# Analysis II (dt. Analysis II)

 Level, degree of commitment Basic module, required module Forms of teaching and learning,workload Lecture (4 SWS), recitation class (2 SWS), Werkstatt (2 SWS), 270 hours (120 h attendance, 150 h private study) Credit points,formal requirements 9 CP Course requirement(s): Successful completion of at least 50 percent of the points from the weekly exercises. Written test (60-120 min.). Examination type: Oral examination (individual examination) Language,Grading German,The grading is done with 0 to 15 points according to the examination regulations for the degree program B.Sc. Mathematics. Duration,frequency One semester, each winter semester Person in charge of the module's outline Prof. Dr. Ilka Agricola, Prof. Dr. Thomas Bauer, Prof. Dr. Oliver Goertsches, Prof. Dr. Pablo Ramacher

## Contents

In addition to the contents of the Analysis I module, which are also relevant for the final oral examination, the following contents are covered in the module:

• Metric spaces: Basic topological concepts, convergence, complete, compact, connected metric spaces, space of continuous functions on a compact set (this subject area can be treated by the lecturer alternatively in Analysis I)
• Differentiation in R^n: total and partial differentiability, gradient, inverse function and implicit function theorem, Taylor formula, local extrema without and with constraints, if possible transformation formula for integrals
• Ordinary differential equations: elementary solution methods, linear differential equation systems, homogeneous and inhomogeneous ordinary differential equations, theorem of Picard-Lindelöf

## Qualification Goals

The general qualification objectives correspond to those of Analysis I. Building on this and going into greater depth: students will

• understand the basic principles of the analysis of several variables and, as a special case, the analysis of one variable - as taught in Analysis I - and can work out the differences,
• understand the linearization of nonlinear problems as a technique of analysis and can apply methods of linear algebra in analysis,
• can model mathematical and scientific processes using the theory of differential equations.

Upon completion of the module, students will understand and master calculus as a unified mathematical discipline in its entirety.

## Prerequisites

None. The competences taught in the following module are recommended: Analysis I.

## Applicability

Module imported from B.Sc. Mathematics.

It can be attended at FB12 in study program(s)

• B.Sc. Data Science
• B.Sc. Mathematics
• BA Minor Mathematics

When studying B.Sc. Business Mathematics, this module must be completed in the study area Basic Modules in Mathematics.

• Forster, O.: Analysis 1 und Analysis 2, Vieweg-Verlag
• Heuser, H.: Lehrbuch der Analysis, Teil 1 und Teil 2, Teubner-Verlag
• Rudin, W.: Analysis, Oldenbourg-Verlag.