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Higher Analysis

Module name (EN):
Name of module in study programme. It should be precise and clear.
Higher Analysis
Degree programme:
Study Programme with validity of corresponding study regulations containing this module.
Mechatronics, Master, ASPO 01.04.2020
Module code: MTM.HAN
Hours per semester week / Teaching method:
The count of hours per week is a combination of lecture (V for German Vorlesung), exercise (U for Übung), practice (P) oder project (PA). For example a course of the form 2V+2U has 2 hours of lecture and 2 hours of exercise per week.
2V+1U+1F (4 hours per week)
ECTS credits:
European Credit Transfer System. Points for successful completion of a course. Each ECTS point represents a workload of 30 hours.
Semester: according to optional course list
Mandatory course: no
Language of instruction:
Written exam/paper

[updated 01.10.2020]
Applicability / Curricular relevance:
All study programs (with year of the version of study regulations) containing the course.

MTM.HAN Mechatronics, Master, ASPO 01.04.2020 , optional course, technical
MST.HAN Mechatronics and Sensor Technology, Master, ASPO 01.04.2016 , optional course, technical
MST.HAN Mechatronics and Sensor Technology, Master, ASPO 01.10.2011 , optional course, technical
Workload of student for successfully completing the course. Each ECTS credit represents 30 working hours. These are the combined effort of face-to-face time, post-processing the subject of the lecture, exercises and preparation for the exam.

The total workload is distributed on the semester (01.04.-30.09. during the summer term, 01.10.-31.03. during the winter term).
60 class hours (= 45 clock hours) over a 15-week period.
The total student study time is 150 hours (equivalent to 5 ECTS credits).
There are therefore 105 hours available for class preparation and follow-up work and exam preparation.
Recommended prerequisites (modules):
Recommended as prerequisite for:
Module coordinator:
Prof. Dr. Barbara Grabowski
Lecturer: Prof. Dr. Barbara Grabowski

[updated 30.01.2019]
Learning outcomes:
After successfully completing this course, students will be able to investigate force and velocity fields and other fields of physics and electrical engineering using vector analysis methods.
In addition, they will be able to describe curves and curved surfaces in R2 and R3 parametrically using curvilinear coordinate systems and calculate properties such as lengths, curvatures, areas, volumes and centers of gravity, solve complex applied extreme value problems for functions in several variables with and without constraints, and handle eigenvalues, eigenvectors, and quadrics in practical applications.

[updated 01.10.2020]
Module content:
1.        Curves as vector-valued functions in a variable
1.1 Definition of vector functions and their geometrical meaning
1.2 Differentiation and integration of curves, Jordan curves
1.3 Tangent vectors and orientation of a curve
1.4 Case studies: Applications
2.        Real-value functions in several variables
2.1 Definition, surfaces of revolution and planes
2.2 The directional derivatives, partial derivatives and their properties
2.4 The gradient, tangent plane and total differential
2.5 Extreme value search methods with and without auxiliary conditions
2.6 Case studies: practical applications
3.        Coordinate transformation _ Curvilinear coordinates
3.1 The Jacobi matrix and its determinants
3.2 Coordinate lines and bases in curvilinear coordinate systems
3.3 Spherical, cylindrical and polar coordinates
3.4 Multiple integrals and integral transform
3.5. Case studies: practical applications
4.        Scalar and vector fields
4.1 Definitions
4.2 Gradient of a scalar field, rotation and divergence of vector fields and their meaning
4.3 Potential fields and potential function
4.4 Del and Laplace operator and useful equations - Maxwell´s equations
4.5  Line, surface and volume integrals over scalar and vector fields and their physical meaning
4.6. Theorems of Gauss and Stokes
4.7 Case studies: applications
5.        Eigenvalues and eigenvectors, quadrics
5.1 Scalar products and orthogonality
5.2. Orthogonal matrices, orthogonal bases, change between orthogonal bases
5.3. Eigenvalues and eigenvectors, eigenvalue estimation
5.4. EWe and EVe of symmetrical matrices, principal axis transformation (diagonalizability of a matrix)
5.5 Square shapes
5.6 Positive/negative (semi) definite matrices
5.7. Quadrics, normal form in R^2 and R^3
5.8 Case studies: practical applications

[updated 01.10.2020]
Teaching methods/Media:
Projector, smart notebook, lecture notes
PC lab: AMSeL

[updated 01.10.2020]
Recommended or required reading:
Papula: Mathematik für Ingenieure und Naturwissenschaftler, Band 1-3, Vieweg 2000.
MARSHDEN, TROMBA: Vektoranalysis, Spektrum, 1995.
Bourne, Kendall: Vektoranalysis, Teubner, 1966.
J.Stoer, R. Bulirsch "Einführung in die Numerische Mathematik I und II", Springer; Auflage: 5. Aufl. 2005 Springer; Auflage: 10., neu bearb. 2007.
D. Wille "Repetitorium der Linearen Algebra, Teil 1" Binomi 1997.
D. Wille, M. Holz "Repetitorium der Linearen Algebra, Teil 2"  Binomi Verlag; Auflage 2, 2006.
G.Merziger, T. Wirth "Repetitorium der höheren Mathematik" Binomi; Auflage 5, 2006.
B.Griese "Übungsbuch zur Linearen Algebra: Aufgaben und Lösungen" Vieweg+Teubner Verlag; Auflage 7, überarb. u. erw. Aufl. 2011.
K.Jänich "Lineare Algebra" Springer; 11. Aufl. 2008. 2., korr. Nachdruck 2013.

[updated 01.10.2020]
[Tue Jun 18 19:30:56 CEST 2024, CKEY=yha, BKEY=mechm, CID=MTM.HAN, LANGUAGE=en, DATE=18.06.2024]