Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Course MAT-00-02-K-1

Higher Mathematics II (4V+2U, 8.0 LP)

Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
- K Lecture with exercise classes (V/U) 8.0 CP 156 h
4 V Lecture 56 h
2 U Exercise class (in small groups) 28 h
(4V+2U) 8.0 CP 84 h 156 h

Basedata

SWS 4V+2U
CP, Effort 8.0 CP = 240 h
Position of the semester 1 Sem. in WiSe/SuSe
Level [1] Bachelor (General)
Language [DE] German
Lecturers
Lecturers of the department Mathematics
Area of study [MAT-Service] Mathematics for other Departments
Livecycle-State [NORM] Active

Possible Study achievement

  • Verification of study performance: proof of successful participation in the exercise classes (ungraded)
  • Examination number (Study achievement): 81102 ("Higher Mathematics II (prerequisite)")
  • Details of the examination (type, duration, criteria) will be announced at the beginning of the course.

Contents

  • Vector Analysis: vectors (in particular: ℝn), subspaces, linear independence, basis, dimension, scalar product, orthogonality, projections, vector product;
  • Matrix calculus: definition, calculation rules, base change, linear mappings, description of linear mappings via matrices, linear systems of equations (description via matrices, structure of solutions, Gaussian algorithm), invertibility, calculation of inverse, normal equations and linear least squares, determinants, eigenvalues and eigenvectors (diagonalizability, principal axis theorem);
  • Differentiation (multidimensional): scalar and vector fields, curves, contour lines, total and partial differentiability, directional derivation, implicit differentiation, inverse function theorem, differentiation rules (in particular: inverse function and chain rule), Taylor expansion, extremes under constraints (scalar functions of several variables), gradient fields, potentials, divergence and rotation, applications;
  • Integration (multidimensional): normal domains (also called type I or type II domains), multiple integrals over normal domains.

Literature

  • K. Burg, A. Haf, H. Wille, F. Meister: Höhere Mathematik für Ingenieure II,
  • G. Bärwolff: Höhere Mathematik für Naturwissenschaftler und Ingenieure,
  • J. Jaeckel: Höhere Mathematik 1-3,
  • H. Neunzert, W.G. Eschmann, A. Blickensdörfer-Ehlers, K. Schelkes: Analysis 2.

Registration

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

Requirements for attendance (informal)

Modules:

Requirements for attendance (formal)

None

References to Course [MAT-00-02-K-1]

Module Name Context
[EIT-BM1-M-2] Mathematisch-naturwissenschaftliche Grundlagen P: Obligatory in Obligatory-Modulteil #B (Höhere Mathematik II) 4V+2U, 8.0 LP
[MAT-00-02-M-1] Higher Mathematics II P: Obligatory 4V+2U, 8.0 LP
[MV-BEMT-1-M-2] Higher Mathematics P: Obligatory 4V+2U, 8.0 LP
[MV-FDT-B139-M-2] Higher Mathematics P: Obligatory 4V+2U, 8.0 LP