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 nonlinear 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 nonlinear regression problems
 GaussNewton method
Numerical integration
 Quadrature formulas, their extrapolation and error calculation
Numerics of ordinary differential equations
 Slope field and approximate solutions
 Euler method and RungeKutta method
 Systems of ordinary differential equations

Teaching materials

 Script and presentations
 Numerische Mathematik: Eine beispielorientierte Einführung, MichaelKnorrenschild, 5. Auflage, ISBN 97834464323386

Supplementary literature

 NumerikAlgorithmen, G. EngelnMüllges, Klaus Niederdrenk, Reinhard Wodicka, 10. Auflage, ISBN 9783642134722
 Numerical Methods for Engineers and Scientists, A. Gilat, V. Subrmaniam, 3. Auflage, 9781118554937

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 
1013 assignments, preparations 
mark 
20% 
Endofsemester 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. 