# Search result: Catalogue data in Autumn Semester 2020

Computational Science and Engineering Bachelor | ||||||

Bachelor Studies (Programme Regulations 2018) | ||||||

Basic Courses | ||||||

Block G1 | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |
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401-0353-00L | Analysis 3 | O | 4 credits | 2V + 2U | M. Iacobelli | |

Abstract | In this lecture we treat problems in applied analysis. The focus lies on the solution of quasilinear first order PDEs with the method of characteristics, and on the study of three fundamental types of partial differential equations of second order: the Laplace equation, the heat equation, and the wave equation. | |||||

Objective | The aim of this class is to provide students with a general overview of first and second order PDEs, and teach them how to solve some of these equations using characteristics and/or separation of variables. | |||||

Content | 1.) General introduction to PDEs and their classification (linear, quasilinear, semilinear, nonlinear / elliptic, parabolic, hyperbolic) 2.) Quasilinear first order PDEs - Solution with the method of characteristics - COnservation laws 3.) Hyperbolic PDEs - wave equation - d'Alembert formula in (1+1)-dimensions - method of separation of variables 4.) Parabolic PDEs - heat equation - maximum principle - method of separation of variables 5.) Elliptic PDEs - Laplace equation - maximum principle - method of separation of variables - variational method | |||||

Literature | Y. Pinchover, J. Rubinstein, "An Introduction to Partial Differential Equations", Cambridge University Press (12. Mai 2005) | |||||

Prerequisites / Notice | Prerequisites: Analysis I and II, Fourier series (Complex Analysis) | |||||

401-0647-00L | Introduction to Mathematical Optimization | O | 5 credits | 2V + 1U | D. Adjiashvili | |

Abstract | Introduction to basic techniques and problems in mathematical optimization, and their applications to a variety of problems in engineering. | |||||

Objective | The goal of the course is to obtain a good understanding of some of the most fundamental mathematical optimization techniques used to solve linear programs and basic combinatorial optimization problems. The students will also practice applying the learned models to problems in engineering. | |||||

Content | Topics covered in this course include: - Linear programming (simplex method, duality theory, shadow prices, ...). - Basic combinatorial optimization problems (spanning trees, shortest paths, network flows, ...). - Modelling with mathematical optimization: applications of mathematical programming in engineering. | |||||

Literature | Information about relevant literature will be given in the lecture. | |||||

Prerequisites / Notice | This course is meant for students who did not already attend the course "Mathematical Optimization", which is a more advance lecture covering similar topics. Compared to "Mathematical Optimization", this course has a stronger focus on modeling and applications. | |||||

401-0663-00L | Numerical Methods for CSE | O | 8 credits | 2V + 2U + 3P | R. Hiptmair | |

Abstract | The course gives an introduction into fundamental techniques and algorithms of numerical mathematics which play a central role in numerical simulations in science and technology. The course focuses on fundamental ideas and algorithmic aspects of numerical methods. The exercises involve actual implementation of numerical methods in C++. | |||||

Objective | * Knowledge of the fundamental algorithms in numerical mathematics * Knowledge of the essential terms in numerical mathematics and the techniques used for the analysis of numerical algorithms * Ability to choose the appropriate numerical method for concrete problems * Ability to interpret numerical results * Ability to implement numerical algorithms afficiently | |||||

Content | * Computing with Matrices and Vectors * Direct Methods for linear systems of equations * Least Squares Techniques * Data Interpolation and Fitting * Filtering Algorithms * Data Interpolation and Data Fitting in 1D * Approximation of Functions in One Dimension * Numerical Quadrature * Iterative Methods for non-linear systems of equations | |||||

Lecture notes | Lecture materials (PDF documents and codes) will be made available to the participants through the course web page, whose address will be announced in the beginning of the course. | |||||

Literature | U. ASCHER AND C. GREIF, A First Course in Numerical Methods, SIAM, Philadelphia, 2011. A. QUARTERONI, R. SACCO, AND F. SALERI, Numerical mathematics, vol. 37 of Texts in Applied Mathematics, Springer, New York, 2000. W. Dahmen, A. Reusken "Numerik für Ingenieure und Naturwissenschaftler", Springer 2006. W. Gander, M.J. Gander, and F. Kwok "Scientific Computing", Springer 2014. M. Hanke-Bourgeois "Grundlagen der Numerischen Mathematik und des wissenschaftlichen Rechnens", BG Teubner, 2002 P. Deuflhard and A. Hohmann, "Numerische Mathematik I", DeGruyter, 2002 | |||||

Prerequisites / Notice | The course will be accompanied by programming exercises in C++ relying on the template library EIGEN. Familiarity with C++, object oriented and generic programming is an advantage. Participants of the course are expected to learn C++ by themselves. |

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