- 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.
Higher Mathematics II (M, 8.0 LP)
|Module Number||Module Name||CP (Effort)|
|MAT-00-02-M-1||Higher Mathematics II||8.0 CP (240 h)|
|CP, Effort||8.0 CP = 240 h|
|Position of the semester||1 Sem. in WiSe/SuSe|
|Level|| Bachelor (General)|
Lecturers of the department Mathematics
|Area of study||[MAT-Service] Mathematics for other Departments|
|Reference course of study||[MV-82.103-SG] B.Sc. Mechanical Engineering|
|Type/SWS||Course Number||Title||Choice in |
|SL||SL is |
required for exa.
Higher Mathematics II
|P||84 h||156 h||
- 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.
Competencies / intended learning achievements
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.
- 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.