Introduction to Ordinary Differential Equations (MAY514)

Undergraduate Courses Outlines - Department of Mathematics

General

School	School of Science
Academic Unit	Department of Mathematics
Level of Studies	Undergraduate
Course Code	ΜΑΥ514
Semester	5
Course Title	Introduction to 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)	Through the platform “e-course” of the University of Ioannina

Learning Outcomes

Learning outcomes	The course is the introductory course to ordinary differential equations and aims to a general introductory description of the area of ordinary differential equations. It is expected that the students take basic knowledge on: How to solve linear ordinary differential equations of first order and some equations of special types. Existence and uniqueness of solutions to ordinary differential equations General theory of linear o.d.e. How to solve linear equations and systems with constant coefficients. How to solve linear o.d.e. of second order by the use of power series. Use of Laplace transformations to solve o.d.e.. How to solve first order linear partial differential equations.
General Competences	Working independently Production of free, creative and inductive thinking Analytic and synthetic thinking

Syllabus

Introduction to differential equations and initial value problems. O.d.e.’s of some special types (Bernoulli, Riccati, Clairaut, Lagrange). Equations with separated variables. Exact equations. Integral factors. Second order equations reduced to first order equations. Existence and uniqueness theorems. General theory of linear o.d.e.’s. Linear equations and systems with constant coefficients. Power series solutions for second order d.e.’s. Partial differential equations: solutions to first order equations, classification of linear equations of second order. Applications of d.e.’s to problems arising in various areas of science and technology.

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

Activity	Semester Workload
Lectures	45
Assignments/Tests	52.5
Individual study	90
Course total	187.5

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. Additionally:

Χ. Φίλος, Μία Εισαγωγή στις Διαφορικές Εξισώσεις
R. Agarwal, D. O’Regan, H. Agarwal, Introductory Lectures on Ordinary Differential Equations
F. Ayres, Differential Equations