Course MAT-10-12-K-2
Fundamentals of Mathematics II (6V+2U+1T, 13.0 LP)
Course Type
SWS | Type | Course Form | CP (Effort) | Presence-Time / Self-Study | |
---|---|---|---|---|---|
- | K | Lecture with exercise classes and tutorials (V/U/T) | 13.0 CP | 264 h | |
6 | V | Lecture | 84 h | ||
2 | U | Exercise class (in small groups) | 28 h | ||
1 | T | Tutorial | 14 h | ||
(6V+2U+1T) | 13.0 CP | 126 h | 264 h |
Basedata
SWS | 6V+2U+1T |
---|---|
CP, Effort | 13.0 CP = 390 h |
Position of the semester | 1 Sem. in WiSe/SuSe |
Level | [2] Bachelor (Fundamentals) |
Language | [DE] German |
Lecturers |
Lecturers of the department Mathematics
|
Area of study | [MAT-GRU] Mathematics (B.Sc. year 1 and 2) |
Livecycle-State | [NORM] Active |
Possible Study achievement (Übungsschein Grundlagen der Mathematik II)
- Verification of study performance: proof of successful participation in the exercise classes (incl. written examination)
- Examination number (Study achievement): 82016
("Exercise Class Fundamentals of Mathematics II")
Qualified proof of successful participation in the exercise classes requiring active participation in the exercises, successful completion of homework and passing the final exam for the exercise classes.
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.
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 via the online administration system URM (https://urm.mathematik.uni-kl.de).
Requirements for attendance (informal)
Courses
- [MAT-10-11A-K-2] Fundamentals of Mathematics I: Analysis (4V+2U+2T, 9.0 LP)
- [MAT-10-11B-K-2] Fundamentals of Mathematics I: Linear Algebra (2V+2U, 6.0 LP)
Requirements for attendance (formal)
None
References to Course [MAT-10-12-K-2]
Module | Name | Context | |
---|---|---|---|
[MAT-10-12P-M-2] | Fundamentals of Mathematics II (for Students of Physics) | P: Obligatory | 6V+2U+1T, 13.0 LP |
[MAT-10-1-M-2] | Fundamentals of Mathematics | P: Obligatory in Obligatory-Modulteil #B (Fundamentals of Mathematics II) | 6V+2U+1T, 13.0 LP |
[PHY-M1-M-2] | Fundamentals of Mathematics (for Physics) | P: Obligatory in Obligatory-Modulteil #B (Grundlagen der Mathematik II) | 6V+2U+1T, 12.0 LP |