Search result: Catalogue data in Autumn Semester 2016
Computational Science and Engineering Bachelor | ||||||
Bachelor Studies (Programme Regulations 2012) | ||||||
Basic Courses | ||||||
Block G1 | ||||||
Number | Title | Type | ECTS | Hours | Lecturers | |
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401-0353-00L | Analysis III | O | 4 credits | 2V + 1U | E. Kowalski | |
Abstract | In this lecture we treat problems in applied analysis. The focus lies on the simplest cases of three fundamental types of partial differential equations of second order: the Laplace equation, the heat equation and the wave equation. | |||||
Objective | ||||||
Content | 1.) Klassifizierung von PDE's - linear, quasilinear, nicht-linear - elliptisch, parabolisch, hyperbolisch 2.) Quasilineare PDE - Methode der Charakteristiken (Beispiele) 3.) Elliptische PDE - Bsp: Laplace-Gleichung - Harmonische Funktionen, Maximumsprinzip, Mittelwerts-Formel. - Methode der Variablenseparation. 4.) Parabolische PDE - Bsp: Wärmeleitungsgleichung - Bsp: Inverse Wärmeleitungsgleichung - Methode der Variablenseparation 5.) Hyperbolische PDE - Bsp: Wellengleichung - Formel von d'Alembert in (1+1)-Dimensionen - Methode der Variablenseparation 6.) Green'sche Funktionen - Rechnen mit der Dirac-Deltafunktion - Idee der Green'schen Funktionen (Beispiele) 7.) Ausblick auf numerische Methoden - 5-Punkt-Diskretisierung des Laplace-Operators (Beispiele) | |||||
Literature | Y. Pinchover, J. Rubinstein, "An Introduction to Partial Differential Equations", Cambridge University Press (12. Mai 2005) Zusätzliche Literatur: Erwin Kreyszig, "Advanced Engineering Mathematics", John Wiley & Sons, Kap. 8, 11, 16 (sehr gutes Buch, als Referenz zu benutzen) Norbert Hungerbühler, "Einführung in die partiellen Differentialgleichungen", vdf Hochschulverlag AG an der ETH Zürich. G. Felder:Partielle Differenzialgleichungen. Link | |||||
Prerequisites / Notice | Prerequisites: Analysis I and II, Fourier series (Komplexe Analysis) | |||||
402-0811-00L | Programming Techniques for Scientific Simulations I | O | 5 credits | 4G | M. Troyer | |
Abstract | This lecture provides an overview of programming techniques for scientific simulations. The focus is on advances 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 | ||||||
401-0663-00L | Numerical Methods for CSE | O | 7 credits | 4V + 2U | 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 | 1. Direct Methods for linear systems of equations 2. Least Squares Techniques 3. Data Interpolation and Fitting 4. Filtering Algorithms 8. Approximation of Functions 9. Numerical Quadrature 10. Iterative Methods for non-linear systems of equations 11. Single Step Methods for ODEs 12. Stiff Integrators | |||||
Lecture notes | Lecture materials (PDF documents and codes) will be made available to participants: Lecture document: Link Lecture Git repository: Link Tablet classroom notes: Link Lecture recording: Link Homework problems: Link | |||||
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. 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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