Partial Differential Equations (MAE713): Διαφορά μεταξύ των αναθεωρήσεων
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[[Undergraduate Courses Outlines]] - [https://math.uoi.gr Department of Mathematics] | |||
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Αναθεώρηση της 08:06, 2 Ιουλίου 2022
Undergraduate Courses Outlines - Department of Mathematics
General
School |
School of Science |
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Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE713 |
Semester |
7 |
Course Title |
Partial Differential Equations |
Independent Teaching Activities |
Lectures, laboratory exercises (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) | - |
Learning Outcomes
Learning outcomes |
The aim of the course is an introduction to Partial Differnential Equations (PDE). By this course the students become familiar with a broad area of Analysis that, moreover, has the most applications in other Sciences. The course highlights the wealth of problems that arise in PDE and proposes methods to overcome them. These are presented exemplarily and aim to show the students ways of generalizing known methods and solutions.
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General Competences |
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Syllabus
Overview of PDE and Systems: Classification with respect to their (non-)linearity, description of the arising problems and of the various kinds of solutions (classical and weak; general and with boundary values)
(for the following we focus on the case of two independent variables)
First order PDE (linear, semi-linear, quasi-linear): Geometric and algebraic observations concerning their qualitative behavior; Initial Value Problems and Method of Characteristics; discussion of the Burgers equation; shock waves and weak solutions; Rankine-Hugoniot condition.
Second order PDE: classification, characteristic directions and curves; wave equation on the line (homogeneous and non-homogeneous); separation of variables for the Laplace and heat equations; Poisson formula.
(alternatively: instead of the discussion of the Burgers equation and of weak solutions, an introduction to the Fourier transform may be given and the heat equation on the line may be discussed)
Teaching and Learning Methods - Evaluation
Delivery |
Classroom (face-to-face) | ||||||||||
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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
Suggested bibliography:
- Γ. Ακρίβης, Ν. Αλικάκος: Μερικές Διαφορικές Εξισώσεις (2η έκδοση), Σύγχρονη Εκδοτική, 2017 (in Greek)
- L. C. Evans: Partial Differential Equations (2 edition), AMS, 2010