## Roger Käppeli: Catalogue data in Autumn Semester 2021 |

Name | Dr. Roger Käppeli |

Address | Professur für Angew. Mathematik ETH Zürich, HG G 52.1 Rämistrasse 101 8092 Zürich SWITZERLAND |

Telephone | +41 44 632 84 95 |

roger.kaeppeli@sam.math.ethz.ch | |

URL | https://people.math.ethz.ch/~karoger/ |

Department | Mathematics |

Relationship | Lecturer |

Number | Title | ECTS | Hours | Lecturers | |
---|---|---|---|---|---|

401-0435-00L | Computational Methods for Engineering Applications | 4 credits | 2V + 2U | R. Käppeli, M. Petrella | |

Abstract | The course gives an introduction to the numerical methods for the solution of ordinary and partial differential equations that play a central role in engineering applications. Both basic theoretical concepts and implementation techniques necessary to understand and master the methods will be addressed. | ||||

Objective | At the end of the course the students should be able to: - implement numerical methods for the solution of ODEs (= ordinary differential equations); - identify features of a PDE (= partial differential equation) based model that are relevant for the selection and performance of a numerical algorithm; - implement the finite difference, finite element and finite volume method for the solution of simple PDEs using C++; - read engineering research papers on numerical methods for ODEs or PDEs. | ||||

Content | Initial value problems for ODE: review of basic theory for ODEs, Forward and Backward Euler methods, Taylor series methods, Runge-Kutta methods, basic stability and consistency analysis, numerical solution of stiff ODEs. Two-point boundary value problems: Green's function representation of solutions, Maximum principle, finite difference schemes, stability analysis. Elliptic equations: Laplace's equation in one and two space dimensions, finite element methods, implementation of finite elements, error analysis. Parabolic equations: Heat equation, Fourier series representation, maximum principles, Finite difference schemes, Forward (backward) Euler, Crank-Nicolson method, stability analysis. Hyperbolic equations: Linear advection equation, method of characteristics, upwind schemes and their stability. | ||||

Lecture notes | Script will be provided. | ||||

Literature | Chapters of the following book provide supplementary reading and are not meant as course material: - A. Tveito and R. Winther, Introduction to Partial Differential Equations. A Computational Approach, Springer, 2005. | ||||

Prerequisites / Notice | (Suggested) Prerequisites: Analysis I-III (for D-MAVT), Linear Algebra, Models, Algorithms and Data: Introduction to Computing, basic familiarity with programming in C++. | ||||

401-0675-00L | Statistical and Numerical Methods for Chemical Engineers | 3 credits | 2V + 2U | R. Käppeli, P. Müller, A. Ruf, C.‑J. Shih, M. Sokolov | |

Abstract | This course covers common numerical algorithms and statistical methods used by chemical engineers to solve typical problems arising in industrial and research practice. | ||||

Objective | This course covers common numerical algorithms and statistical methods used by chemical engineers to solve typical problems arising in industrial and research practice. The focus is on application of these algorithms to real world problems, while the underlying mathematical principles are also explained. The MATLAB environment is adopted to integrate computation, visualization and programming. | ||||

Content | Topics covered: Part I: Numerical Methods: - Interpolation & Numerical Calculus - Non-linear Equations - Ordinary Differential Equations - Partial Differential Equations - Linear and Non-linear Least Squares Part II: Statistical Methods: - Data analysis and regression methods - Statistical experimental design - Multivariate analysis of spectra | ||||

Lecture notes | For the numerics part, see http://www.sam.math.ethz.ch/~karoger/numci/2020/ For the statistics part, see http://stat.ethz.ch/lectures/as21/statistical-numerical-methods.php | ||||

Literature | Recommended reading: 1) U. Ascher and C. Greif, A First Course in Numerical Methods, SIAM, Philadelphia, 2011 2) K. J. Beers, Numerical Methods for Chemical Engineering : Applications in MATLAB, Cambridge : Cambridge University Press, 2006 3) W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes, Cambridge University Press 4) W. A. Stahel, Statistische Datenanalyse, Vieweg, 4th edition 2002 | ||||

402-0811-00L | Programming Techniques for Scientific Simulations I | 5 credits | 4G | R. Käppeli | |

Abstract | This lecture provides an overview of programming techniques for scientific simulations. The focus is on basic and advanced C++ programming techniques and scientific software libraries. Based on an overview over the hardware components of PCs and supercomputer, optimization methods for scientific simulation codes are explained. | ||||

Objective | The goal of the course is that students learn basic and advanced programming techniques and scientific software libraries as used and applied for scientific simulations. |