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
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 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 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 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
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.
Notes on the module handbook of the department Physics
Die offiziellen Modulhandbücher finden Sie unter https://www.physik.uni-kl.de/studium/modulhandbuecher/ .