Partial Differential Equations (MAE713)
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General
| School |
School of Science |
|---|---|
| Academic Unit |
Department of Mathematics |
| Level of Studies |
Undergraduate |
| Course Code |
MAE713 |
| Semester |
7 |
| Course Title |
Partial Differential Equations |
| Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
| Course Type |
Special Background |
| Prerequisite Courses | - |
| Language of Instruction and Examinations |
Greek, English |
| 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 introduces the students to Partial Differential Equations (PDE). The importance of the fact that their solutions are scalar or vector-valued functions of more than one independent variables is stressed and that, in contrast to Ordinary Differential Equations, this has significant consequences, in the sense that for PDEs, next to the analytical properties of the solutions, also the algebraic structure of the equations plays a distinguished role, which implies also geometric properties of the solutions. Also, the connection with and origin from the Natural Sciences and Geometry for many of them is stressed and that this implies not only that the focus mainly on certain types of equations results from the questions posed by other scientific fields but also that the latter dictate to a big extend in a natural way the methods for solving and studying the properties of the various classes of PDEs. In this way, the course strengthens the ability of the students to examine a problem from several perspectives and to take into account knowledge and results from other scientific areas. In particular, the course introduces the students to the main classes of PDEs, highlights the fact that each class relies on its own analysis techniques, that their solutions have properties which are characteristic for the class to which they belong, and that results which are obtained for one class can be used partly also for the analysis of equations of a different class, although under essential restrictions. In this introductory course initially only classical solutions are studied and an emphasis is given on the explicit solving of prototypical equations for each class and on a first study of their characteristic properties. |
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| General Competences |
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Syllabus
Introduction: definition of a PDE, definition of classical solutions. Classification with respect to (non) linearity. Examples of equations and systems. First order equations. Method of characteristics. Transport equation. Linear PDEs of second order. Laplace and Poisson equation, heat equation, wave equation: representation formulas of solutions and energy method.
Teaching and Learning Methods - Evaluation
| Delivery |
Classroom (face-to-face) | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Use of Information and Communications Technology |
The students may contact the lecturer by e-mail | ||||||||||
| Teaching Methods |
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| Student Performance Evaluation |
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Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Δάσιος, Γ., Κυριάκη, Κ., & Βαφέας, Π. (2023). Μερικές Διαφορικές Εξισώσεις [Προπτυχιακό εγχειρίδιο]. Κάλλιπος, Ανοικτές Ακαδημαϊκές Εκδόσεις. http://dx.doi.org/10.57713/kallipos-317
- L. C. Evans. Partial Differential Equations. Second edition. AMS, 2010.
- G. B. Folland. Introduction to Partial Differential Equations. Princeton University Press, 1995.