Search result: Catalogue data in Autumn Semester 2021
Computational Science and Engineering Bachelor  
Basic Courses  
Block G1  
Number  Title  Type  ECTS  Hours  Lecturers  

401035300L  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)  
401064700L  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.  
401267300L  Numerical Methods for CSE  O  9 credits  2V + 2U + 4P  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 * Iterative Methods for nonlinear systems of equations * Filtering Algorithms * Approximation of Functions * Numerical Quadrature  
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. HankeBourgeois "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. Knowledge of C++ is taken for granted.  
Competencies 

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