Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-81-15-M-7

Asymptotic Analysis (M, 9.0 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-81-15-M-7 Asymptotic Analysis 9.0 CP (270 h)

Basedata

CP, Effort 9.0 CP = 270 h
Position of the semester 1 Sem. irreg.
Level [7] Master (Advanced)
Language [EN] English
Module Manager
Lecturers
+ further Lecturers of the department Mathematics
Area of study [MAT-TEMA] Industrial Mathematics
Reference course of study [MAT-88.105-SG] M.Sc. Mathematics
Livecycle-State [NORM] Active

Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
2V MAT-81-15-K-7
Asymptotic Analysis
P 28 h 107 h - - PL1 4.5 irreg.
  • About [MAT-81-15-K-7]: Title: "Asymptotic Analysis"; Presence-Time: 28 h; Self-Study: 107 h

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: irregular (by arrangement)
  • Examination number: 86150 ("Asymptotic Analysis")

Evaluation of grades

The grade of the module examination is also the module grade.


Contents

The mathematical techniques for flow computation and the theory of asymptotic expansions for differential equations are provided and analysed. In particular, the following topics are covered:
  • regular and singular disturbed problems,
  • scaling,
  • multi-scale expansions,
  • boundary layers for differential equations.

Competencies / intended learning achievements

Upon successful completion of this module, the students know and understand advanced methods for the asymptotic development of equations, in particular, differential equations. They are able to name the essential propositions of the lecture as well as to classify and to explain the presented correlations. They understand the proofs presented in the lecture and are able to reproduce and explain them. In particular, they can outline the conditions and assumptions that are necessary are necessary for the validity of the statements.

On the basis of concrete exercises, they have worked out a skilled, precise and independent handling of the terms, propositions and methods of the lecture. They have learned to transfer the methods to new problems, to analyse them and to develop solution strategies.

Literature

  • G. I. Barenblatt: Scaling,
  • N. G. De Bruijn: Asymptotic methods in analysis,
  • M. H. Holmes: Introduction to perturbation methods,
  • U. Hornung: Homogenization and porous media,
  • J. K. Hunter: Asymptotic analysis and singular perturbation theory (Lecture Notes).

References to Module / Module Number [MAT-81-15-M-7]

Module-Pool Name
[MAT-70-MPOOL-7] Specialisation Stochastic Analysis (M.Sc.)
[MAT-81-MPOOL-7] Specialisation Partial Differential Equations (M.Sc.)
[MAT-8x-MPOOL-7] Specialisation Modelling and Scientific Computing (M.Sc.)
[MAT-AM-MPOOL-7] Applied Mathematics (Advanced Modules M.Sc.)