Differential Equations (AN5): Διαφορά μεταξύ των αναθεωρήσεων
Χωρίς σύνοψη επεξεργασίας |
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[[ | * [[Διαφορικές Εξισώσεις (AN5)|Ελληνική Έκδοση]] | ||
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=== General === | === General === | ||
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|- | |- | ||
! Course Type | ! Course Type | ||
| | | Special Background | ||
|- | |- | ||
! Prerequisite Courses | ! Prerequisite Courses | ||
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! Learning outcomes | ! Learning outcomes | ||
| | | | ||
This course is aiming at familiarizing the students with a variety of advanced subjects related to differential equations. Both classical and modern subjects are studied. After attending this course, the students should be able to: | |||
* be familiar with a vast set of subjects related to differential equations, | |||
* start researching on subjects regarding the qualitative theory of differential equations, and | |||
* familiarize himself with the bibliography related to the subjects he was taught. | |||
|- | |- | ||
! General Competences | ! General Competences | ||
| | | | ||
* Working independently. | |||
* Team work. | |||
* Production of new research ideas. | |||
* Production of free, creative and inductive thinking. | |||
* Search for, analysis and synthesis of data and information, with the use of the necessary technology. | |||
* Develop critical thinking skills. | |||
|} | |} | ||
=== Syllabus === | === Syllabus === | ||
Second order linear ordinary differential equations: Sturm-type theorems, oscillation and non-oscillation theorems. Reducing differential equation problems to integral ones. Volterra integral equations: existence and uniqueness of solutions. Existence of solutions. The linear equation. The first order linear equation. Some problems on the semi-axis. Fredholm theory for linear integral equations: the resolvent kernel. The entire functions of Fredholm and their applications. Eigenvalues, eigenfunctions and conjugate functions. Some integral inequalities: Gronwall and Bihari Lemmas, and their applications. Delay differential equations: Introduction, Examples and the stepping method. Some remarkable examples and some "wrong" questions. Lipschitz condition and uniqueness for the basic initial problem. Notations and uniqueness for systems with bounded delay. Existence for systems with bounded delay. Linear delay differential systems: superposition. Fixed coefficients. Variation of parameters. Stability for delayed differential systems: Definitions and examples. Asymptotic stability. Linear and almost linear differential systems. Fractional differential equations: Definitions and basic calculus. Initial and boundary systems. Dynamical systems: definitions and calculus. Equations and problems. Various subjects. | |||
=== Teaching and Learning Methods - Evaluation === | === Teaching and Learning Methods - Evaluation === | ||
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! Delivery | ! Delivery | ||
| | | | ||
Lectures on class | |||
|- | |- | ||
! Use of Information and Communications Technology | ! Use of Information and Communications Technology | ||
| | | - | ||
|- | |- | ||
! Teaching Methods | ! Teaching Methods | ||
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| 39 | | 39 | ||
|- | |- | ||
| | | Exercises / Homework | ||
| | | 52.5 | ||
|- | |- | ||
| | | Autonomous Study | ||
| | | 96 | ||
|- | |- | ||
| Course total | | Course total | ||
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! Student Performance Evaluation | ! Student Performance Evaluation | ||
| | | | ||
The students can choose one of the following options: | |||
* Presentation in the class - Written homework - Exercises. | |||
* Written final exam. | |||
If both methods are used, then the final grade is the maximum of the two. The criteria regarding the grading are publised in the "E-Course" platform. | |||
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Τελευταία αναθεώρηση της 16:26, 15 Ιουνίου 2023
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General
| School | School of Science |
|---|---|
| Academic Unit | Department of Mathematics |
| Level of Studies | Graduate |
| Course Code | AN5 |
| Semester | 2 |
| Course Title | Differential Equations |
| Independent Teaching Activities | Lectures (Weekly Teaching Hours: 3, Credits: 7.5) |
| Course Type | Special 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 |
This course is aiming at familiarizing the students with a variety of advanced subjects related to differential equations. Both classical and modern subjects are studied. After attending this course, the students should be able to:
|
|---|---|
| General Competences |
|
Syllabus
Second order linear ordinary differential equations: Sturm-type theorems, oscillation and non-oscillation theorems. Reducing differential equation problems to integral ones. Volterra integral equations: existence and uniqueness of solutions. Existence of solutions. The linear equation. The first order linear equation. Some problems on the semi-axis. Fredholm theory for linear integral equations: the resolvent kernel. The entire functions of Fredholm and their applications. Eigenvalues, eigenfunctions and conjugate functions. Some integral inequalities: Gronwall and Bihari Lemmas, and their applications. Delay differential equations: Introduction, Examples and the stepping method. Some remarkable examples and some "wrong" questions. Lipschitz condition and uniqueness for the basic initial problem. Notations and uniqueness for systems with bounded delay. Existence for systems with bounded delay. Linear delay differential systems: superposition. Fixed coefficients. Variation of parameters. Stability for delayed differential systems: Definitions and examples. Asymptotic stability. Linear and almost linear differential systems. Fractional differential equations: Definitions and basic calculus. Initial and boundary systems. Dynamical systems: definitions and calculus. Equations and problems. Various subjects.
Teaching and Learning Methods - Evaluation
| Delivery |
Lectures on class | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Use of Information and Communications Technology | - | ||||||||||
| Teaching Methods |
| ||||||||||
| Student Performance Evaluation |
The students can choose one of the following options:
If both methods are used, then the final grade is the maximum of the two. The criteria regarding the grading are publised in the "E-Course" platform. |
Attached Bibliography
- C. Corduneanu, Principles of Differential and Integral Equations
- R. D. Driver, Ordinary and Delay Differential Equations
- T. A. Burton, Volterra Integral and Differential Equations
- R. K. Miller, Nonlinear Volterra Integral Equations
- P. Hartman, Ordinary Differential Equations
- Κ. Diethelm, The Analysis of Fractional Differential Equations
- Y. Zhou, Basic Theory of Fractional Differential Equations
- M. Bohner and A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications.