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Fachbereich Mathematik


Benutzerspezifische Werkzeuge

Marcel Schaub

fotoSchaubKontakt / Contact Information

Marcel Schaub
Universität Tübingen
Fachbereich Mathematik
AB Mathematische Physik
Auf der Morgenstelle 10
72076 Tübingen
Raum: C6 P22
Tel: +49 (0)7071 29 72419
E-Mail: marcel.schaub cxee uni-tuebingen.de

Sprechstunde: Nach Vereinbarung per e-Mail


Lehre / Teaching

SS 2018

WS 2017/18


Skripten / Lecture Notes

Here are some TeX'ed lecture notes from the lectures I attended in Munich. If you find mistakes/typos, please let me know (via the e-mail above). Note that the e-mail-address frequently written in the notes is not valid anymore. There is no guarantee on correctness.

  • Analysis II (german): Metric spaces and differential calculus in euclidean space.
  • Analysis III (german): Measures and integration theory, differential forms on manifolds.
  • Functional Analysis 1 (english): topological spaces, Banach-/Hilbert spaces, bounded linear operators, weak-/weak*-topologies and -convergence, cornerstones (Baire, Hahn-Banach, uniform boundedness principle, open mapping), compact operators.
  • Functional Analysis 2 (english): spectral theory and functional calculus for compact, bounded self-adjoint, and unbounded self-adjoint operators; projection valued measures, existence of self-adjoint extensions
  • PDE 1 (german): solution theory to transport, Laplace/Poisson, heat, and wave equation; weak derivatives and Sobolev spaces (only 1-d).
  • PDE 2 (english): uniformly elliptic, linear equations of 2nd order. Weak derivatives, Sobolev spaces on bounded domains, approximation of Sobolev functions, extension, trace, embeddings; weak solutions (existence, uniqueness, continuity in "data"), elliptic regularity.
  • Semilinear elliptic PDE 1 and 2 (english): Differential calculus in Banach-/Hilbert spaces, existence of weak solutions to semilinear elliptic equations via direct method and minimax methods; convexity, coercivity, (sub)critical growth, abstract result on admissible minimax-classes, mountain pass theorem, saddle point theorem; constrained minimization, fixpoint methods.
  • Distributions and Sobolev spaces (german): topology on smooth functions with compact support, distributions, convolution, Fourier transform, fundamental solutions, Sobolev embeddings (continuous and compact), trace operator, fractional Sobolev spaces.
  • Mathematical Quantum Mechanics 1 (english): stability of matter (first & second kind), electrostatics, instability of second kind for bosons.
  • Mathematical Quantum Mechanics 2 (english): scattering theory; RAGE theorem, wave operators, asymptotic completeness via Cook's, trace-class-, and Enß-method; Von-Neumann-Schatten-classes, relative boundedness and compactness.