Numerical Programming 1 (CSE)

Fundamentals of analysis and linear algebra;
Condition numbers, floating point arithmetic, stability;
Solving linear systems (Gaussian elimination, least squares);
Eigenvalue problems;
Interpolation (algebraic and trigonometric polynomials, splines);
Intgration (sum rules, Gaussian quadrature);
Iterative methods (Jacobi, Gauß-Seidel, conjugate gradient method (CG), Newton);
Runge-Kutta method.

At the end of the module, the students are able to understand the mathematical principles of basic numerical algorithms for solving linear systems and eigenvalue problems, for interpolation and integration.

working knowledge of analysis and linear algebra

This module comprises lectures and accompanying tutorials. Students will be encouraged to study the literature and to get involved with the topics in depth. In the tutorials, concrete numerical problems will be solved and selected examples will be discussed.

blackboard, LCD projector, assignments

Quarteroni /Saleri /Gervasio: Scientific Computing with MATLAB and Octave, Springer 2010.
Moler: Numerical Computing with MATLAB, SIAM, 2004.
Press, Flannery, Teukolsky, Vetterling: Numerical Recipes.Cambridge University Press, http://www.nr.com/.
Strang: Introduction to Linear Algebra, Wellesley-Cambridge, 2009.
Strang, Calculus, Wellesley-Cambridge, 1991.

The course examination will happen as three online graded homework assignments (G1, G2, G3), managed via the TUMexam system. The final grade is the next smallest grade to the average (G1+G2+G3)/3 according to the TUM grading system (x.0, x.3, x.7).
Students demonstrate that they have gained deeper knowledge of the mathematical concepts of the numerical algorithms presented in the course. The students are expected to be able to derive the methods, to explain their properties, to read and write pseudocode of the algorithms, and to apply them to specific examples.