# Suchergebnis: Katalogdaten im Herbstsemester 2021

Rechnergestützte Wissenschaften Bachelor  Grundlagenfächer  Block G1
NummerTitelTypECTSUmfangDozierende
401-0353-00LAnalysis 3  O4 KP2V + 2UM. Iacobelli
KurzbeschreibungIn 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.
LernzielThe 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.
Inhalt1.) 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
LiteraturY. Pinchover, J. Rubinstein, "An Introduction to Partial Differential Equations", Cambridge University Press (12. Mai 2005)
Voraussetzungen / BesonderesPrerequisites: Analysis I and II, Fourier series (Complex Analysis)
401-0647-00LIntroduction to Mathematical OptimizationO5 KP2V + 1UD. Adjiashvili
KurzbeschreibungIntroduction to basic techniques and problems in mathematical optimization, and their applications to a variety of problems in engineering.
LernzielThe 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.
InhaltTopics 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.
LiteraturInformation about relevant literature will be given in the lecture.
Voraussetzungen / BesonderesThis 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.
401-2673-00LNumerical Methods for CSEO9 KP2V + 2U + 4PR. Hiptmair
KurzbeschreibungThe 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++.
Lernziel* 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
Inhalt* Computing with Matrices and Vectors
* Direct Methods for linear systems of equations
* Least Squares Techniques
* Data Interpolation and Fitting
* Iterative Methods for non-linear systems of equations
* Filtering Algorithms
* Approximation of Functions
SkriptLecture 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.
LiteraturU. 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
Voraussetzungen / BesonderesThe course will be accompanied by programming exercises in C++ relying on the template library EIGEN. Knowledge of C++ is taken for granted.
Kompetenzen Fachspezifische Kompetenzen Konzepte und Theorien geprüft Verfahren und Technologien geprüft Methodenspezifische Kompetenzen Analytische Kompetenzen geprüft Medien und digitale Technologien gefördert Problemlösung geprüft Projektmanagement gefördert
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