Course MAT-12-25-K-3
Introduction to Ordinary Differential Equations (2V+1U, 4.5 LP)
Course Type
| SWS | Type | Course Form | CP (Effort) | Presence-Time / Self-Study | |
|---|---|---|---|---|---|
| - | K | Lecture with exercise classes (V/U) | 4.5 CP | 93 h | |
| 2 | V | Lecture | 28 h | ||
| 1 | U | Exercise class (in small groups) | 14 h | ||
| (2V+1U) | 4.5 CP | 42 h | 93 h | ||
Basedata
| SWS | 2V+1U |
|---|---|
| CP, Effort | 4.5 CP = 135 h |
| Position of the semester | 1 Sem. in SuSe |
| Level | [3] Bachelor (Core) |
| Language | [DE] German |
| Lecturers |
+ further Lecturers of the department Mathematics
|
| Area of study | [MAT-GRU] Mathematics (B.Sc. year 1 and 2) |
| Livecycle-State | [NORM] Active |
Possible Study achievement
- Verification of study performance: proof of successful participation in the exercise classes (ungraded)
- Examination number (Study achievement): 83120 ("Exercise Class Introduction to Ordinary Differential Equations")
- Details of the examination (type, duration, criteria) will be announced at the beginning of the course.
Contents
- first-order differential equations: autonomous first-order differential equations, variation of constants, explicitly solvable cases, initial value problems,
- existence and uniqueness: functional-analytical foundations, Banach fixed-point theorem, Picard-Lindelöf theorem, the continuability of solutions, Peano's existence theorem,
- qualitative behaviour: Gronwall's lemma, continuous dependency on data, upper and lower functions,
- linear differential equations: homogeneous linear systems, matrix exponential function, variation of constants, nth-order differential equations,
- stability: dynamical systems, phase space, Hamiltonian systems, asymptotic behaviour, stability theory according to Lyapunov.
Competencies / intended learning achievements
The students know the basic concepts, statements and methods of the theory of ordinary differential equations. By combining results from analysis and linear algebra, they are able to investigate advanced questions and solve minor application problems from science and technology using mathematical methods.
Literature
- V.I. Arnold: Gewöhnliche Differentialgleichungen,
- L. Grüne, O. Junge: Gewöhnliche Differentialgleichungen,
- H. Heuser: Gewöhnliche Differentialgleichungen,
- J.W. Prüss, M. Wilke: Gewöhnliche Differentialgleichungen und dynamische Systeme,
- W. Walter: Gewöhnliche Differentialgleichungen,
- G. Teschl: Ordinary Differential Equations and Dynamic Systems.
Materials
Further literature will be announced in the lecture(s); exercise material is provided.
Registration
Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de).
Requirements for attendance (informal)
Knowledge of Linear Algebra from the course [MAT-10-12-K-2] or [MAT-10-12L-K-2].
Courses
- [MAT-10-11A-K-2] Fundamentals of Mathematics I: Analysis (4V+2U+2T, 9.0 LP)
- [MAT-10-11B-K-2] Fundamentals of Mathematics I: Linear Algebra (2V+2U, 6.0 LP)
Requirements for attendance (formal)
None
References to Course [MAT-12-25-K-3]
| Module | Name | Context | |
|---|---|---|---|
| [MAT-12-10P-M-3] | Build-Up Module Mathematics (for Students of Physics) | WP: Obligation to choose | 2V+1U, 5.0 LP |
| [MAT-12-2-M-3] | Measure Theory and Differential Equations | P: Obligatory | 2V+1U, 4.5 LP |
| [MAT-14-10L-M-3] | Topic Module B: Mathematics as an Interdisciplinary Cross-Sectional Science | WP: Obligation to choose | 2V+1U, 4.5 LP |
| Course-Pool | Name | ||
| [MAT-10-KPOOL-3] | Pure Mathematics (B.Sc. Mathematics) | ||
| [PHY-M2-KPOOL-3] | Höhere Analysis (für Studierende der Physik) |