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German original

Partial Differential Equations
(dt. Partielle Differentialgleichungen)

Level, degree of commitment in original study programme Advanced module, compulsory elective module
Forms of teaching and learning,
workload
Lecture (4 SWS), recitation class (2 SWS),
270 hours (90 h attendance, 180 h private study)
Credit points,
formal requirements
9 CP
Course requirement: Successful completion of at least 50 percent of the points from the weekly exercises.
Examination type: Written or oral examination
Language,
Grading
German,
The grading is done with 0 to 15 points according to the examination regulations for study course M.Sc. Mathematics.
Original study programme M.Sc. Mathematik / Vertiefungsbereich Mathematik
Duration,
frequency
One semester,
Regelmäßig im Wechsel mit anderen intermediate moduleen im Gebiet Analysis
Person in charge of the module's outline Prof. Dr. Ilka Agricola, Prof. Dr. Stephan Dahlke, Prof. Dr. Pablo Ramacher

Contents

  • classical partial differential equations (Laplace equation, wave equation, heat equation)
  • distributions, fundamental solutions of differential operators, Sobolev spaces
  • weak solutions, boundary value problems for partial differential equations

Qualification Goals

The students shall

  • Learn about and be able to use differential equations as a means of mathematical modeling,
  • Apply results from functional analysis to the systematic theory of partial differential equations,
  • practice mathematical working methods (development of mathematical intuition and its formal justification, training of the ability to abstract, proof techniques),
  • improve their oral communication skills in the exercises by practicing free speech in front of an audience and during discussion.

Prerequisites

None. The competences taught in the following modules are recommended: either Linear Algebra I and Linear Algebra II or Basic Linear Algebra or Linear Algebra incl. Foundations of Mathematics, either Analysis I and Analysis II or Basic Real Analysis or Analysis I and Analysis II.


Recommended Reading

  • Lawrence Evans, Partial differential equations. AMS, 1998.
  • G.B. Folland, Introduction to Partial Differential Equations,
  • Princeton University Press, 1995.



Please note:

This page describes a module according to the latest valid module guide in Sommersemester 2021. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:

The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.

The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.