Short description

Basic concepts and methods of differential and integral calculus in one real variable, as well as their applications. 
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 with integral, quotient or comparison criteria. 
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 with symbolic methods. 
F, M 
K3 
You know how the Euler process works 
F, M 
K2 

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, Euler methods 
Teaching materials

Documents lecturerdependent 
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 





Endofsemester exam 
Exam 
Written 
90 min 
Grade 
100% 

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. 