Partial Differential Equations and Applications (EM3): Διαφορά μεταξύ των αναθεωρήσεων
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=== General === | === General === | ||
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|- | |- | ||
! Course Code | ! Course Code | ||
| | | EM3 | ||
|- | |- | ||
! Semester | ! Semester | ||
| | | 1 | ||
|- | |- | ||
! Course Title | ! Course Title | ||
| | | | ||
Partial Differential Equations and Applications | |||
|- | |- | ||
! Independent Teaching Activities | ! Independent Teaching Activities | ||
Γραμμή 27: | Γραμμή 30: | ||
|- | |- | ||
! Course Type | ! Course Type | ||
| | | Special Background | ||
|- | |- | ||
! Prerequisite Courses | ! Prerequisite Courses | ||
Γραμμή 34: | Γραμμή 37: | ||
! 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 52: | ||
! Learning outcomes | ! Learning outcomes | ||
| | | | ||
The student in this course will apply the mathematical tools obtained from previous courses to better understand concepts arising from natural (and not only) | |||
phenomena and the way these are transformed into mathematical problems. More specifically, by completing this course, students should be able to | |||
* use the method of characteristics to solve partial differential equations | |||
* classify partial differential equations of second order in elliptic, parabolic and hyperbolic type | |||
* use Green’s functions to solve elliptic type equations | |||
* have a basic understanding of diffusion equations | |||
* use separation of variables to solve linear partial differential equations | |||
|- | |- | ||
! General Competences | ! General Competences | ||
| | | | ||
* Adapting to new situations | |||
* Decision-making | |||
* Working independently | |||
* Team work | |||
|} | |} | ||
=== Syllabus === | === Syllabus === | ||
Basic concepts. Linear, quasi-linear and semi-linear equations of the first order. The Cauchy problem and its solution by the method of characteristic. Linear equations of 2nd order: classification (hyperbolic, parabolic, elliptic), examples (wave equation, heat equation, Laplace equation). Problems of initial and boundary values for the wave and heat equations. Boundary value problems and the Laplace equation. The Cauchy problem for the wave and heat equations. | |||
=== Teaching and Learning Methods - Evaluation === | === Teaching and Learning Methods - Evaluation === | ||
Γραμμή 66: | Γραμμή 78: | ||
! Delivery | ! Delivery | ||
| | | | ||
In class | |||
|- | |- | ||
! Use of Information and Communications Technology | ! Use of Information and Communications Technology | ||
| | | - | ||
|- | |- | ||
! Teaching Methods | ! Teaching Methods | ||
Γραμμή 81: | Γραμμή 92: | ||
| 39 | | 39 | ||
|- | |- | ||
| | | Self study | ||
| | | 78 | ||
|- | |- | ||
| | | Homework - Projects | ||
| | | 70.5 | ||
|- | |- | ||
| Course total | | Course total | ||
Γραμμή 93: | Γραμμή 104: | ||
! Student Performance Evaluation | ! Student Performance Evaluation | ||
| | | | ||
* Weekly assignments | |||
* Final project | |||
|} | |} | ||
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General
School | School of Science |
---|---|
Academic Unit | Department of Mathematics |
Level of Studies | Graduate |
Course Code | EM3 |
Semester | 1 |
Course Title |
Partial Differential Equations and Applications |
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 (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The student in this course will apply the mathematical tools obtained from previous courses to better understand concepts arising from natural (and not only) phenomena and the way these are transformed into mathematical problems. More specifically, by completing this course, students should be able to
|
---|---|
General Competences |
|
Syllabus
Basic concepts. Linear, quasi-linear and semi-linear equations of the first order. The Cauchy problem and its solution by the method of characteristic. Linear equations of 2nd order: classification (hyperbolic, parabolic, elliptic), examples (wave equation, heat equation, Laplace equation). Problems of initial and boundary values for the wave and heat equations. Boundary value problems and the Laplace equation. The Cauchy problem for the wave and heat equations.
Teaching and Learning Methods - Evaluation
Delivery |
In class | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | - | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
|
Attached Bibliography
- Fluid Mechanics with Applications, M. Xenos and E. Tzirtzilakis, 2018 (in Greek)
- Fluid Mechanics, Volume 1, A. Papaioanou, 2nd Edition, 2001 (in Greek).
- Computational Fluid Mechanics, I. Soulis, 1st Edition, 2008 (in Greek).
- Numerical heat transfer and fluid flow, S.V. Patankar, McGraw-Hill, New York, 1980.
- The Finite Element Method, Vol. 1, The Basis, O.C. Zienkiewicz, R.L. Taylor, 5th Ed., Butterworth-Heinemann, Oxford, 2000.
- Computational Techniques for fluid Dynamics, C.A.J. Fletcher Volumes I and II, 2nd Ed. Springer-Verlag, Berlin, 1991.