Introduction to Ordinary Differential Equations (MAY514): Διαφορά μεταξύ των αναθεωρήσεων

Τελευταία αναθεώρηση της 15:09, 14 Αυγούστου 2024

Ελληνική Έκδοση
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Department of Mathematics
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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

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

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 === General ===
@@ Γραμμή 28: / Γραμμή 28: @@
 ! Course Title
 |
-Introduction to Differential Equations
+Introduction to Ordinary Differential Equations
 |-
 ! Independent Teaching Activities
@@ Γραμμή 59: / Γραμμή 59: @@
 ! 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:
+Bloom's Taxonomy.
-* 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
+(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 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
+Working independently and in groups. Production of free, creative and inductive thinking. Creative, analytic and synthetic thinking.
-* 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.
+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 ===