Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-80-11A-M-4

Numerics of ODE (M, 4.5 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-80-11A-M-4 Numerics of ODE 4.5 CP (135 h)

Basedata

CP, Effort 4.5 CP = 135 h
Position of the semester 1 Sem. in WiSe
Level [4] Bachelor (Specialization)
Language [EN] English
Module Manager
Lecturers
Area of study [MAT-TEMA] Industrial Mathematics
Reference course of study [MAT-88.105-SG] M.Sc. Mathematics
Livecycle-State [NORM] Active

Notice

This module can be combined with the module [MAT-80-11B-M-4] Introduction to PDE to the module [MAT-80-11-M-4] Differential Equations: Numerics of ODE & Introduction to PDE.

Without a proof of successful participation in the exercise classes, only 3 credit points will be awarded for the module.

Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
2V+1U MAT-80-11A-K-4
Numerics of ODE
P 42 h 93 h
U-Schein
- PL1 4.5 WiSe
  • About [MAT-80-11A-K-4]: Title: "Numerics of ODE"; Presence-Time: 42 h; Self-Study: 93 h
  • About [MAT-80-11A-K-4]: The study achievement [U-Schein] proof of successful participation in the exercise classes (ungraded) must be obtained.

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: each semester
  • Examination number: 84230 ("Numerical Methods for ODE")

Evaluation of grades

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


Contents

Numeric methods which deal with initial value problems will be discussed. In particular, the following contents are covered:
  • One-step method (explicit/implicit): consistency, convergence, stability,
  • Runge-Kutta methods,
  • Control of step size,
  • Methods for stiff problems: Gauß algorithm, collocation method.

Competencies / intended learning achievements

The students have studied and understand the basic concepts of the numerical treatment of initial value problems as well as the mathematical techniques required to analyze them. They are able to analyze the algorithms and apply them to practical problems. They understand the proofs presented in the lecture and are able to comprehend and explain them.

By completing the given exercises, the students have developed a skilled, precise and independent handling of the terms, propositions and techniques taught in the lecture. In addition, they have learnt how to apply these techniques to new problems, analyze them and develop solution strategies.

Literature

  • P. Deuflhard, F. Bornemann: Numerische Mathematik II,
  • J. Stoer, R. Bulirsch: Einführung in die Numerische Mathematik II,
  • A. Quarteroni, R. Sacco, F. Saleri: Numerische Mathematik I, II,
  • E. Hairer, G. Wanner: Solving Ordinary Differential Equations I, II,
  • H. Heuser: Ordinary Differential Equations,
  • W. Walter: Ordinary Differential Equations,
  • G. Teschl: Ordinary Differential Equations and Dynamical Systems.

Registration

Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de).

References to Module / Module Number [MAT-80-11A-M-4]

Course of Study Section Choice/Obligation
[MAT-88.B84-SG] M.Sc. Actuarial and Financial Mathematics Statistics and Computational Methods [WP] Compulsory Elective
[MAT-88.105-SG] M.Sc. Mathematics Applied Mathematics [WP] Compulsory Elective
[MAT-88.706-SG] M.Sc. Mathematics International Applied Mathematics [WP] Compulsory Elective
[MAT-88.118-SG] M.Sc. Industrial Mathematics General Mathematics [WP] Compulsory Elective
[MAT-88.276-SG] M.Sc. Business Mathematics General Mathematics [WP] Compulsory Elective