Technische Universität München, Fakultät für Informatik
 Forschungs- und Lehreinheit Informatik V Lehrstuhl für Informatik mit Schwerpunkt Wissenschaftliches Rechnen Scientific Computing in Computer Science

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# Numerical Programming I (for CSE)

## Prof. Dr. H.-J. Bungartz, S. Schraufstetter

Audience:
Time and Place:
• Lecture: Tuesdays 9:00 - 10:30, Thursdays, 12:00 - 13:30, lecture room 02.07.023
• Tutorial: Mondays, 14:00 - 15:30, lecture room 02.07.023

Contents:
• Foundations of numerical algorithms from calculus and linear algebra
• Floating point arithmetic (rounding error analysis, condition, and stability)
• Solving linear systems (Gaussian elimination, LR-factorization, pivoting, least squares, QR-factorization)
• Interpolation (polynomial ~, Spline ~, trigonometric ~, Fast Fourier Transform)
• Quadrature (Newton-Cotes formulae, extrapolation, Gaussian ~)
• Eigenvalue problems (symmetric, non-symmetric)
• Fundamentals of iterative methods (Jacobi and Gauss-Seidel ~, gradient ~, fixed point iteration, Newton ~)
• Basics of numerical methods for ordinary differential equations (Finite Differences, Euler and Runge-Kutta, consistency and convergence)

Course Material:

Tutorial:

Organization:
Problems will be available one week before being discussed in the tutorial. Within this time, you should try to solve them either on your own or within a small group. Some of the exercises are marked with a black triangle. These problems are intended to be presented in the tutorial by a student. So you should be able to demonstrate the marked problems at the board. Active participation is crucial for admission to the final exam.
Problems marked with 'P' are programming assignments. Solve this problems with MATLAB. A solution will be demonstrated and discussed in the tutorial.
Examination:

The final exam will take place on February, 21st from 12:15 to 13:45. We will meet at 12:00 in the seminar room 02.07.023. Please be there in time!
Assisting material is allowed, but limited to one DIN A4 sheet of paper with your own notes and reminders. It has to be handwritten by yourself, copies or printed versions will not be accepted. Except for this sheet, no other utilities (as lecture notes, calculators, notebooks, ...) are permitted.
For admission, it is required that you have presented at least two problems in the tutorial, thereof at least one problem of numerics (exercise sheet 6 and later).