Focus topic: Applied Mathematics - Analysis, Numerics, Scientific Computing

Applied Mathematics deals with the development of analytical and numerical mathematical concepts and methods that can (potentially) be applied to treat questions from other scientific disciplines. This includes mathematical modelling of problems in the life, natural, and engineering sciences and the analytical and/or numerical treatment of the resulting, usually nonlinear, systems of differential equations and optimization problems. Also the efficient implementation for computer simulations is covered.

From the mathematical perspective, particularly methods from analysis (theory of partial differential equations, functional analysis, theory of dynamical systems, regularity analysis, calculus of variations, ...), methods from numerics (discretization methods, convergence analysis, a priori and a posteriori error estimation, model reduction, ...) as well as the development and mathematical analysis of efficient algorithms are employed.

Depending on the focus, connections to other mathematical areas abound, e.g. differential geometry, functional analysis, and stochastics. In addition to the mathematical focus it is possible to write the thesis in close collaboration with groups from the application side, e.g. biology and medicine in Münster.

Simulation of blood flow through a constricted carotid artery of a mouse to study causes of atherosclerosis.

Courses for the specialisation in Applied Mathematics (AM) and Scientific Computing (SC)

Winter semester 2019/2020

  • Prof. Dr. Christian Engwer: scientific computing (type I, II, SC)
  • JProf. Dr. Manuel Friedrich: partial differential equations II (type I,II,AM)
  • Prof. Dr. Angela Stevens: calculus of variations (type I,II, AM)
  • Prof. Dr. Carsten Wolters: new mathematical methods in bioelectromagnetism and their neuroscientific applications (type I,II, AM/SC); 2+1 hours lecture, continuing in summer semester 2020
  • Prof. Dr. Caterina Zeppieri: geometric measure theory (type I,II, AM)

Summer semester 2020

  • Prof. Dr. Arnulf Jentzen: Mathematical Introduction to Machine Learning (Type I, WR)
  • Prof. Dr. Mario Ohlberger: Numerical Analysis for Partial Differential Equations II (Type II, WR)
  • Prof. Dr. Carsten Wolters: New athematical methods in bioelectromagnetism and their neuroscientific applications (type I,II, AM/SC); 2+1 hours lecture, continuation of winter semester 2019/2020
  • Prof. Dr. Caterina Zeppieri: Functions of bounded variation and free-discontinuity problems (Type I, AM)

Seminars

Winter semester 2019/2020

  • JProf. Dr. Manuel Friedrich: calculus of variations (AM, SC)
  • Prof. Dr. Christian Seis
  • Prof. Dr. Angela Stevens: Partial differential equations and mathematical modelling (AM)
  • Dr. Fank Wübbeling: mathematical image processing (AM, SC)
  • Prof. Dr. Caterina Zeppieri

Summer semester 2020

  • Prof. Dr. Christian Engwer: Scientific cumputing (WR)
  • Prof. Dr. Arnulf Jentzen: Mathematics of Deep Learning (WR)
  • Prof. Dr. Christian Seis: Mathematical flud dynamics (AM)
  • Prof. Dr. Benedikt Wirth: Mathematical optimization (AM, WR)
  • Prof. Dr. Caterina Zeppieri, Prof. Dr. Martin Huesmann: Stochastic homogenization (AM)

Seminars for AM and SC are always courses of type II. The seminars in both specialisations can in principle also be used as "first course" in the complementary module.
 

Practical courses

Winter semester 2019/2020

  • Prof. Dr. Christian Engwer, Prof. Dr. Mario Ohlberger: nonlinear modelling in the natural sciences (AM, SC)
  • Dr. Frank Wübbeling: mathematical methods in biomedical imaging (AM, SC)

Summer semester 2020

  • Prof. Dr. Christian Engwer, Prof. Dr. Mario Ohlberger: nonlinear modelling in the sciences (AM, SC)

Practical courses for AM and SC are always courses of type II.

Prerequisites

Specialisation Applied Mathematics

Basic courses on ordinary and partial differential equations, covering:

Fundamentals of ordinary differential equations, Gauß' theorem, examples of partial differential equations, method of characteristics and differential equations of first order, elliptic partial differential equations and weak formulation, Sobolev spaces, parabolic differential equations

Specialisation Scientific Computing

Basic courses on numerical analysis and programming courses, covering:

Fundamentals of iterative methods to solve linear systems of equations, Newton method, fundamentals of ordinary differential equations, fundamentals of programming, a basic understanding of partial differential equations, weak and strong formulations, Gauß' theorem, Sobolev spaces

Contact and module representatives

Contact: Prof. Dr. Benedikt Wirth

Module representatives: Prof. Dr. Mario Ohlberger (SC), Prof. Dr. Angela Stevens (AM), Prof. Dr. Benedikt Wirth (AM, SC)