Lehrinhalte
Theory of Discontinuous Galerkin methods; Boundedness, Stability, Consistency, Approximation; Upwinding, Limiting; INterior Penalty (IP), local DG (LDG), aso.; Implementation and practical examples (e.g. in Matlab)
Literatur
D. A. Di Pietro, A. Ern: Mathematical Aspects of Discontinuous Galerkin Methods (Book, Springer)
B. Riviere: Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations (Book, SIAM)
Voraussetzungen
recommended: required: Introduction to Numerical Analysis or similar knowledge as taught in an engineering programme;
useful courses: Numerical Analysis of Partial Differential Equations, Funcitonal Analysis
Theory of Discontinuous Galerkin methods; Boundedness, Stability, Consistency, Approximation; Upwinding, Limiting; INterior Penalty (IP), local DG (LDG), aso.; Implementation and practical examples (e.g. in Matlab)
Literatur
D. A. Di Pietro, A. Ern: Mathematical Aspects of Discontinuous Galerkin Methods (Book, Springer)
B. Riviere: Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations (Book, SIAM)
Voraussetzungen
recommended: required: Introduction to Numerical Analysis or similar knowledge as taught in an engineering programme;
useful courses: Numerical Analysis of Partial Differential Equations, Funcitonal Analysis
- Lehrende: Jan Giesselmann
- Lehrende: Teresa Kunkel
Semester: ST 2020
Lehrinhalte
Probability spaces and random variables, distribution functions, expectation and variance, independence and elementary conditional expectations, discrete and absolutely continuous distributions, Law of Large Numbers, Central Limit Theorem, estimation and confidence intervals, testing under the hypothesis of normality. Application and analysis of selected basic models of probability theory.
Literatur
Eckle-Kohler, Kohler: Eine Einführung in die Statistik und ihre Anwendungen;
Irle: Wahrscheinlichkeitstheorie und Statistik;
Krengel: Einführung in dieWahrscheinlichkeitstheorie und Statistik;
Georgii: Stochastik: Einführung in die Wahrscheinlichkeitstheorie und Statistik;
Voraussetzungen
recommended: Analysis and Linear Algebra
Probability spaces and random variables, distribution functions, expectation and variance, independence and elementary conditional expectations, discrete and absolutely continuous distributions, Law of Large Numbers, Central Limit Theorem, estimation and confidence intervals, testing under the hypothesis of normality. Application and analysis of selected basic models of probability theory.
Literatur
Eckle-Kohler, Kohler: Eine Einführung in die Statistik und ihre Anwendungen;
Irle: Wahrscheinlichkeitstheorie und Statistik;
Krengel: Einführung in dieWahrscheinlichkeitstheorie und Statistik;
Georgii: Stochastik: Einführung in die Wahrscheinlichkeitstheorie und Statistik;
Voraussetzungen
recommended: Analysis and Linear Algebra
- Lehrende: Gelöschter User
- Lehrende: Frank Aurzada
- Lehrende: Volker Martin Betz
Semester: ST 2020
Lehrinhalte
Numerical Analysis: linear equations, interpolation, numerical integration,
systems of nonlinear equations, initial value problems for ODEs, numerical
methods for eigenvalue problems
Statistics: basic concepts of statistics and probability theory, regression,
multivariate distributions, methods of estimation, confidence intervals, tests
for normally distributed random variables, robust statistics
Online-Angebote
moodle
Numerical Analysis: linear equations, interpolation, numerical integration,
systems of nonlinear equations, initial value problems for ODEs, numerical
methods for eigenvalue problems
Statistics: basic concepts of statistics and probability theory, regression,
multivariate distributions, methods of estimation, confidence intervals, tests
for normally distributed random variables, robust statistics
Online-Angebote
moodle
- Lehrende: Isabel Jacob
- Lehrende: Marc Pfetsch
Semester: ST 2020
Lehrinhalte
Systems of linear equations: iterative methods, singular value decomposition, eigenvalue problems.
Literatur
Trefethen/Bau: Numerical Linear Algebra, SIAM
Demmel: Applied Numerical Linear Algebra, SIAM
Stoer/Bulirsch: Numerische Mathematik 2, Springer
Voraussetzungen
recommended: Linear Algebra, Introduction to Numerical Analysis or similar knowledge
Systems of linear equations: iterative methods, singular value decomposition, eigenvalue problems.
Literatur
Trefethen/Bau: Numerical Linear Algebra, SIAM
Demmel: Applied Numerical Linear Algebra, SIAM
Stoer/Bulirsch: Numerische Mathematik 2, Springer
Voraussetzungen
recommended: Linear Algebra, Introduction to Numerical Analysis or similar knowledge
- Lehrende: Jan Giesselmann
- Lehrende: Gelöschter User (TU-ID gelöscht)
Semester: ST 2020
Lehrinhalte
Classical treatment of the heat equation. Functional analytic prerequisites
for nonstationary partial differential equations. Solution of initial boundary value problems by Galerkins method,
regularity. Semigroup approach.
Classical treatment of the heat equation. Functional analytic prerequisites
for nonstationary partial differential equations. Solution of initial boundary value problems by Galerkins method,
regularity. Semigroup approach.
- Lehrende: Matthias Hieber
Semester: ST 2020
Lehrinhalte
depending on topic,
examples include:
- conservation equations
- stochastic PDEs
- geo-physical flows
- free boundary value problems
- chemotaxis
- Besov spaces
- pseudo differential operators
Literatur
depending on topic
Voraussetzungen
recommended: depending on topic, typically Functional Analysis
depending on topic,
examples include:
- conservation equations
- stochastic PDEs
- geo-physical flows
- free boundary value problems
- chemotaxis
- Besov spaces
- pseudo differential operators
Literatur
depending on topic
Voraussetzungen
recommended: depending on topic, typically Functional Analysis
- Lehrende: Gelöschter User (TU-ID gelöscht)
Semester: ST 2020
Lehrinhalte
This course focuses on the formalisation of concepts related to sets of variable assignments rather than individual assignments, with an emphasis on a model-theoretic treatment. Team semantics has roots in the modelling and logical treatment of notions of dependence and independence in connection with first-order quantification and characteristically introduces some second-order features, even on the basis
of weak fragments of first-order logic and starting from propositional logic.
In the course we look at the addition of team semantic primitives in the range between propositional logic and first-order logic. Most notably these involve atomic team properties for dependence, independence, inclusion and exclusion. A main goal is the model-theoretic investigation of the expressive power of the resulting logics.
Some keywords:
team semantics and team properties, dependence/independence, inklusion/exclusion;
proposituional, modal and first-order team logics; relationships with second-order logic;
model-theoretic games and equivalences; relevant fragments of first- and second-order logic.
Literatur
among other sources:
Vaananen: Dependence Logic (2007)
Abramsky, Kontinen, Vaananen, Vollmer (eds): Dependence Logic (2016)
Voraussetzungen
recommended: depending on topic
Online-Angebote
moodle
This course focuses on the formalisation of concepts related to sets of variable assignments rather than individual assignments, with an emphasis on a model-theoretic treatment. Team semantics has roots in the modelling and logical treatment of notions of dependence and independence in connection with first-order quantification and characteristically introduces some second-order features, even on the basis
of weak fragments of first-order logic and starting from propositional logic.
In the course we look at the addition of team semantic primitives in the range between propositional logic and first-order logic. Most notably these involve atomic team properties for dependence, independence, inclusion and exclusion. A main goal is the model-theoretic investigation of the expressive power of the resulting logics.
Some keywords:
team semantics and team properties, dependence/independence, inklusion/exclusion;
proposituional, modal and first-order team logics; relationships with second-order logic;
model-theoretic games and equivalences; relevant fragments of first- and second-order logic.
Literatur
among other sources:
Vaananen: Dependence Logic (2007)
Abramsky, Kontinen, Vaananen, Vollmer (eds): Dependence Logic (2016)
Voraussetzungen
recommended: depending on topic
Online-Angebote
moodle
- Lehrende: Martin Otto
Semester: ST 2020