13037 - Linear and Weakly Non-Linear Differential Equations in Physics Modulübersicht

Module Number: 13037 - module is no longer offered from SS 2025
Module Title:Linear and Weakly Non-Linear Differential Equations in Physics
  Lineare und schwach nichtlineare Differentialgleichungen in der Physik
Department: Faculty 1 - Mathematics, Computer Science, Physics, Electrical Engineering and Information Technology
Responsible Staff Member:
  • Prof. Dr. rer. nat. habil. Bestehorn, Michael
Language of Teaching / Examination:English
Duration:1 semester
Frequency of Offer: On special announcement
Credits: 6
Learning Outcome:After successfully completing the module, students have a profound knowledge of using and solving of ordinary and partial differential equations in physics. They are able to formulate model equations and solving them independently. Additionally the module supported synergetic connections to other fields (interdisciplinarity).
Contents:Differential equations in mechanics, hydrodynamics, and nonequilibrium chemistry. Linear and nonlinear diffusion equation, complex Ginzburg-Landau equation, Swift-Hohenberg equation. Methods: linear stability analysis, normal forms, Turing and Hopf instabilities
Recommended Prerequisites:
  • Knowledge of theoretical physics (level Bachelor studies)
  • Firm knowledge in analysis and linear algebra
Mandatory Prerequisites:None
Forms of Teaching and Proportion:
  • Lecture / 2 Hours per Week per Semester
  • Exercise / 2 Hours per Week per Semester
  • Self organised studies / 120 Hours
Teaching Materials and Literature:
  • Guckenheimer, Holmes: Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
  • H. Haken: Synergetik
  • J. Argyris: Die Erforschung des Chaos
  • M. Bestehorn: Hydrodynamik und Strukturbildung
Further references will be provided during the lecture.
Module Examination:Prerequisite + Final Module Examination (MAP)
Assessment Mode for Module Examination:Prerequisite:
  • Successful completion of exercise assignments (75% must be reached)
Final module examination:
  • Oral examination, 30-45 min.
Evaluation of Module Examination:Performance Verification – graded
Limited Number of Participants:None
Part of the Study Programme:
  • no assignment
Remarks:
  • Study programme Physics M.Sc.: Compulsory elective module in complex „Physical Specialization with theoretical focus“, topic area „Theory, Simulation and further topics“
  • Study programme Applied Mathematics M.Sc.: Compulsory elective module in complex „Applications“, field  „Physics“

Self organised studies:
  • re-work of the lecture
  • treatment of homework
  • literature work
Module Components:
  • Lecture:  Linear and Weakly Non-Linear Differential Equations in Physics (2 Hours per Week per Semester)
  • Accompanying exercises (2 Hours per Week per Semester)
  • Related examination
Components to be offered in the Current Semester:
  • no assignment
Follow-up Module/s: Phase-out module since: 14.01.2025
  • without Follow-up Module/s