Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-00-02-M-1

Higher Mathematics II (M, 8.0 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-00-02-M-1 Higher Mathematics II 8.0 CP (240 h)

Basedata

CP, Effort 8.0 CP = 240 h
Position of the semester 1 Sem. in WiSe/SuSe
Level [1] Bachelor (General)
Language [DE] German
Module Manager
Lecturers
Area of study [MAT-Service] Mathematics for other Departments
Reference course of study [MV-82.103-SG] B.Sc. Mechanical Engineering
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.
4V+2U MAT-00-02-K-1
Higher Mathematics II
P 84 h 156 h
U-Schein
ja PL1 8.0 WiSe/SuSe
  • About [MAT-00-02-K-1]: Title: "Higher Mathematics II"; Presence-Time: 84 h; Self-Study: 156 h
  • About [MAT-00-02-K-1]: The study achievement "[U-Schein] proof of successful participation in the exercise classes (ungraded)" must be obtained.
    • It is a prerequisite for the examination for PL1.

Examination achievement PL1

  • Form of examination: written exam (Klausur) (90 Min.)
  • Examination Frequency: each semester
  • Examination number: 81200 ("Higher Mathematics II")

Evaluation of grades

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


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.

Competencies / intended learning achievements

The following competences are to be promoted:

Professional competence, methodological competence, social competence

Upon successful completion of the module, students will be able

  • to deepen the concepts and methods of higher dimensional analysis and linear algebra specific to their subject and their practical application as required in the further course of their studies, since they have acquired a solid basis for the proper handling of mathematics in the engineering sciences;
  • to model problems from the engineering sciences and to work on and solve them using mathematical methods, as they have learned and practiced this exemplarily.

In the exercise classes, the students have acquired a confident and independent handling of the terms, statements and methods from the lecture. They can apply the methods and concepts they have learned in examples.

Moreover, In the exercise classes, the presentation and communication skills of the students were trained via the written elaboration of solutions and the presentation in the face-to-face exercise classes. The ability to work in a team was promoted by working in small groups.

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 of the module (informal)

Modules:

Requirements for attendance of the module (formal)

None

References to Module / Module Number [MAT-00-02-M-1]

Course of Study Section Choice/Obligation
[EIT-82.781-SG#2019] B.Sc. Electrical and Computer Engineering [2019] [Fundamentals] Fundamentals of Mathematics and Sciences (MNG) [P] Compulsory
[EIT-82.A44-SG#2018] B.Sc. Media and Communication Technology [2018] [Fundamentals] Fundamentals of Mathematics and Sciences (MNG) [P] Compulsory
[EIT-82.?-SG#2021] B.Sc. Electrical and Computer Engineering [2021] [Fundamentals] Fundamentals of Mathematics and Sciences (MNG) [P] Compulsory
[EIT-82.?-SG#2021] B.Sc. Media and Communication Technology [2021] [Fundamentals] Fundamentals of Mathematics and Sciences (MNG) [P] Compulsory
[MV-82.103-SG] B.Sc. Mechanical Engineering [Fundamentals] Mathematical and scientific fundamentals [P] Compulsory
[MV-82.814-SG] B.Sc. Mechanical Engineering with a minor in Economics [Fundamentals] Mathematisch-naturwissenschaftliche Grundlagen [P] Compulsory
[MV-82.B10-SG] B.Sc. Energy and Process Engineering [Fundamentals] Mathematisch-naturwissenschaftliche Grundlagen [P] Compulsory
[MV-82.A29-SG] B.Sc. Biological and Chemical Engineering [Fundamentals] Mathematisch-Naturwissenschaftliche Grundlagen [P] Compulsory
[PHY-82.B90-SG] B.Sc. TechnoPhysics [Fundamentals] Grundlagen der Höheren Mathematik [P] Compulsory
[WIW-82.178-SG] B.Sc. Business Administration and Engineering specialising in Electrical Engineering [Fundamentals] Quantitative Methods [P] Compulsory
[WIW-82.176-SG] B.Sc. Business Administration and Engineering specialising in Computer Science [Fundamentals] Quantitative Methods [P] Compulsory
[WIW-82.179-SG] B.Sc. Business Administration and Engineering specialising in Mechanical Engineering [Fundamentals] Quantitative Methods [P] Compulsory
[WIW-82.175-SG] B.Sc. Business Administration and Engineering specialising in Environmental and Process Engineering [Fundamentals] Quantitative Methods [P] Compulsory
[WIW-82.?-SG#2021] B.Sc. Business Administration and Engineering specialising in Electrical Engineering 2021 [2021] [Fundamentals] Scientific Basics and Methods [P] Compulsory
[WIW-82.?-SG#2021] B.Sc. Business Administration and Engineering specialising in Computer Science 2021 [2021] [Fundamentals] Scientific Basics and Methods [P] Compulsory
[WIW-82.?-SG#2021] B.Sc. Business Administration and Engineering specialising in Mechanical Engineering 2021 [2021] [Fundamentals] Scientific Basics and Methods [P] Compulsory
[WIW-82.?-SG#2021] B.Sc. Business Administration and Engineering specialising in Energy and Process Engineering [2021] [Fundamentals] Scientific Basics and Methods [P] Compulsory