Main content
Analysis II
(dt. Analysis II)
Level, degree of commitment | Basic module, compulsory elective 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
- B.Sc. Business Mathematics
- BA Minor Mathematics
When studying B.Sc. Data Science, this module can be attended in the study area Basic and Continuing Modules in Mathematics.
Recommended Reading
- 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.
Please note:
This page describes a module according to the latest valid module guide in Winter semester 2023/24. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:
- Winter 2016/17 (no corresponding element)
- Summer 2018 (no corresponding element)
- Winter 2018/19 (no corresponding element)
- Winter 2019/20 (no corresponding element)
- Winter 2020/21 (no corresponding element)
- Summer 2021 (no corresponding element)
- Winter 2021/22 (no corresponding element)
- Winter 2022/23 (no corresponding element)
- Winter 2023/24
The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.
The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.