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t.BA.XXM4.NUM.19HS (Numerics)
Module: Numerics
This information was generated on: 30 November 2023
No.
t.BA.XXM4.NUM.19HS
Title
Numerics
Organised by
T IAMP
Credits
4
Description
Version: 1.0 start 01 February 2020
Short description
Introduction to numerical methods for engineers.
Module coordinator
Full Name (ZHAW username)
Learning objectives (competencies)
Objectives
Competences
Taxonomy levels
Providing the analytical and numerical tools needed in engineering subjects. Introduction to the way of thinking of discrete and numerical mathematics. To convey the role of applied mathematics in science and technology.
You know the terms consistency, convergence, local/global error, error order, stability. You can calculate and visualize both local and global errors for suitable examples.
M, F
K3
You know important algorithms and numerical parameters for solving linear systems of equations and apply them correctly using examples.
M, F
K3
You are able to solve linear compensation problems with the help of QR decomposition and know the geometrical interpretation of the normal equation.
M, F
K3
You can approximate a function using cubic splines.
M, F
K3
You know common explicit as well as implicit one-step procedures, e.g. procedures according to Euler, Runge, Trapez, classical Runge-Kutta, Heun, and can use them for the approximate solution of initial value problems.
M, F
K3
You can use finite differences to solve one-dimensional boundary value problems.
M, F
K3
Module contents
Numerical methods for ordinary differential equations
One-step procedure
Discretization error, convergence
Explicit and implicit numerical methods
Explicit: Euler, Runge, Heun, classic Runge-Kutta
Implicit: trapezoid, center point rule
(optional) 4th order Gauss Legendre
(optional) Semi-implicit procedures
(optional) step size control
Linear equations
triangular matrices, LR decomposition, Cholesky, tridiagonal matrices
finite difference method for one-dimensional boundary value problems
(optional) time dependent boundary value problems
explicit, implicit Euler method
Linear least square methods
Normal equation, Condition
Cholesky, QR decomposition
Splines
Introduction cubic splines
(optional) B-Splines
(optional) data fit with (smoothing) B-Splines
Teaching materials
script, exercise material
Supplementary literature
Wolfgang Dahmen, Arnold Reusken, Numerik für Ingenieure und Naturwissenschaftler, Springer-Lehrbuch
Prerequisites
Analysis I - III, Lineare Algebra I & II bzw. Algebra und Statistik I & II
Teaching language
(X) German ( ) English
Part of International Profile
( ) Yes (X) No
Module structure
Type 3a
For more details please click on this link:
T_CL_Modulauspraegungen_SM2025
Exams
Description
Type
Form
Scope
Grade
Weighting
Graded assignments during teaching semester
max. zwei Standortbestimmungen
Note
je max. 20%
End-of-semester exam
schriftlich
120 Minuten
Note
min. 60%
Remarks
The implementation of numerical methods on the computer is an integral part of the lecture.
Legal basis
The module description is part of the legal basis in addition to the general academic regulations. It is binding. During the first week of the semester a written and communicated supplement can specify the module description in more detail.
Course: Numerik - Praktikum
No.
t.BA.XXM4.NUM.19HS.P
Title
Numerik - Praktikum
Note
No module description is available in the system for the cut-off date of 01 August 2099.
Course: Numerik - Vorlesung
No.
t.BA.XXM4.NUM.19HS.V
Title
Numerik - Vorlesung
Note
No module description is available in the system for the cut-off date of 01 August 2099.