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Numerical Analysis I
(dt. Numerische Analysis I)

Level, degree of commitment Advanced module, compulsory elective module
Forms of teaching and learning,
workload		 Lecture (3 SWS), recitation class (1 SWS),
180 hours (60 h attendance, 120 h private study)
Credit points,
formal requirements		 6 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		 German,
The grading is done with 0 to 15 points according to the examination regulations for the degree program B.Sc. Mathematics.
Duration,
frequency		 One semester,
irregular
Person in charge of the module's outline Prof. Dr. Christian Rieger

Contents

Elliptic differential equations, weak solutions, variation formulation, Galerkin method, finite elements


Qualification Goals

Students will

  • recognize the limitations of standard procedures when the problem entails special requirements,
  • can find problem-adequate solutions,
  • can exemplify how concrete practical developments influence the problems of applied mathematics,
  • recognize how strongly theoretical analysis determines the framework for numerical procedures; in particular, the importance of functional analytical concepts for numerical problems has become clear,
  • have practiced mathematical working methods (developing mathematical intuition and its formal justification, training of the ability to abstract, reasoning),
  • 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 Foundations of Mathematics and Linear Algebra I and Linear Algebra II or Basic Linear Algebra, either Analysis I and Analysis II or Basic Real Analysis, Numerical Analysis. Functional analysis is helpful but not required.


Applicability

Module imported from B.Sc. Mathematics.

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

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

When studying M.Sc. Business Mathematics, this module can be attended in the study area Free Compulsory Elective Modules.


Recommended Reading

  • Wird jeweils in der Modulankündigung angegeben.
  • Standardwerke sind z.B.:
  • Hackbusch, W., Theorie und Numerik elliptischer Differentialgleichungen, Teubner 1986
  • Brenner, S.C., Scott, L.R, The mathematical theory of finite element methods, Springer, 1994



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:

  • Winter 2016/17 (no corresponding element)
  • Summer 2018 (no corresponding element)
  • Winter 2018/19 (no corresponding element)
  • Winter 2019/20 (no corresponding element)
  • Winter 2020/21 (no corresponding element)
  • Summer 2021 (no corresponding element)
  • Winter 2021/22 (no corresponding element)
  • Winter 2022/23 (no corresponding element)
  • Winter 2023/24

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.