63-911 Introduction to Numerical Approaches

Veranstaltungsdetails
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Lehrende: Prof. Dr. Jörn Behrens

Veranstaltungsart: Vorlesung + Übung

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Semesterwochenstunden: 2

Credits: 3,0

Unterrichtssprache: Englisch

Min. | Max. Teilnehmerzahl: - | 20

Kommentare/ Inhalte:
Since most climate sciences rely heavily on modeling, and since many such models are based on numerical simulations, this course introduced basic numerical concepts inside a computer program. The following general topics will be covered:


  • Floating Point arithmetic (the reason, why numerical analysis differs from calculus)
  • Solving linear systems of equations (by LU factorization or interatively)
  • Condition and stability as two major concepts in analyzing numerical methods
  • Polynomial Interpolation
  • Trigonometric interpolation and Fourier analysis of data
  • Least Squares Approximation
  • Quadrature (aka numerical integration)
  • Eigenvalue Problems
  • Multi-Grid methods
  • Solving non-linear systems

Lernziel:
It is the aim of the course to introduce basic algorithms for solving the above mentioned problems, to learn basic concepts on how to assess efficiency and accuracy of the methods, and to implement simple examples of such algorithms.

Literatur:
A few helpful textbooks contain material that might be useful:


  • Cleve Moler: Numerical Computing with MATLAB, SIAM, Philadelphia, 2004 (http://dx.doi.org/10.1137/1.9780898717952)
  • A. Quarteroni, F. Saleri, P. Gervasio: Scientific Computing with MATLAB and Octave, Springer, Heidelberg, 2010 (https://doi.org/10.1007/978-3-642-12430-3)

Termine
Datum Von Bis Raum Lehrende
1 Mi, 16. Okt. 2019 10:15 11:45 GB 5, Rm. 006 Prof. Dr. Jörn Behrens
2 Mi, 23. Okt. 2019 10:15 11:45 GB 5, Rm. 006 Prof. Dr. Jörn Behrens
3 Mi, 30. Okt. 2019 10:15 11:45 GB 5, Rm. 006 Prof. Dr. Jörn Behrens
4 Mi, 6. Nov. 2019 10:15 11:45 GB 5, Rm. 006 Prof. Dr. Jörn Behrens
5 Mi, 13. Nov. 2019 10:15 11:45 GB 5, Rm. 006 Prof. Dr. Jörn Behrens
6 Mi, 20. Nov. 2019 10:15 11:45 GB 5, Rm. 006 Prof. Dr. Jörn Behrens
7 Mi, 27. Nov. 2019 10:15 11:45 GB 5, Rm. 006 Prof. Dr. Jörn Behrens
8 Mi, 4. Dez. 2019 10:15 11:45 GB 5, Rm. 006 Prof. Dr. Jörn Behrens
9 Mi, 11. Dez. 2019 10:15 11:45 GB 5, Rm. 006 Prof. Dr. Jörn Behrens
10 Mi, 18. Dez. 2019 10:15 11:45 GB 5, Rm. 006 Prof. Dr. Jörn Behrens
11 Mi, 8. Jan. 2020 10:15 11:45 GB 5, Rm. 006 Prof. Dr. Jörn Behrens
12 Mi, 15. Jan. 2020 10:15 11:45 GB 5, Rm. 006 Prof. Dr. Jörn Behrens
13 Mi, 22. Jan. 2020 10:15 11:45 GB 5, Rm. 006 Prof. Dr. Jörn Behrens
14 Mi, 29. Jan. 2020 10:15 11:45 GB 5, Rm. 006 Prof. Dr. Jörn Behrens
Prüfungen im Rahmen von Modulen
Modul (Startsemester)/ Kurs Prüfung Datum Lehrende Bestehens­pflicht
ICSS-M-1.4 Climate Science Specialization (WiSe 19/20) / ICSS-M-1.4.1  Introduction to Numerical Approaches 1  Klausur oder mündliche Prüfung k.Terminbuchung Prof. Dr. Jörn Behrens Ja
Veranstaltungseigene Prüfungen
Beschreibung Datum Lehrende Pflicht
1. Report k.Terminbuchung Ja
Übersicht der Kurstermine
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Lehrende
Prof. Dr. Jörn Behrens