Content: The course provides an introduction into important concepts in scientific computing, including the solution of linear systems, least squares problems, matrix decomposition, and (fast) Fourier representations. Each subject will be exemplified by a practical application which is developed in detail and implemented by the students.

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News

• There will be a lecture on 2/7/2019, usual time and place.
• The second assignment has been extended until 6. June, 11:00.
• In the week of 1. June tutorial and lecture are swapped, i.e. the tutorial will take place on Tuesday and the lecture on Thursday.
• Some students had trouble with lib.py with numpy 1.13. Here is a patched version.
• The first assignment is online. Due 10/05/2018.
• There will be no lecture or tutorial in the week of 8. April.
• See the Vorlesungsverzeichnis for details.

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Lectures

Week 1: Linear algebra recap Week 2: Floating point numbers Week 3/4: Linear systems Week 5/6: Least squares, Cholesky, and LU decomposition Week 7: Eigen decomposition and diagonalization of matrices Week 8: Principal component analysis and singular value decomposition Week 9 and 10: Discrete Fourier transform   Complex numbers

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Tutorials

Week 1: Introduction to python and Numpy

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Assignments

Assignments 1: Programming   Skeleton code   Theory Assignments 2: Programming   Skeleton code   Data   Theory Assignments 3: Programming   Skeleton code   Data   data.npz   Theory Assignments 4: Programming   Skeleton code   Example animation

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Software

We will be working with python and the Numpy library in this course. On Linux you can install it using your package manager. On other operating systems it is convenient to use the Anaconda distribution which contains all necessary packages.

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Literature

There are plenty of books on the material covered in the course. Some that I found useful over the years are:

• G. Strang, Lineare Algebra. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003.
• G. Strang, Wissenschaftliches Rechnen. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010.
• G. H. Golub and C. F. Van Loan, Matrix Computations. The Johns Hopkins University Press, 1996.
• W. Dahmen and A. Reusken, Numerik für Ingenieure und Naturwissenschaftler, second ed. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008.
• T. Huckle and S. Schneider, Numerik für Informatiker. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002.

Please find the text that best matches your intuition and thinking.