t.BA.ITM.HM2.19HS (Higher Mathematics for Computer Scientists 2)
Module: Higher Mathematics for Computer Scientists 2
This information was generated on: 28 May 2024
No.
t.BA.ITM.HM2.19HS
Title
Higher Mathematics for Computer Scientists 2
Organised by
T IAMP
Credits
4

### Description

Version: 4.0 start 01 February 2021

#### Short description

Using Python, students learn the advanced basics of numerical mathematics for computer scientists. Topics include the numerical solution of nonlinear equation systems, numerical integration, interpolation and curve fitting, and the solution of ordinary differential equations.

#### Module coordinator

Reto Knaack (knaa)

#### Learning objectives (competencies)

 Objectives Competences Taxonomy levels Students deepen their knowledge of Python and can apply Python to advanced problems in numerical mathematics in weekly group work. F, M, SO K3 Students can explain the principles of the most important solution methods for nonlinear systems and apply them to concrete problems. F, M K2, K3 Students can solve typical problems in the fields of interpolation and linear or non-linear regression numerically. F, M K2, K3 Students can integrate functions of a single variable and quantify the errors that occur. Students know the most important numerical solution methods for ordinary differential equations. They can solve simple systems of such differential equations using Python. F, M K2, K3

#### Module contents

Numerical solution of nonlinear systems of equations
• Functions with several variables
• Newton method and damped Newton method
Regression analysis
• Polynomial interpolation & spline interpolation
• Linear and non-linear regression problems
• Gauss-Newton method
Numerical integration
• Quadrature formulas, their extrapolation and error calculation
Numerics of ordinary differential equations
• Slope field and approximate solutions
• Euler method and Runge-Kutta method
• Systems of ordinary differential equations

#### Teaching materials

• Script and presentations
• Numerische Mathematik: Eine beispielorientierte Einführung, MichaelKnorrenschild, 5. Auflage, ISBN 978-34464323386

#### Supplementary literature

• Numerik-Algorithmen, G. Engeln-Müllges, Klaus Niederdrenk, Reinhard Wodicka, 10. Auflage, ISBN 978-3642134722
• Numerical Methods for Engineers and Scientists, A. Gilat, V. Subrmaniam, 3. Auflage, 978-1118554937

#### Prerequisites

• Analysis 1 & 2
• Diskrete Mathematik
• Lineare Algebra
• The contents of "Höhere Mathematik für Informatiker 1" are required

#### Teaching language

(X) German ( ) English

( ) Yes (X) No

Type 3a

#### Exams

 Description Type Form Scope Grade Weighting Graded assignments during teaching semester weekly assignments and preparations written 10-13 assignments, preparations mark 20% End-of-semester exam exam written 120 min mark 80%

#### 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.

### Note

Course: Höhere Mathematik für Informatiker 2 - Praktikum
No.
t.BA.ITM.HM2.19HS.P
Title
Höhere Mathematik für Informatiker 2 - Praktikum

### Note

• No module description is available in the system for the cut-off date of 01 August 2099.
Course: Höhere Mathematik für Informatiker 2 - Vorlesung
No.
t.BA.ITM.HM2.19HS.V
Title
Höhere Mathematik für Informatiker 2 - Vorlesung

### Note

• No module description is available in the system for the cut-off date of 01 August 2099.