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.

Basic Information

PH9111 is a semester module in German or English 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 workloadContact hoursCredits (ECTS)
180 h 75 h 6 CP

Responsible coordinator of the module PH9111 is Dietrich Einzel.

Content, Learning Outcome and Preconditions


Ordinary differential equations of first order:

physics examples for differential equations, direction fields, separation of variables, homogeneous and inhomogeneous differential equations, particulate solution by variation of constants, relaxator, approximation methods.


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, variational problems with side condition, Fermat principle, Hamilton principle

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.


Mathematical Methods of Physics 1 (PH9110)

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

VU 5 Mathematische Methoden der Physik 2 Einzel, D. Montag, 15:00–17:00
sowie Termine in Gruppen

Learning and Teaching Methods

lecture: teacher-centred teaching


writing on blackboard, presentation


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

The learning outcome is tested in a written or an oral exam.

Condensed Matter

When atoms interact things can get interesting. Fundamental research on the underlying properties of materials and nanostructures and exploration of the potential they provide for applications.

Nuclei, Particles, Astrophysics

A journey of discovery to understanding our world at the subatomic scale, from the nuclei inside atoms down to the most elementary building blocks of matter. Are you ready for the adventure?


Biological systems, from proteins to living cells and organisms, obey physical principles. Our research groups in biophysics shape one of Germany's largest scientific clusters in this area.