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t.BA.XXM1.AN1.19HS (Analysis 1)

Module: Analysis 1

This information was generated on: 27 September 2021

No.

t.BA.XXM1.AN1.19HS

Title

Analysis 1

Organised by

T IAMP

Credits

4

Description

Version: 3.0 start 01 August 2021

Short description

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

Module coordinator

Zaugg Christoph (zght)

Learning objectives (competencies)

Objectives

Competences

Taxonomy levels

Polynomials:
The students understand the concepts of a drivative and a definite integral. They are able to do a curve sketching and to calculate definite integrals using the fundamental theorem of calculus.

F,M

K2 K3

The students understand the concept of a sequence and calculate values of sequences, which are given explicitly or directly.
They are able to verify monotonicity and boundedness and show convergence using its definition. They calculate limits
using symbolic methods.

F,M

K2, K3 K3 K3

The students know the derivitives of elementary functions. They use the rules of differential calculus, perform curve sketching and solve optimization problems. They find roots using Newtons method.

F,M

K2, K3 K3 K3

Module contents

1. Concepts of Calculus - Derivative (tangent, curve sketching)
- antiderivative and area content, fundamental theorem of calculus
2. Sequences, series (summation sign)
- sequences (direct, recursive, arithmetic, geometric) - limits (monotonicity, boundedness, rules for limits)
- series (arithmetic, geometric)
3. Extension of differential calculus
Derivative of elementary functions, rules of differential calculus, curve sketching, Newtons method for finding roots

Teaching materials

Notes and exercises distributed by lectures, Moodle

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.