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# Mathematical Methods of Physics 2

## Module PH9111

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 2018 (current)

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 2018WS 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.

180 h 75 h 6 CP

Responsible coordinator of the module PH9111 is 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:

1. classify and solve ordinary differential equations of first order
2. analyse and solve ordinary differential equations of second order
3. 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

VU 5 Mathematical Methods of Physics 2 Einzel, D. Mon, 15:00–17:00
and 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.

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