Partial Differential Equations and Applications (EM3)
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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
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| General Competences |
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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 | ||||||||||
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| Use of Information and Communications Technology | - | ||||||||||
| Teaching Methods |
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| Student Performance Evaluation |
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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.