MSE Master of Science in Engineering

The Swiss engineering master's degree

Jedes Modul umfasst 3 ECTS. Sie wählen insgesamt 10 Module/30 ECTS in den folgenden Modulkategorien:

  • ​​​​12-15 ECTS in Technisch-wissenschaftlichen Modulen (TSM)
    TSM-Module vermitteln Ihnen profilspezifische Fachkompetenz und ergänzen die dezentralen Vertiefungsmodule.
  • 9-12 ECTS in Erweiterten theoretischen Grundlagen (FTP)
    FTP-Module behandeln theoretische Grundlagen wie die höhere Mathematik, Physik, Informationstheorie, Chemie usw. Sie erweitern Ihre abstrakte, wissenschaftliche Tiefe und tragen dazu bei, den für die Innovation wichtigen Bogen zwischen Abstraktion und Anwendung spannen zu können.
  • 6-9 ECTS in Kontextmodulen (CM)
    CM-Module vermitteln Ihnen Zusatzkompetenzen aus Bereichen wie Technologiemanagement, Betriebswirtschaft, Kommunikation, Projektmanagement, Patentrecht, Vertragsrecht usw.

In der Modulbeschreibung (siehe: Herunterladen der vollständigen Modulbeschreibung) finden Sie die kompletten Sprachangaben je Modul, unterteilt in die folgenden Kategorien:

  • Unterricht
  • Dokumentation
  • Prüfung
Numerical Analysis and Computer Algebra (FTP_CompAlg)

After successful studying students are capable to solve selected practical mathematical problems by combining appropriate numerical methods with suitable computer algebra tools. Moreover, students know how to interprete and visualize computational outcomes resulting from numerical algorithms.

Eintrittskompetenzen

Linear Algebra

  • Algebra with vectors and matrices
  • Elementary solving linear systems of equations (Gauss Pivoting)
  • Eigenvectors and Eigenvalues

Analysis

  • Univariate and multivariate calculus (differentials, integrals)
  • Knowing of simple numerical recipes for equations and integrals (e.g. Bi-Section, Newton, Trapezoidal-Rule, Simpson-Rule...)
  • Ordinary differential equations including simple numerical recipes (e.g. Euler)

Basics in Computer Handling

  • Operating system, software installation
  • Elementary skills in procedural programming

Hardware and Software

  • Notebook
  • Mathematical software installed (e.g. Mathematica, Matlab, Maple ... according to preference and experience)

 

Lernziele

Solving mathematical problems with practial relevance by

  • capable handling a computer algebra system (CAS) or appropriate mathematical software
  • mastering selected numerical methods

Knowing limits of computer based methods and comprehension of

  • some internals of CAS (e.g. representations of numbers and functions)
  • the problems of numerical stability, errors from rounding and discretization
  • algorithmic complexity (e.g. convergence speed)

Combining analytical methods of CAS with efficient numerical software

Interpreting and visualizing computational results

Modulinhalt

Processing

  • data from problems with practical relevance
  • by tools from numerical mathematics and analytics
  • up to interpretation and visualization of results

Based on a selection of methods listed below

  • Solving systems of linear equations (LU-Decomposition, Cholesky Decomposition, Householder Transformations, QR Decomposition, sparse matrix strategies and Gauss-Seidel ...)
  • Computations of zeroes and non-linear optimization
  • Univariate and multivariate interpolation and approximation (Collocation, Osculation, Splining, Least-Squares Approximation, Chebyshev Approximation ...)
  • Numerical differentiation and integration
  • Initial and boundary value problems of ordinary differential equations

With consideration of

  • Accuracy, efficiency and condition
  • Problem identification and method selection
  • Computeralgebra in order to establish analytical relations

Lehr- und Lernmethoden

  • Derivation of mathematical facts in lectures
  • Software demonstrations and visualizations by the lecturer during the lectures
  • Teaching based on problems with practical relevance
  • Software examples and additional materials on complimentary website (Zuerich)
  • Hints to sources and literature on complimentary website (Zuerich)
  • Self-studies based on sources and literature
  • Doing homework as a preparation for dedicated exercise lessons

Bibliografie

  • Schaum’s Outlines of Numerical Analysis, McGraw-Hill Professional, 2nd edition
  • Schwarz, Hans R.; Köckler, Norbert; Numerische Mathematik, Vieweg & Teubner, 7. Auflage
  • Bronstein et al., Taschenbuch der Mathematik, Harri Deutsch
  • Bradie, Brian, A Friendly Introduction to Numerical Analysis, Prentice-Hall
  • Alfio Quarteroni, Riccardo Sacco, Fausto Saleri, M´ethodes Num´eriques - Algorithmes, analyse et applications, Springer, 2007
  • Jean-Philippe Grivet, Méthodes numériques appliqués, EDP sciences
  • Koepf, Wolfram, Computeralgebra, Springer
  • Moler Cleve, Numerical Computing with Matlab, www.mathworks.com/moler/chapters.html
  • Erwin Kreyszig, Advanced Engineering Mathematics, Wiley
  • Erwin Kreyszig, Advanced Engineering Mathematics – Students Solution Manual and Study Guide, Wiley
  • Erwin Kreyszig/E.J. Norminton, Mathematica Computer Guide for Erwin Kreiszigs Advanced Engineering Mathematics, Wiley
  • Michael Trott, The Mathematica Guide Book for Numerics, Springer

Vollständige Modulbeschreibung herunterladen

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