Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-80-11-M-4

Differential Equations: Numerics of ODE & Introduction to PDE (M, 9.0 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-80-11-M-4 Differential Equations: Numerics of ODE & Introduction to PDE 9.0 CP (270 h)

Basedata

CP, Effort 9.0 CP = 270 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

The module comprises the modules [MAT-80-11A-M-4] and [MAT-80-11B-M-4].

Without a proof of successful participation in the exercise classes, only 6 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
2V+1U MAT-80-11B-K-4
PDE: An Introduction
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.
  • About [MAT-80-11B-K-4]: Title: "PDE: An Introduction"; Presence-Time: 42 h; Self-Study: 93 h
  • About [MAT-80-11B-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: 84235 ("Numerical Methods for ODE; PDE: An Introduction")

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.
This course gives an introduction to the classical theory of partial differential equations. In particular, the following contents are dealt with:
  • Classification and well-posed problems,
  • Quasilinear equations: Cauchy problem,
  • Wave equation: existence, uniqueness, stability, maximum principle,
  • Poisson equation: separation ansatz, fundamental solutions, Green's function, maximum principle, existence and uniqueness,
  • Heat equation: separation of variables, Fourier transformation, semigroups, maximum principle, existence and uniqueness.

Competencies / intended learning achievements

The students have studied and understand the basic concepts of the numerical treatment of initial value problems, the mathematics techniques for analyzing the methods and the extension of the theory of ordinary differential equations (ODE) to partial differential equations (PDE). 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,
  • L.C. Evans: Partial differential equations,
  • F. John: Partial differential equations.

Registration

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

Requirements for attendance (informal)

Desirable is knowledge from the course [MAT-12-27-K-3].

Modules:

Courses

Requirements for attendance (formal)

None

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

Course of Study Section Choice/Obligation
[INF-88.79-SG] M.Sc. Computer Science Formal Fundamentals [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