Module Handbook

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Module MAT-10-12P-M-2

Fundamentals of Mathematics II (for Students of Physics) (M, 13.0 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-10-12P-M-2 Fundamentals of Mathematics II (for Students of Physics) 13.0 CP (390 h)

Basedata

CP, Effort 13.0 CP = 390 h
Position of the semester 1 Sem. in 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

Courses

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 264 h
qU-Schein
- PL1 13.0 WiSe/SuSe
  • About [MAT-10-12-K-2]: Title: "Fundamentals of Mathematics II"; Presence-Time: 126 h; Self-Study: 264 h
  • About [MAT-10-12-K-2]: The study achievement "[qU-Schein] proof of successful participation in the exercise classes (incl. written examination)" must be obtained.

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: each semester

Evaluation of grades

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


Contents

  • basic topological terms (metric spaces, connectedness, compactness),
  • differentiation (in the multi-dimensional case) - in particular: Taylor expansion, curves, implicit functions theorem, inverse function theorem, extremes under constraints,
  • integration (multi-dimensional) - in particular: Fubini's theorem, variable transformation,
  • geometry of Euclidean space (especially: orthogonal transformations, projections),
  • eigenvalues, diagonalisability, principal axis transformation, calculation of the Jordan normal form,
  • dual space.

Competencies / intended learning achievements

Upon successful completion of this module, the students
  • know and understand the basic concepts, propositions and methods of Linear Algebra and multi-dimensional Analysis; through the exercises and the tutorials they have acquired a confident, precise and independent handling of the terms, statements and methods dealt with in the lectures;
  • recognise the connections between the areas of Linear Algebra and Analysis;
  • are trained in analytical thinking; they are able to recognise abstract structures and to work on mathematical problems imaginatively;
  • have learned, on the basis of a proof- and structure-oriented approach, to comprehend mathematical proofs and to independently prove or disprove mathematical statements in simple examples;
  • are able to convey elementary mathematical facts; their teamwork and communication skills have been trained through exercises and tutorials.

Literature

  • O. Forster: Analysis 2,
  • H. Heuser: Lehrbuch der Analysis, Teil 2,
  • M. Barner, F. Flohr: Analysis II,
  • K. Königsberger: Analysis 2,
  • G. Fischer: Lineare Algebra,
  • K. Jänich: Lineare Algebra,
  • H.-J. Kowalsky, G.O. Michler: Lineare Algebra,
  • S. Bosch: Lineare Algebra.

Materials

Further literature will be announced in the lecture(s); exercise material is provided.

Registration

Registration for the exercise classes and tutorials via the online administration system URM (https://urm.mathematik.uni-kl.de).

Requirements for attendance of the module (informal)

Modules:

Requirements for attendance of the module (formal)

Proof of successful participation in the exercise classes of "Fundamentals of Mathematics I" is prerequisite for participation in the module examination.

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

Course of Study Section Choice/Obligation
[PHY-82.128-SG] B.Sc. Physics [Fundamentals] Mathematikmodule [P] Compulsory