M1107-CMS13
Basic Numerical Methods
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| Module Owner: |
Prof. Dr. sc. techn. Ivo Fabian Sbalzarini |
| Displayed in timetable as: |
CMS-COR-NUM |
| Duration: |
7 |
| Number of electives: |
0 |
| Credits: |
5,0
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| Start Semester: |
WiSe 2020/21 |
| Lecturer Responsible |
Prof. Dr. Ivo Sbalzarini
ivo.sbalzarini@tu-dresden.de
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| Qualification Goals |
Upon completin this module, the students will acquire the basics of numerical mathematics and numerical simulation methods. This includes the theoretical understanding of how a computer calculates with finite floating-point numbers and what kind of errors and inaccuracies may arise from these, and how to reduce or control them same. They will be familiar with basic numerical methods for modelling and simulating statistical models, linear algebra models, and ordinary and partial differential equations. They will be able to estimate the approximation errors of the methods and determine the algorithmic intensity, and will be able to implement these methods themselves. |
| Content |
Floating point arithmetic, rounding errors, cancellation, numerical interpolation (Lagrange, Newton, Splines), Taylor developments, finite differences and their approximation errors, explicit and implicit time integrators, direct and iterative algorithms for matrix inversion, matrix decomposition (LU), solution for the Poisson equation. |
| Forms of Teaching and Learning |
The module includes 2 SWS worth of lectures, 2 SWS worth of exercises and the self-study. |
| Prerequisites for Participation |
Knowledge in sequential computer programming, algorithms and data structures, analysis of functions of one and several variables, linear algebra (vector and matrix calculation), as well as probability calculation and Statistics at the Bachelor's level is required.
With the following literature, students can prepare for the module:
Harel: Algorithmics - The Spirit of Computing, Addison-Wesley, 2004
Schildt: C ++ from the ground up, McGraw-Hill, 2003
Abelson, Hal; Sussman, Gerald Jay: Structure and Interpretation of Computer Programs. MIT Press, 1985;
Cormen, Leiserson, Rivest & Stein: Introduction to Algorithms, 2nd Edition, MIT Press 2001;
Lax, Terrell: Multivariable Calculus with Applications (Undergraduate Texts in Mathematics), Springer, 2018
Hefferon, Jim: Linear Algebra, http://joshua.smcvt.edu/linearalgebra/, 2008.
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| Applicability |
In the Computational Modelling and Simulation Master's programme, the module is one of ten compulsory elective modules (for students of Computational Life Science: nine), of which three must be chosen. Completion of this fulfills the prerequisite for the module CMS-CE-CFD. |
| Prerequisites for the Assignment of Credit Points |
The credit points are awarded if the module examination is passed. If there are more than 10 registered students, the module examination consists of a written examination, with a duration of 90 minutes. If there are 10 or fewer registered students, it consists of an oral examination as an individual examination performance amounting to 30 minutes; this will be announced to the enrolled students at the end of the enrollment period. |
| Credit Points and Grades |
This module allows for the earning of 5 credit points. The module grade corresponds to the grade of the examination performance. |
| Frequency of Offer |
The module is offered every winter semester. |
| Workload |
The workload is a total of 150 hours. |
| Duration of Module |
The module takes one semester. |
| Module Number Module Handbook TU Dresden |
CMS-COR-NUM |
