- 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.
Fundamentals of Mathematics II (for Students of Physics) (M, 13.0 LP)
|Module Number||Module Name||CP (Effort)|
|MAT-10-12P-M-2||Fundamentals of Mathematics II (for Students of Physics)||13.0 CP (390 h)|
|CP, Effort||13.0 CP = 390 h|
|Position of the semester||1 Sem. in WiSe/SuSe|
|Level|| Bachelor (Fundamentals)|
|Area of study||[MAT-Service] Mathematics for other Departments|
|Reference course of study||[PHY-82.128-SG] B.Sc. Physics|
|Type/SWS||Course Number||Title||Choice in |
|SL||SL is |
required for exa.
Fundamentals of Mathematics II
|P||126 h||264 h||
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.
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.
- 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.
Further literature will be announced in the lecture(s); exercise material is provided.
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)
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|