t.BA.ITM.HM2.19HS (Higher Mathematics for Computer Scientists 2) 
Module: Higher Mathematics for Computer Scientists 2
This information was generated on: 20 April 2021
No.
t.BA.ITM.HM2.19HS
Title
Higher Mathematics for Computer Scientists 2
Organised by
T IAMP
Credits
4

Description

Version: 3.0 start 01 February 2021
 

Short description

 The course Higher Mathematics 2 is the continuation of Higher Mathematics 1 and teaches students the advanced basics of numerical mathematics for computer scientists based on Python. Topics include the numerical solution of systems of nonlinear equations, 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

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 weekly assignments and preparations written 10-13 assignments, preparations mark 20%
End-of-semester exam exam written 120 min mark 80%

Remarks

  

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.