Introduction to Ordinary Differential Equations (MAY514)

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• 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)	See eCourse, the Learning Management System maintained by 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. 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