Ordinary Differential Equations I (MAE614)
General
School |
School of Science |
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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) | -
Course description: https://math.uoi.gr
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Learning Outcomes
Learning outcomes |
Learning outcomes according to Bloom Taxonomy: Remembering: # The notion of a system of first order differential equations. # The notion of a linear system of differential equations. # The notion of a homogenous linear system of differential equations. # The notion of a fundamental set of solutions for a system of differential equations. # The notion of the fundamental matrix of a system of differential equations. # The characteristic polynomial for a system of differential equations with constant coefficients. # Similarity of matrices. # Jordan canonical form. # The notion of autonomous systems. # The notion of the phase space. # The notion of the critical point for a system of differential equations. # The notion of the proper node, the improper node, the saddle point and the spiral point for the phase space. # The notion of stability for systems of differential equations. # The notion of the equilibrium point. # The notions of the asymptotic stability and the instability of equilibrium points. # The notion of asymptotic equivalence of systems of differential equations. # The notion of the dynamical system. Comprehension: # Conditions for the existence of solutions for a differential equation. # Conditions for the uniqueness of the solution for a differential equation. # Finding the maximum domain of the solutions for a differential equation. # Conditions for the existence of solutions for a system of differential equations. # Conditions for the uniqueness of the solution for a system of differential equations. # Finding the maximum domain of the solutions for a system of differential equations. # The Gronwall inequality. # The method known as “variation of constants” for solving systems of differential equations. # Study of the asymptotic behaviour of solutions of systems of differential equations. # Study of autonomous systems. # Finding the phase space for solutions of systems of differential equations. # Study of linear systems of differential equations with periodic coefficients. # Dependence of the solutions of systems of differential equations on the initial conditions. # Study of the stability for systems of differential equations. # Using the Lyapunov method in order to study the stability of systems of differential equations. # Studying dynamical systems. Applying: # Studying oscillations which do not tend toward a state of rest. # Studying the motion of a pendulum. # Studying predator - prey models. Evaluating: Teaching undergraduate and graduate courses. |
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General Competences |
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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 |
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Use of Information and Communications Technology | -
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Teaching Methods |
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Student Performance Evaluation |
Language of evaluation: Greek and English. Methods of evaluation:
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Attached Bibliography
(see Eudoxus)