Courses in Winter Term 2023/24
Our group offers the following courses in winter term 2023/24:
Introduction to Numerical Methods
Numerical Methods for Ordinary Differential Equations
Scientific Computing in Solid Mechanics
Introduction to Numerical Methods
Contents
The basic concepts and algorithms for the numerical solution of problems from linear algebra and analysis are covered:
- error analysis: condition of a problem, stability of an algorithm
- approximation theory: interpolation by polynomial and spline functions
- numerical methods for linear systems of equations
- linear curve fitting
- eigenvalue problems
- numerical integration: interpolation and Gaussian quadrature
- nonlinear and parameter-dependent systems of equations
Numerical Methods for Ordinary Differential Equations
Contents
Most problems in science, technology, and engineering can be modeled by a set of differential equations. In general, these equations are too complex to be solved analytically. This course provides the necessary tools and methods to treat initial value problems numerically.
The following topics will be covered:
- explicit and implicit one-step methods (Runge-Kutta methods)
- error estimation and step size control
- multistep methods (Adams and BDF methods)
- consistency, stability, and convergence
- methods for stiff problems
Scientific Computing in Solid Mechanics
Links / Contact
Lecturer: Prof. Dr. Bernd Simeon
KIS entry:
Scientific Computing in Solid Mechanics
Course in OLAT:
RPTUScientific Computing in Solid Mechanics WS 2023/24
Courses in Summer Term 2023
Our group offers the following courses in summer term 2023:
Introduction to Ordinary Differential Equations
Higher Mathematics II
Introduction to Ordinary Differential Equations
Contents
- first-order differential equations: autonomous first-order differential equations, variation of constants, explicitly solvable cases, initial value problems
- existence and uniqueness: functional-analytical foundations, Banach fixed-point theorem, Picard-Lindelöf theorem, the continuability of solutions, Peano's existence theorem
- qualitative behaviour: Grönwall's lemma, continuous dependency on data, upper and lower functions
- linear differential equations: homogeneous linear systems, matrix exponential function, variation of constants, nth-order differential equations
- stability: dynamical systems, phase space, Hamiltonian systems, asymptotic behaviour, stability theory according to Lyapunov
Higher Mathematics II
Contents
- vector analysis: vectors, subspaces, linear independence, basis, dimension, scalar product, orthogonality, projections, vector product
- matrix calculus: definition, calculation rules, base change, linear mappings, description of linear mappings via matrices, linear systems of equations (description via matrices, structure of solutions, Gaussian algorithm), invertibility, calculation of inverse, normal equations and linear least squares, determinants, eigenvalues and eigenvectors (diagonalizability, principal axis theorem)
- differentiation (multidimensional): scalar and vector fields, curves, contour lines, total and partial differentiability, directional derivation, implicit differentiation, inverse function theorem, differentiation rules (in particular: inverse function and chain rule), Taylor expansion, extremes under constraints (scalar functions of several variables), gradient fields, potentials, divergence and rotation, applications
- integration (multidimensional): normal domains, multiple integrals over normal domains
Links / Contact
Lecturer: Prof. Dr. Bernd Simeon
KIS entries:
Higher Mathematics II (Lecture)
Higher Mathematics II (Tutorial)
Course in OLAT:
RPTU Higher Mathematics II SS 2023
Courses in Winter Term 2022/23
Our group offers the following courses in winter term 2022/23:
Differential-Algebraic Equations
Differential-Algebraic Equations
Contents
The theory and numerical analysis of differential-algebraic equations are discussed, in particular:
- application fields (electrical circuits and multibody mechanical systems)
- relation with singularly perturbed problems
- solution theory and index concepts
- normal form for linear DAEs
- numerical aspects
Courses in Summer Term 2022
Our group offers the following courses in summer term 2022:
Scientific Computing in Solid Mechanics
Spline Functions
Scientific Computing in Solid Mechanics
Links / Contact
Lecturer: Prof. Dr. Bernd Simeon
KIS entry:
Scientific Computing in Solid Mechanics
Course in OLAT:
TUK Scientific Computing in Solid Mechanics SS 2022
Spline Functions
Links / Contact
Lecturer: Prof. Dr. Bernd Simeon
KIS entry:
Spline Functions
Course in OLAT:
TUK Spline Functions SS 2022
Courses in Winter Term 2021/22
Our group offers the following courses in winter term 2021/22:
Numerical Methods for Ordinary Differential Equations
Differential-Algebraic Equations
Proseminar "B-Splines and NURBS"
Numerical Methods for Ordinary Differential Equations
Contents
Most problems in science, technology, and engineering can be modeled by a set of differential equations. In general, these equations are too complex to be solved analytically. This course provides the necessary tools and methods to treat initial value problems numerically.
The following topics will be covered:
- explicit and implicit one-step methods (Runge-Kutta methods)
- error estimation and step size control
- multistep methods (Adams and BDF methods)
- consistency, stability, and convergence
- methods for stiff problems
Differential-Algebraic Equations
Contents
The theory and numerical analysis of differential-algebraic equations are discussed, in particular:
- application fields (electrical circuits and multibody mechanical systems)
- relation with singularly perturbed problems
- solution theory and index concepts
- normal form for linear DAEs
- numerical aspects
Proseminar "B-Splines and NURBS"
Links / Contact
Lecturer: Prof. Dr. Bernd Simeon
KIS entries: Proseminar B-Splines and NURBS (Seminar)
Course in OLAT:
TUK Proseminar "B-Splines and NURBS" WS 2021/22
Courses in Summer Term 2021
Our group offers the following courses in summer term 2021:
Numerical Methods for Partial Differential Equations I
Scientific Computing in Solid Mechanics
Numerical Methods for Partial Differential Equations I
Contents
To describe real-world processes, one often makes use of partial differential equations, which, in general, cannot be solved analytically. In this course, we will discuss and study the mathematical techniques required for solving such equations numerically. The focus lies on the discretization of boundary value problems for elliptic differential equations with finite difference or finite element methods. At the end of the course, these ideas will be applied to parabolic differential equations.
The following topics will be covered:
- approximation methods for elliptic problems
- theory of weak solutions
- consistency, stability, and convergence
- approximation methods for parabolic problems
Scientific Computing in Solid Mechanics
Links / Contact
Lecturer: Prof. Dr. Bernd Simeon
KIS entry:
Scientific Computing in Solid Mechanics
Course in OLAT:
TUK Scientific Computing in Solid Mechanics SS 2021
Courses in Winter Term 2020/21
Our group offers the following courses in winter term 2020/21:
Introduction to Numerical Methods
Introduction to Numerical Methods
Contents
The basic concepts and algorithms for the numerical solution of problems from linear algebra and analysis are covered:
- error analysis: condition of a problem, stability of an algorithm
- approximation theory: interpolation by polynomial and spline functions
- numerical methods for linear systems of equations
- linear curve fitting
- eigenvalue problems
- numerical integration: interpolation and Gaussian quadrature
- nonlinear and parameter-dependent systems of equations