Ordinary Differential Equations
Module MA2005
This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.
Module version of SS 2012
There are historic module descriptions of this module. A module description is valid until replaced by a newer one.
Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.
| available module versions | ||||
|---|---|---|---|---|
| WS 2021/2 | SS 2020 | SS 2017 | SS 2012 | WS 2011/2 |
Basic Information
MA2005 is a semester module in German language at Bachelor’s level which is offered in summer semester.
This Module is included in the following catalogues within the study programs in physics.
- Further Modules from Other Disciplines
| Total workload | Contact hours | Credits (ECTS) |
|---|---|---|
| 150 h | 45 h | 5 CP |
Content, Learning Outcome and Preconditions
Content
Basic concepts and elementary methods of integration, vector fields and phase flows on the real line. Non-autonomous equations. Existence, uniqueness and smooth dependence on initial data as well as other parameters for the solutions of general first-order systems. Rectifiability of vector fields near non-singular points. Applications to systems of higher-order. Existence and non-existence for boundary value problems. Integral curves and phase flows of autonomous systems. Linear systems: systems of first-order with constant coefficients (including complex eigenvalues). Stability. Eigenvalue problems (Sturm.Liouville Theorie).
Learning Outcome
After successful completion of the modul, students are able to understand and apply the elementary theory of ordinary differential equations, stressing their analytical investigation as well as geometric features of the solutions.
Preconditions
MA1001 Analysis 1, MA1002 Analysis 2, MA1101 Linear Algebra 1, MA1102 Linear Algebra 2, MA2004 Vector Analysis
Courses, Learning and Teaching Methods and Literature
Courses and Schedule
| Type | SWS | Title | Lecturer(s) | Dates | Links |
|---|---|---|---|---|---|
| VO | 2 | Ordinary Differential Equations [MA2005] | Prähofer, M. |
Thu, 10:15–11:45, virtuell |
eLearning |
| UE | 1 | Ordinary Differential Equations (Exercise Session) [MA2005] | Prähofer, M. |
Mon, 12:00–13:00, virtuell and dates in groups |
eLearning |
Learning and Teaching Methods
lecture, exercise module, presentation
Media
blackboard
Literature
V.I. Arnold, Gewöhnliche Differentialgleichungen, 2. Auflage, Springer-Verlag 2001.
W. Walter, Gewöhnliche Differentialgleichungen: eine Einführung, 7. Auflage, Springer-Verlag Berlin 2000.
V.I. Arnold: "Ordinary Differential Equations", translated and edited by RA Silverman - 1973 - MIT Press, Cambridge.
W. Walter, Gewöhnliche Differentialgleichungen: eine Einführung, 7. Auflage, Springer-Verlag Berlin 2000.
V.I. Arnold: "Ordinary Differential Equations", translated and edited by RA Silverman - 1973 - MIT Press, Cambridge.
Module Exam
Description of exams and course work
Requirement for successful completion of the modul is to pass a written exam. By the written exam, students prove to know the mathematical concepts and methods of the elementary theory of ordinary differential equations and to be able to apply those to solve mathematical problems from that area.
Exam Repetition
The exam may be repeated at the end of the semester.