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# Numerical Analysis

## Module MA0008

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 2019/20

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
SS 2021WS 2020/1WS 2019/20

### Basic Information

MA0008 is a semester module in German language at Bachelor’s level which is offered in winter semester.

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

• Further Modules from Other Disciplines
270 h 120 h 9 CP

### Content, Learning Outcome and Preconditions

#### Content

Matrix factorizations with applications (direct solvers for linear systems of equations, linear least-squares problems); finite precision arithmetic (IEEE standard, condition of a problem, stability); solution of nonlinear systems of equations (fixed point iteration, Newton's method); interpolation (polynomials, splines); quadrature; additional selected topics: singular value decomposition, fast Fourier transform, eigenvalue problems, Monte Carlo quadrature, sparse matrices

#### Learning Outcome

Successful students of this module will understand the algorithmic-numerical way of thinking by means of the basic algorithms from numerical analysis and numerical linear algebra. Students know and can apply the basic techniques for the assessment of the efficiency and accuracy of numerical algorithms, can implement the algorithms with computer programs (using, e.g., MATLAB or Julia), and can apply basic techniques for the estimation of approximation errors.

#### Preconditions

MA0001 Analysis 1, MA0004 Linear Algebra 1, MA0010 Introduction to Programming

### Courses, Learning and Teaching Methods and Literature

#### Courses and Schedule

VO 4 Numerical Analysis [MA0008] Beddrich, J. Lunowa, S. Muhr, M. Wohlmuth, B. Mon, 16:15–17:45, MI HS1
Fri, 14:15–15:45, MI HS1
and singular or moved dates
eLearning
UE 2 Numerical Analysis (Exercise Session) [MA0008] Beddrich, J. Lunowa, S. Muhr, M. Wohlmuth, B. dates in groups
UE 2 Numerical Analysis (Central Exercise Session) [MA0008] Beddrich, J. Lunowa, S. Muhr, M. Wohlmuth, B. Fri, 10:15–11:45, EI-HS Garching
and singular or moved dates

#### Learning and Teaching Methods

lecture, exercise sessions, assignments and programming for self-study
The module is offered as lectures with accompanying practice sessions. In the lectures, the contents will be presented in a talk with demonstrative examples, as well as through discussion with the students. The lectures should motivate the students to carry out their own analysis of the themes presented and to independently study the relevant literature. Corresponding to each lecture, practice sessions will be offered, in which exercise sheets and solutions will be available. In this way, students can deepen their understanding of the methods and concepts taught in the lectures and independently check their progress.

#### Media

blackboard, computer experiments

#### Literature

Quarteroni/Sacco/Saleri: Numerical Mathematics, 2nd Edition, Springer, 2007
Ascher/Greif: A First Course in Numerical Methods, SIAM, 2011.
Quarteroni/Saleri/Gervasio: Scientific Computing with MATLAB and Octave, 4th Edition, Springer, 2014.

### Module Exam

#### Description of exams and course work

The module examination is based on a written exam (90 minutes). The algorithmic numerical way of thinking of the students will be assessed together with their ability to implement basic algorithms in a computer program. Students have to show in a limited amount of time that they know and can apply basic techniques for the evaluation of the efficiency and accuracy of numerical algorithms and the estimation of approximation errors.

#### Exam Repetition

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

#### Current exam dates

Currently TUMonline lists the following exam dates. In addition to the general information above please refer to the current information given during the course.

Title
TimeLocationInfoRegistration
Numerical Analysis
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