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Numerical Programming 1 (CSE)

Module MA3305

This Module is offered by TUM Department of Mathematics.

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Module version of WS 2011/2

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

available module versions
SS 2012WS 2011/2

Basic Information

MA3305 is a semester module in English language at Master’s level which is offered in winter semester.

This Module is included in the following catalogues within the study programs in physics.

  • Catalogue of non-physics elective courses
Total workloadContact hoursCredits (ECTS)
240 h 90 h 8 CP

Content, Learning Outcome and Preconditions

Content

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.

Learning Outcome

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.

Preconditions

working knowledge of analysis and linear algebra

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

Learning and Teaching Methods

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.

Media

blackboard, LCD projector, assignments

Literature

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.

Module Exam

Description of exams and course work

The exam will be in written form (90 minutes). 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.

Exam Repetition

The exam may be repeated at the end of the semester.

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