t.BA.XXM1.AN1.19HS (Analysis 1) 
Module: Analysis 1
This information was generated on: 07 October 2024
No.
t.BA.XXM1.AN1.19HS
Title
Analysis 1
Organised by
T IAMP
Credits
4

Description

Version: 4.0 start 01 August 2024
 

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%
End-of-semester 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.

Note

Course: Analysis 1 - Praktikum
No.
t.BA.XXM1.AN1.19HS.P
Title
Analysis 1 - Praktikum

Note

  • No module description is available in the system for the cut-off date of 01 August 2099.
Course: Analysis 1 - Vorlesung
No.
t.BA.XXM1.AN1.19HS.V
Title
Analysis 1 - Vorlesung

Note

  • No module description is available in the system for the cut-off date of 01 August 2099.