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
Lecturers of the department Mathematics
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 (informal)

Modules:

Requirements for attendance (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 Mathematikmodule [P] Compulsory