14272 - Special Topics of Analysis Modulübersicht

Module Number: 14272
Module Title:Special Topics of Analysis
  Spezielle Kapitel der Analysis
Department: Faculty 1 - Mathematics, Computer Science, Physics, Electrical Engineering and Information Technology
Responsible Staff Member:
  • Prof. Dr. rer. nat. habil. Hauer, Daniel
Language of Teaching / Examination:English
Duration:1 semester
Frequency of Offer: On special announcement
Credits: 8
Learning Outcome:After successfully completing the module, students are familiar with problems and the current state of knowledge in differential geometry, calculus of variations, optimal control and minimal surfaces.
Contents:
  • Studies of curves, surfaces, and manifolds: Fundamental forms and curvatures, Inner geometry and bending problems for surfaces, Theorem of Gauss-Bonnet, Isothermal parameters
  • Minimal surfaces and Plateau's problem, Bernstein's theorem, Geodesics and the exponential mapping, H-surface
  • Fermat's problem,  2-dimensional Riemannian geometry, an outlook on the n-dimensional Riemann space
  • Solution of variational and optimization problems, Direct and indirect methods, Duality theory, Regularity theory,  Extremal problems, Optimal control theory
Recommended Prerequisites:Knowledge of the content of the modules
  • 11103: Analysis I
  • 11104: Analysis II
  • 11201: Analysis III
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:
  • U. Dierkes, S. Hildebrandt, F. Sauvigny: Minimal Surfaces, Grundlehren der mathematischen Wissenschaften, Band 339,  Springer-Verlag, 2010
  • Ioffe, A.D. and V.M. Tichomirov: Theorie der Extremalaufgaben, Deutscher Verlag der Wissenschaften, 1979.
  • W. Klingenberg: Eine Vorlesung über Differentialgeometrie., Springer, Berlin, 1973.
Module Examination:Final Module Examination (MAP)
Assessment Mode for Module Examination:
  • Oral examination, 60 minutes
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 Wirtschaftmathematik B.Sc.: Compulsory elective module in complex „Vertiefung“, in limited extend
Module Components:
  • Lecture: Special Topics of Analysis
  • Accompanying exercise
  • Related examination
Components to be offered in the Current Semester:
  • no assignment