Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-10-12A-M-2

Fundamentals of Mathematics II: Analysis (M, 8.0 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-10-12A-M-2 Fundamentals of Mathematics II: Analysis 8.0 CP (240 h)

Basedata

CP, Effort 8.0 CP = 240 h
Position of the semester 1 Sem. in WiSe/SuSe
Level [2] Bachelor (Fundamentals)
Language [DE] German
Module Manager
Lecturers
Lecturers of the department Mathematics
Area of study [MAT-MaNF] Special Offers for Mathematics as a Minor
Reference course of study [INF-82.79-SG] B.Sc. Computer Science
Livecycle-State [NORM] Active

Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
4V+2U MAT-10-12A-K-2
Fundamentals of Mathematics II: Analysis
P 84 h 156 h
qU-Schein
ja PL1 8.0 WiSe/SuSe
  • About [MAT-10-12A-K-2]: Title: "Fundamentals of Mathematics II: Analysis"; Presence-Time: 84 h; Self-Study: 156 h
  • About [MAT-10-12A-K-2]: The study achievement [qU-Schein] proof of successful participation in the exercise classes (incl. written examination) must be obtained. It is a prerequisite for the examination for PL1.

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: each semester
  • Examination number: 81107 ("Fundamentals of mathematics II (analysis)")

Evaluation of grades

The grade of the module examination is also the module grade.


Contents

  • basic topological terms (metric spaces, connection, compactness),
  • differentiation (in the multidimensional case) - in particular:Taylor expansion, curves, implicit functions theorem, inverse function theorem, extremes under constraints,
  • integration (multidimensional) - in particular: Fubini's theorem, variable transformation.

Competencies / intended learning achievements

The students know and understand the basic concepts, statements and methods of multidimensional Analysis. Their ability to abstract has been enhanced. They are trained in analytical thinking and their mathematical imagination has been stimulated. By means of a proof- and structure-oriented approach, they have learned to understand mathematical evidence and to independently prove or disprove mathematical statements in simple examples.

In the exercise classes they have acquired a confident, precise and independent handling of the terms, statements and methods from the lectures.

In the exercise classes and tutorials, the students' presentation and communication skills were trained through written work and presentations held by themselves; the students are able to acquire knowledge through self-study and at the same time their ability to work in a team was promoted by working in small groups.

Literature

  • O. Forster: Analysis 2,
  • H. Heuser: Lehrbuch der Analysis, Teil 2,
  • M. Barner, F. Flohr: Analysis II,
  • K. Königsberger: Analysis 2.

Requirements for attendance (informal)

None

Requirements for attendance (formal)

None

References to Module / Module Number [MAT-10-12A-M-2]