Mathematical Methods of Physics 2
Module PH9111
Module version of WS 2010/1
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 | |
|---|---|
| SS 2018 | WS 2010/1 |
Basic Information
PH9111 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.
- Physics Modules for Students of Education
If not stated otherwise for export to a non-physics program the student workload is given in the following table.
| Total workload | Contact hours | Credits (ECTS) |
|---|---|---|
| 180 h | 75 h | 6 CP |
Responsible coordinator of the module PH9111 in the version of WS 2010/1 was Dietrich Einzel.
Content, Learning Outcome and Preconditions
Content
Physics examples for differential equations, classification of ordinary differential equations, ordinary differential equations, direction fields, separation of variables, homogeneous and inhomogeneous first order differential equations, particulate solution by variation of constants, relaxator, approximation methods (Picard-Lindelöf, Euler, Runge-Kutta).
Ordinary differential equations of second order, homogeneous differential equations, linear independence of solutions: Wronski determinant, Abelian identity, inhomogeneous differential equations, particulate solution by variation of constants, oscillation differential equation with and without damping.
Calculus of variations, Euler-Lagrange equation for one variable, Euler-Lagrange equation for multiple variables, the brachistochrone, variational problems with side condition, Fermat principle, Lagrangiagn and Hamilton principle, Noether Theorem, mechanical similarity.
Learning Outcome
After the successful participation in the module the student is able to:
- classify and solve ordinary differential equations of first order
- analyse and solve ordinary differential equations of second order
- know and apply the methods of variational calculus and its significance to Physics.
Preconditions
Mathematical Methods of Physics 1 (PH9110)
Courses, Learning and Teaching Methods and Literature
Courses and Schedule
| Type | SWS | Title | Lecturer(s) | Dates | Links |
|---|---|---|---|---|---|
| VO | 3 | Mathematical Methods of Physics 2 | Einzel, D. |
Mon, 14:00–16:00, PH-Cont. C.3202 |
|
| UE | 2 | Exercise to Mathematical Methods of Physics 2 | Einzel, D. | dates in groups |
Learning and Teaching Methods
lecture: teacher-centred teaching
Exercise: The exercise is held in small groups. In the weekly session exercises are presented by the students and the tutor. They also provide room for discussions and additional explanations to the lectures.
Media
writing on blackboard, presentation
Literature
Mathematische Hilfsmittel der Physik, W. Kuhn, H. Stöckel und H. Glaßl, Johann Ambrosius Barth Verlag, Heidelberg, Leipzig, 1995
Mathematische Methoden in der Physik, C. B. Lang, N. Pucker, Spektrum Akademischer Verlag, Heidelberg, Berlin, 1998
Der mathematische Werkzeugkasten – Anwendungen in der Natur und Technik, G. Glaeser, Spektrum Akademischer Verlag, Heidelberg, Berlin, 2004
Module Exam
Description of exams and course work
There will be a written exam of 90 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using calculation problems and comprehension questions.
For example an assignment in the exam might be:
- Solution of homogeneous first order differential equations by separation of variables and inhomogeneous by variation of constants.
- Wronski determinant and linear independence of solution of homogeneous second order differential equations; finding a special solution to the inhomogeneous equation using variation of constants.
- Derivation and solution (path y(x)) of Euler-Lagrange equations from a given action J{y(x)}.
Participation in the exercise classes is strongly recommended since the exercises prepare for the problems of the exam and rehearse the specific competencies.