Differential Equations: Numerics of ODE & Introduction to PDE (4V+2U, 9.0 LP)
|SWS||Type||Course Form||CP (Effort)||Presence-Time / Self-Study|
|-||K||Lecture with exercise classes (V/U)|
|4||V||Lecture||6.0 CP||56 h||124 h|
|2||U||Exercise class (in small groups)||3.0 CP||28 h||62 h|
|(4V+2U)||9.0 CP||84 h||186 h|
|CP, Effort||9.0 CP = 270 h|
|Position of the semester||1 Sem. in WiSe|
|Level|| Bachelor (Specialization)|
|Area of study||[MAT-TEMA] Industrial Mathematics|
Possible Study achievement
- Verification of study performance: proof of successful participation in the exercise classes (ungraded)
- Details of the examination (type, duration, criteria) will be announced at the beginning of the course.
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 fundamental concepts for 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).
- 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.
Further literature will be announced in the lecture; Exercise material is provided.
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].
- [MAT-10-1-M-2] Fundamentals of Mathematics (M, 28.0 LP)
- [MAT-14-11-M-3] Introduction to Numerical Methods (M, 9.0 LP)
Requirements for attendance (formal)None
References to Course [MAT-80-11-K-4]
|[MAT-70-4V-KPOOL-4]||Elective Courses Analysis and Stochastics (4V, B.Sc.)|
|[MAT-70-KPOOL-4]||Specialisation Analysis and Stochastics (B.Sc.)|
|[MAT-80-4V-KPOOL-4]||Elective Courses Modelling and Scientific Computing (4V, B.Sc.)|
|[MAT-80-KPOOL-4]||Specialisation Modelling and Scientific Computing (B.Sc.)|