Short description

In this course, students learn the basic concepts of calculus of one real variable. 
Module coordinator

Lichtensteiger Lukas (licn) 
Learning objectives (competencies)

Objectives 
Competences 
Taxonomy levels 
For polynomial type functions:
 You understand the concepts of derivative and definite integral.
 You conduct a curve discussion and calculate definite integrals using the main theorem.

F, M 
K2
K3 
You understand the concept of a sequence and calculate values of sequences that are given explicitly or recursively.
You show the convergence of a sequence using the limit definition.
You calculate limit values using symbolic methods. 
F, M 
K2, K3
K3
K3 
You know the derivatives of the elementary functions.
You use the derivative rules, perform a curve discussion, and solve extreme value problems.
You use Newton's method to form recursion formulas. 
F, M 
K1
K2, K3
K3 

Module contents

1. Concepts of differential and integral calculus
 Derivation (tangent, curve discussion)
 Antiderivatives and areas, main theorem for polynomials
2. Sequences, series (with sums) and limits
 Sequences (direct, recursive, arithmetic/geometric)
 Concept of limit values (arithmetic rules, limits of a function), continuity
 Series (arithmetic/geometric)
3. Extension of differential calculus
 Derivation of elementary functions
 Derivation rules
 Curve discussion
 Fractional rational functions (pole positions, liftable definition gaps, asymptotes)
 Extreme value problems
 Newton's method 
Teaching materials

Notes and exercises distributed by lecturers, Moodle 
Supplementary literature

Mathematik für Ingenieure und Naturwissenschaftler, Lothar Papula, Vieweg+Teubner
Mathematik, Tilo Arens et al., Springer Verlag 
Prerequisites

Mathematik der technischen BM 
Teaching language

German 
Part of International Profile

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. 