: Teaching undergraduate and graduate courses.

General Competences

Creative, analytical and inductive thinking. Required for the creation of new scientific ideas. Working independently. Working in groups. Decision making.

Syllabus

This course is designed to be the continuation of the compulsory course “Introduction to Differential Equations” and is comprised of two main, closely related parts. The first part consists of the study of ordinary differential equations regarding their qualitative properties. The second part studies the methods of solving as well as the study of the qualitative properties of systems of ordinary differential equations.
In the first part, initial value problems for ordinary differential equations are studied regarding the existence, uniqueness, continuation and dependence on the initial conditions of their solutions.
The second part consists of the study of systems of ordinary differential equations. Specifically, this part studies the existence and the uniqueness of solutions, algorithms for finding solutions of specific forms of such systems, the phase space and the stability of solutions. Also, the well-known Lyapunov Theorems are presented.
For each part, specific real-life applications are presented.

Teaching and Learning Methods - Evaluation

Delivery	Lectures in class. Teaching is assisted by Learning Management System. Teaching is assisted by the use of online forums where students can participate in order to improve their problem solving skills, as well as their understanding of the theory they are taught. Teaching is assisted by the use of pre-recorded videos.
Use of Information and Communications Technology	Use of Learning Management System, combined with File Sharing Platform as well as Blog Management System for distributing teaching material, submission of assignments, course announcements, gradebook keeping for all students evaluation procedures, communicating with students. Use of Appointment Scheduling System for organising appointments between students and the teacher. Use of Survey Web Application for submitting anonymous evaluations regarding the teacher. Use of Wiki Engine for publishing manuals regarding the regulations applied at the exams processes, the way teaching is organized, the grading methods, as well as the use of the online tools used within the course.
Teaching Methods	Activity Semester Workload Lectures (7x3) 21 Seminars (6x3) 18 Individual study 78 Exrecises/projects 33 Course total 150
Student Performance Evaluation	Language of evaluation: Greek and English. Methods of evaluation: Weekly written assignments. Few number of tests during the semester. Based on their grades in the aforementioned weekly assignments and tests, limited number of students can participate in exams towards the end of the semester, before the beginning of the exams period. 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: