Special Topics of Analysis
Spezielle Kapitel der Analysis
8 CPirregularlyEN
Prerequisites
Recommended, as written
Knowledge of the content of the modules • 11103: Analysis I • 11104: Analysis II • 11201: Analysis III
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
Learning outcomes
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.
Assessment
• Oral examination, 60 minutes
Literature (3)
- 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.
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
Source: BTU's module description · retrieved 29 Sep 2026Original