Semester 2 in Hamburg
Numerical – Modelling Training
Semester 2 in Hamburg;
Numerical – Modelling Training
The Institute of Mathematics at TU Hamburg puts into place a group combining four chairs: Applied Analysis, Computational Mathematics, Numerical Mathematics, and Stochastics.
The computational part of this semester is taught by experts in the fields such as Sabine Le Borne (Professor in numerical mathematics with longstanding experience with computational mathematics programs) and Daniel Ruprecht (an expert in the parallelization of numerical methods).
Two additional courses are offered in this semester. A first one on Probability Theory provides a sound theoretical basis on stochastic modelling and an overview on its applications. This course is taught by Matthias Schulte, an internationally acknowledged expert in the field with wide range of expertise on probability, stochastics, large deviations, and random graphs (this course prepares for the specialization branch taught in Nice). A second complementary course on Variational Calculus provides a sound basis to the topics of Semester 3 at TUHH on biomedical imaging. This course is taught by Thomas Schmidt, an expert of calculus of variations and geometric PDEs, and by Ingenuin Gasser, who is an internationally acknowledged applied mathematician and a longstanding expert in managing international MSc programmes as well.
#Semester 2 in Hamburg EMJMD InterMaths Study Track
Numerical – Modelling Training;
ECTS Credits: 6 | Semester: 2 | Year: 1 | Campus: Hamburg University of Technology | Language: English | Code: DT0651
Unit Coordinator: Daniel Ruprecht
Students are able to list numerical methods for the solution of ordinary differential equations and explain their core ideas, repeat convergence statements for the treated numerical methods (including the prerequisites tied to the underlying problem), explain aspects regarding the practical execution of a method, select the appropriate numerical method for concrete problems, implement the numerical algorithms efficiently and interpret the numerical results.
Analysis, Linear Algebra, Basic MATLAB knowledge
ECTS Credits: 6 | Semester: 2 | Year: 1 | Campus: Hamburg University of Technology | Language: English | Code: DT0654
Unit Coordinator: Matthias Schulte
This course provides an introduction to probability theory and stochastic processes with special emphasis on applications and examples.
The first part covers some important concepts from measure theory, stochastic convergence and conditional expectation, while the second part deals with some important classes of stochastic processes.
Familiarity with the basic concepts of probability
ECTS Credits: 9 | Semester: 2 | Year: 1 | Campus: Hamburg University of Technology | Language: English | Code: DT0652
Unit Coordinator: Sabine Le Borne, Daniel Ruprecht
Students can list classical and modern iteration methods and their interrelationships, repeat convergence statements for iterative methods and explain aspects regarding the efficient implementation of iteration methods.
They will learn the fundamental concepts of parallel programming and how to translate them into efficient, parallel code.
They will learn how to compile parallel code and how to model and measure performance of parallelized software.
ECTS Credits: 6 | Semester: 2 | Year: 1 | Campus: Hamburg University of Technology | Language: English | Code: DT0653
Unit Coordinator: Thomas Schmidt, Ingenuin Gasser,
The module introduces to variational minimization problems and/or variational methods for PDEs.
It may cover problems in a classical smooth setting as well as theory in Sobolev spaces.
A selection out of the following:
- Model problems and examples (Dirichlet energy, isoperimetric and brachistochrone problems, minimal surfaces, Bolza and Weierstrass examples, …),
- Existence and uniqueness of minimizers by direct methods,
- Weak lower semicontinuity of (quasi)convex variational integrals,
- Necessary and sufficient (PDE) conditions for minimizers,
- Problems with constraints (obstacles, capacities, manifold and volume constraints, ...),
- Generalized minimizers (relaxation, Young measures, ...),
- Variational principles and applications,
- Duality theory,
- Outlook on regularity.
A solid background in analysis and linear algebra is necessary.
Familiarity with functional analysis, Sobolev spaces, and PDEs can be advantageous.
ECTS Credits: 3 | Semester: 2 | Year: 1 | Campus: Hamburg University of Technology | | Code: DT0668
Will be announced in lectures.