14275 - Partial Differential Equations Modulübersicht

Module Number: 14275
Module Title:Partial Differential Equations
  Partielle Differentialgleichungen
Department: Faculty 1 - Mathematics, Computer Science, Physics, Electrical Engineering and Information Technology
Responsible Staff Member:
  • Prof. Dr. rer. nat. habil. Wachsmuth, Gerd
Language of Teaching / Examination:English
Duration:1 semester
Frequency of Offer: On special announcement
Credits: 8
Learning Outcome:After successfully completing the module, students have deeper knowledge on Analysis and Complex Analysis. They are familiar with the most important concepts and interrelations of partial differential equations and have competently mastered the various analytic methods to solve partial differential equations. Using topics on partial differential equations as examples, students have gained experience in independent scientific work.
Contents:On the functional analytic basis, the classical and weak solution theories for linear elliptic differential equations in n variables shall be treated within this lecture. From the lecture notes below, the following themes will be discussed: Potential theoretic foundations, Dirichlet's problem for the Laplace equation and Perron's method, Schauder's continuity method and the Dirichlet problem in Hölder spaces, Existence of weak solutions and their regularity, Moser's iteration method, Green's function for elliptic differential operators.
Recommended Prerequisites:Knowledge of the content of the modules
  • 11103: Analysis I     
  • 11104: Analysis II      
  • 11201: Analysis III
    • 11303: Funktionalanalysis or 
    • 13844: Functional Analysis
  • 11438: Funktionentheorie
Mandatory Prerequisites:None
Forms of Teaching and Proportion:
  • Lecture / 4 Hours per Week per Semester
  • Exercise / 2 Hours per Week per Semester
  • Self organised studies / 150 Hours
Teaching Materials and Literature:
  • Friedrich Sauvigny: Partial Differential Equations 1 & 2, UNIVERSITEXT, Springer-Verlag 2006 (Second edition in preparation 2011/12)
Module Examination:Prerequisite + Final Module Examination (MAP)
Assessment Mode for Module Examination:Prerequisite:
  • Successful completion of homework
Final module examination:
  • Written examination, 90 min. OR
  • Oral examination, 30 min.
It will be announced in the first class whether the examination will organized in written or oral form.
Evaluation of Module Examination:Performance Verification – graded
Limited Number of Participants:None
Part of the Study Programme:
  • no assignment
Remarks:
  • Study programme Mathematics M.Sc.: Compulsory elective module in complex „Analysis/Algebra/Combinatorics“
  • Study programme Mathematik B.Sc.: Compulsory elective module in complex „Vertiefung“, in limited extend 
  • Study programme Wirtschaftsmathematik B.Sc.: Compulsory elective module in complex „Vertiefung“, in limited extend 
  • Study programme Physik B.Sc.: Compulsory elective module in  complex „Nebenfach“
Module Components:
  • Lecture: Partial Differential Equations
  • Accompanying exercise
  • Related examination
Components to be offered in the Current Semester:
  • no assignment