t.BA.XXM1.AN1.19HS (Analysis 1)
Module: Analysis 1
This information was generated on: 24 July 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

German

No

Type 3a

#### 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 02 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 02 August 2099.