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Partial Differential Equations
(dt. Partielle Differentialgleichungen)

Level, degree of commitment Specialization 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(s): Successful completion of at least 50 percent of the points from the weekly exercises.
Examination type: Written or oral examination (individual examination)
Language,
Grading		 English,
The grading is done with 0 to 15 points according to the examination regulations for the degree program M.Sc. Mathematics.
Duration,
frequency		 One semester,
Regularly alternating with other advanced modules im Gebiet Analysis
Person in charge of the module's outline Prof. Dr. Ilka Agricola, 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

Students will

  • understand differential equations as a means of mathematical modeling and can use them,
  • can apply knowledge from functional analysis to the systematic theory of partial differential equations,
  • have deepened mathematical working methods(developing mathematical intuition and its formal justification, abstraction, proof),
  • have improved their oral communication skills in the exercises by practicing free speech in front of an audience and in 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.


Applicability

Module imported from M.Sc. Mathematics.

It can be attended at FB12 in study program(s)

  • B.Sc. Mathematics
  • B.Sc. Business Mathematics
  • M.Sc. Computer Science
  • M.Sc. Mathematics
  • M.Sc. Business Mathematics
  • LAaG Mathematics

When studying LAaG Mathematics, this module can be attended in the study area Advanced Modules.

The module is assigned to Pure Mathematics. Further information on eligibility can be found in the description of the study area.


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 Winter semester 2023/24. 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.