Partial Differential Equations (AN6): Διαφορά μεταξύ των αναθεωρήσεων
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=== General === | === General === | ||
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|- | |- | ||
! Course Code | ! Course Code | ||
| | | AN6 | ||
|- | |- | ||
! Semester | ! Semester | ||
| | | 2 | ||
|- | |- | ||
! Course Title | ! Course Title | ||
| | | | ||
Partial Differential Equations | |||
|- | |- | ||
! Independent Teaching Activities | ! Independent Teaching Activities | ||
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|- | |- | ||
! Prerequisite Courses | ! Prerequisite Courses | ||
| | | | ||
Vector Analysis (undergraduate), Real Analysis, Functional Analysis | |||
|- | |- | ||
! Language of Instruction and Examinations | ! Language of Instruction and Examinations | ||
| | | | ||
Greek | |||
|- | |- | ||
! Is the Course Offered to Erasmus Students | ! Is the Course Offered to Erasmus Students | ||
| Yes | | | ||
Yes (in English) | |||
|- | |- | ||
! Course Website (URL) | ! Course Website (URL) | ||
Γραμμή 49: | Γραμμή 54: | ||
! Learning outcomes | ! Learning outcomes | ||
| | | | ||
The course, apart from the instruction in the classical quartet of Partial Differential Equations (PDEs) (transport, Laplace, heat and wave) in several space variables, aims, first, to highlight the modern, analytic approach to the theory of PDEs and the reasons that suggest it, and, second, to provide an introduction to nonlinear PDEs, especially concerning first-order and hyperbolic equations. The skills and competences the students will acquire concern, on the one hand, the paradigmatic transition from the resolution of a problem to the theoretical analysis of its properties and the investigation of its structural foundation, and, on the other hand, the recognition of the essential difference between linear and nonlinear problems and the limitations of the method of approximation of a nonlinear problem by linear problems. | |||
|- | |- | ||
! General Competences | ! General Competences | ||
| | | | ||
* Search for, analysis and synthesis of data and information | |||
* Adapting to new situations | |||
* Decision-making | |||
* Working independently | |||
* Working in an interdisciplinary environment | |||
* Criticism and self-criticism | |||
* Production of free, creative and inductive thinking | |||
|} | |} | ||
=== Syllabus === | === Syllabus === | ||
Transport, Laplace, heat and wave equations for several space variables. Nonlinear first-order equations (method of characteristics, introduction to Hamilton-Jacobi equations and to conservation laws, weak solutions). The Cauchy-Kovalevskaya Theorem. Sobolev Spaces and weak derivatives. Theory of second-order linear equations. Semigroup Theory. Nonlinear hyperbolic and dispersion equations. | |||
=== Teaching and Learning Methods - Evaluation === | === Teaching and Learning Methods - Evaluation === | ||
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! Delivery | ! Delivery | ||
| | | | ||
Face-to-face | |||
|- | |- | ||
! Use of Information and Communications Technology | ! Use of Information and Communications Technology | ||
| | | - | ||
|- | |- | ||
! Teaching Methods | ! Teaching Methods | ||
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| 39 | | 39 | ||
|- | |- | ||
| | | Self-study | ||
| | | 78 | ||
|- | |- | ||
| | | Homework | ||
| | | 70.5 | ||
|- | |- | ||
| Course total | | Course total | ||
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! Student Performance Evaluation | ! Student Performance Evaluation | ||
| | | | ||
The evaluation is carried out as a combination of | |||
* Written exam. | |||
* Assigned homework. | |||
* Presentation and oral examination. | |||
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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 | AN6 |
Semester | 2 |
Course Title |
Partial Differential Equations |
Independent Teaching Activities | Lectures (Weekly Teaching Hours: 3, Credits: 7.5) |
Course Type | General Background |
Prerequisite Courses |
Vector Analysis (undergraduate), Real Analysis, Functional Analysis |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The course, apart from the instruction in the classical quartet of Partial Differential Equations (PDEs) (transport, Laplace, heat and wave) in several space variables, aims, first, to highlight the modern, analytic approach to the theory of PDEs and the reasons that suggest it, and, second, to provide an introduction to nonlinear PDEs, especially concerning first-order and hyperbolic equations. The skills and competences the students will acquire concern, on the one hand, the paradigmatic transition from the resolution of a problem to the theoretical analysis of its properties and the investigation of its structural foundation, and, on the other hand, the recognition of the essential difference between linear and nonlinear problems and the limitations of the method of approximation of a nonlinear problem by linear problems. |
---|---|
General Competences |
|
Syllabus
Transport, Laplace, heat and wave equations for several space variables. Nonlinear first-order equations (method of characteristics, introduction to Hamilton-Jacobi equations and to conservation laws, weak solutions). The Cauchy-Kovalevskaya Theorem. Sobolev Spaces and weak derivatives. Theory of second-order linear equations. Semigroup Theory. Nonlinear hyperbolic and dispersion equations.
Teaching and Learning Methods - Evaluation
Delivery |
Face-to-face | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | - | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
The evaluation is carried out as a combination of
|
Attached Bibliography
- H.Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer, 2011
- L.C. Evans, Partial Differential Equations (2nd ed.). AMS, 2010
- G. Folland, Introduction to Partial Differential Equations, Princeton University Press, 1976
- L. Hörmander, The Analysis of Linear Partial Differential Operators, Vol. 1-4, Springer, 1983-85
- J. Jost, Partial Differential Equations (2nd ed.), Springer, 2007
- T. Tao, Nonlinear Dispersive Equations: Local and Global Analysis, CBMS, AMS, 2006
- M. Taylor, Partial Differential Equations, Vol. I-III, Springer, 1996
- G.B.Whitham, Linear and Nonlinear Waves, Wiley-Interscience, 1974.