Numerical Analysis
Module MA0008
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 2021 (current)
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 2021 | WS 2020/1 | WS 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
| Total workload | Contact hours | Credits (ECTS) |
|---|---|---|
| 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
| Type | SWS | Title | Lecturer(s) | Dates | Links |
|---|---|---|---|---|---|
| VO | 4 | Numerical Analysis [MA0008] | Beddrich, J. Wohlmuth, B. |
Mon, 16:15–17:45, MI HS1 Fri, 14:15–15:45, MI HS1 |
|
| UE | 2 | Numerical Analysis (Central Exercise Session) [MA0008] | Beddrich, J. Wohlmuth, B. |
Fri, 10:15–11:45, EI-HS Garching |
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.
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.
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.