Short description

Basic concepts and methods of differential and integral calculus of one real variable, as well as their application. 
Module coordinator

Lichtensteiger Lukas (licn) 
Learning objectives (competencies)

Objectives 
Competences 
Taxonomy levels 
You use the elementary integration methods: partial integration, substitution method and integration with partial fraction decomposition. 
F, M 
K3 
You use integral calculus to calculate the length of a curve, the coordinates of a centroid, and the volume content of a rotation object. 
F, M 
K2 
You use the rule of Bernoulli and determine the values of improper integrals with symbolic methods. 
F, M 
K3 
You determine the convergence or divergence of a series of numbers using the quotient criterion. 
F, M 
K3 
You determine the radius of convergence for a given power series and use operations with power series correctly. 
F, M 
K3 
You develop a given function into a Taylor series and use it to derive approximation formulas. 
F, M 
K3 
You determine the direction fields for ordinary differential equations and graphically determine integral curves to given initial values. 
F, M 
K3 
You solve the initial value problem for simple linear and separable differential equations using various methods. 
F, M 
K3 

Module contents

1. Extension of the integral calculus
Elementary integration methods (partial integration, substitution method, integration with partial fraction decomposition), applications of integral calculus, rule of Bernoulli, improper integrals
2. Power series and Taylor series
Convergence and divergence of series, power series, convergence radius, Taylor series, function approximation formulas
3. Introduction to ordinary differential equations
Graphical solution methods (direction fields, integral curves), symbolic solution methods for linear and separable differential equations 
Teaching materials

Notes and exercises distributed by lecturers, Moodle 
Supplementary literature

Mathematik für Ingenieure und Naturwissenschaftler, Lothar Papula, Vieweg+Teubner 
Prerequisites

Mathematics of technical BM
Knowledge of the contents of the module Analysis 1 
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 
regular assessments 
written 
max. 45 minutes each 
grade 
maximum 20% 
Endofsemester exam 
exam 
written 
90 minutes 
grade 
at least 80% 

Remarks

During the first week of classes, a module agreement will be communicated which applies to all module courses and in which the exact number and scope of the graded assignments during the semester as well as the calculation method for the module grade are determined. 
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. 