Fachbereich Mathematik

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Home > Marcel Schaub

# Kontakt / Contact Information

Marcel SchaubUniversität TübingenFachbereich MathematikAB Mathematische PhysikAuf der Morgenstelle 1072076 Tübingen
Raum: C6 P22Tel: +49 (0)7071 29 72419E-Mail: marcel.schaub  uni-tuebingen.deSprechstunde: nach Vereinbarung per E-Mail

WS 2018/19

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.