Module Handbook

  • Dynamischer Default-Fachbereich geändert auf PHY

Module PHY-M1-M-2

Fundamentals of Mathematics (for Physics) (M, 24.0 LP)

Module Identification

Module Number Module Name CP (Effort)
PHY-M1-M-2 Fundamentals of Mathematics (for Physics) 24.0 CP (720 h)

Basedata

CP, Effort 24.0 CP = 720 h
Position of the semester 3 Sem. from WiSe/SuSe
Level [2] Bachelor (Fundamentals)
Language [DE] German
Module Manager
Lecturers
Area of study [MAT-Service] Mathematics for other Departments
Reference course of study [PHY-82.128-SG] B.Sc. Physics
Livecycle-State [NORM] Active

Notice

siehe auch [MAT-10-1-M-2] "Fundamentals of Mathematics"

Module Part #A "Grundlagen der Mathematik I" (Obligatory, 12.0 LP)

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
2V+2U MAT-10-11B-K-2
Fundamentals of Mathematics I: Linear Algebra
P 56 h 94 h
SL1
ja PL1 5.0 WiSe/SuSe
4V+2U+2T MAT-10-11A-K-2
Fundamentals of Mathematics I: Analysis
P 112 h 98 h
SL1
ja PL1 7.0 WiSe/SuSe
  • About [MAT-10-11B-K-2]: Title: "Fundamentals of Mathematics I: Linear Algebra"; Presence-Time: 56 h; Self-Study: 94 h
  • About [MAT-10-11B-K-2]: The study achievement SL1 must be obtained.
    • It is a prerequisite for the examination for PL1.
  • About [MAT-10-11A-K-2]: Title: "Fundamentals of Mathematics I: Analysis"; Presence-Time: 112 h; Self-Study: 98 h
  • About [MAT-10-11A-K-2]: The study achievement SL1 must be obtained.
    • It is a prerequisite for the examination for PL1.

Module Part #B "Grundlagen der Mathematik II" (Obligatory, 12.0 LP)

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
6V+2U+1T MAT-10-12-K-2
Fundamentals of Mathematics II
P 126 h 234 h
SL1
ja PL1 12.0 WiSe/SuSe
  • About [MAT-10-12-K-2]: Title: "Fundamentals of Mathematics II"; Presence-Time: 126 h; Self-Study: 234 h
  • About [MAT-10-12-K-2]: The study achievement SL1 must be obtained.
    • It is a prerequisite for the examination for PL1.

Study achievement SL1

  • Verification of study performance: proof of successful participation in the exercise classes (incl. written examination)
  • Study achievement is a prerequisite for the examination.
  • Examination number (Study achievement): 80110 ("Fundamentals of Mathematics (for Physics)")
    Qualifizierter Übungsschein wahlweise zu "Grundlagen der Mathematik I" oder [MAT-10-12-K-2] "Fundamentals of Mathematics II" durch aktive Teilnahme an den Übungen, erfolgreiches Bearbeiten von Hausaufgaben sowie Bestehen der Abschlussklausur zu den Übungen (Zwischenklausur zur Mitte und Endklausur ca. zwei Wochen nach Ende der Vorlesungszeit).

    Der qualifizierte Übungsschein zum Teil "Grundlagen der Mathematik I" kann in Form von zwei Teilen (qualifizierter Übungsschein zu [MAT-10-11B-K-2] "Fundamentals of Mathematics I: Linear Algebra" und qualifizierter Übungsschein zu [MAT-10-11A-K-2] "Fundamentals of Mathematics I: Analysis") erbracht werden.

Examination achievement PL1

  • Form of examination: oral examination (30-45 Min.)
  • Examination Frequency: each semester
  • Examination number: 82017 ("Fundamentals of Mathematics I/II")

Evaluation of grades

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


Contents

  • real and complex numbers (axiomatic),
  • sequences, limit values, and series; power series; elementary functions,
  • continuity,
  • differentiation (especially: Taylor expansion, curves, implicit function theorem, inverse function theorem, extrema under constraints),
  • integration (one- and multi-dimensional; in particular: Fubini's theorem, variable transformation),
  • basic topological terms (metric spaces, connection, compactness),
  • vector spaces; linear mappings, matrices and linear systems of equations; dual space; determinants,
  • geometry of the Euclidean space (especially: orthogonal transformations, projections),
  • eigenvalues, diagonalisability, principal axis transformation, calculation of the Jordan normal form.

In particular, the respective courses treat the following contents:

A.1 Fundamentals of Mathematics I: Analysis

real and complex numbers; sequences, limit values, and series; power series; elementary functions; continuity and differentiation in the one-dimensional case; integration in the one-dimensional case;

A.2 Fundamentals of Mathematics I: Linear Algebra

vector spaces; linear mappings, matrices and linear systems of equations;

B. Fundamentals of Mathematics II:

metric spaces; differentiation and integration in the multidimensional case; geometry of Euclidean space; diagonalisability, principal axis transformation, calculation of the Jordan normal form.

Competencies / intended learning achievements

The students know and understand the basic concepts, statements and methods of Analysis and Linear Algebra. They realise the connections between Analysis and Linear Algebra. 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

Materials

Registration

Requirements for attendance of the module (informal)

None

Requirements for attendance of the module (formal)

None

References to Module / Module Number [PHY-M1-M-2]