de | en

# Numerical Programming 1 (CSE)

## Module MA3305

This Module is offered by 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 SS 2012

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

Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.

available module versions
WS 2021/2WS 2020/1SS 2020SS 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
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);
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

VO 4 Numerical Programming 1 CSE Bornemann, F. Mon, 12:00–14:00, MI HS2
Wed, 12:00–14:00, MI HS3
documents
UE 2 Numerical Programming 1 CSE (Exercise Session) Bornemann, F. Ludwig, C. Thu, 11:45–13:30, MW 1237
and dates in groups
documents

#### 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.

Top of page