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School of Science
Department of Mathematics
|Level of Studies||
Partial Differential Equations
|Independent Teaching Activities||
Lectures (Weekly Teaching Hours: 3, Credits: 6)
|Language of Instruction and Examinations||
|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.|
The aim of the course is an introduction to Partial Differential Equations. By this course the students become familiar with a broad area of Analysis that has many applications to other sciences. The course highlights the wealth of problems that arise and proposes methods to overcome them. These are presented exemplarily and aim to teach ways of transcending and generalizing known methods and solutions. The students learn to analyze methodically externally given problems, taking into account relevant informations and aims, and to try to apply knowledge from other areas of Pure Mathematics in order to solve these problems. Moreover, the students learn to interpret the obtained mathematical results. On the level of content, the students learn about, mainly linear, Partial Differential Equations of first and second order for functions of two variables with respect to both, their explicit solution and their qualitative behavior, and obtain an elementary overview of further problems.
- Overview of Partial Differential Equations (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).
(In the following the focus is given on 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 characteristic curves, wave equation on the line (homogeneous and inhomogeneous), separation of variables for the Laplace and heat equations, Poisson formula.
(Alternatively: instead of the discussion of the (non-linear) 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
|Use of Information and Communications Technology||
The students may contact the lecturer by e-mail
|Student Performance Evaluation||
- L. C. Evans: Partial Differential Equations (2 edition), AMS, 2010