260203 VO Introduction to vector and tensor calculus II (2020S)

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Details

Language: German

Examination dates

Lecturers

Paul Wagner

Classes (iCal) - next class is marked with N

Tuesday 10.03. 13:00 - 14:30 Lise-Meitner-Hörsaal, Boltzmanngasse 5, 1. Stk., 1090 Wien
Tuesday 17.03. 13:00 - 14:30 Lise-Meitner-Hörsaal, Boltzmanngasse 5, 1. Stk., 1090 Wien
Tuesday 24.03. 13:00 - 14:30 Lise-Meitner-Hörsaal, Boltzmanngasse 5, 1. Stk., 1090 Wien
Tuesday 31.03. 13:00 - 14:30 Lise-Meitner-Hörsaal, Boltzmanngasse 5, 1. Stk., 1090 Wien
Tuesday 21.04. 13:00 - 14:30 Lise-Meitner-Hörsaal, Boltzmanngasse 5, 1. Stk., 1090 Wien
Tuesday 28.04. 13:00 - 14:30 Lise-Meitner-Hörsaal, Boltzmanngasse 5, 1. Stk., 1090 Wien
Tuesday 05.05. 13:00 - 14:30 Lise-Meitner-Hörsaal, Boltzmanngasse 5, 1. Stk., 1090 Wien
Tuesday 12.05. 13:00 - 14:30 Lise-Meitner-Hörsaal, Boltzmanngasse 5, 1. Stk., 1090 Wien
Tuesday 19.05. 13:00 - 14:30 Lise-Meitner-Hörsaal, Boltzmanngasse 5, 1. Stk., 1090 Wien
Tuesday 26.05. 13:00 - 14:30 Lise-Meitner-Hörsaal, Boltzmanngasse 5, 1. Stk., 1090 Wien
Tuesday 09.06. 13:00 - 14:30 Lise-Meitner-Hörsaal, Boltzmanngasse 5, 1. Stk., 1090 Wien
Tuesday 16.06. 13:00 - 14:30 Lise-Meitner-Hörsaal, Boltzmanngasse 5, 1. Stk., 1090 Wien
Tuesday 23.06. 13:00 - 14:30 Lise-Meitner-Hörsaal, Boltzmanngasse 5, 1. Stk., 1090 Wien

Information

Aims, contents and method of the course

Goals:
Students will get acquainted with curvilinear coordinates, the corresponding basis vectors and their behaviour under transformations. Starting with the length of curves and the metric tensor they recognize the significance of Riemann space. In connection with the description of the spacial variability of vectors the students acquire a well-founded understanding of the covariant derivative and its applications to simple physical problems. Further the covariant derivative leads to a characterization of curvature of a Riemann space.
Contents:
Description of curves and surfaces, tangential and normal vectors. Curvilinear coordinate systems, definitions of coordinate lines and coordinate surfaces, as well as covariant and contravariant vector bases, transformation behavior. Length of curves, definition of metric tensor, Riemann space, flat space, Euklidian space. Definition of covariant derivative of scalars and vectors, definition of Christoffel symbols, vector differential operators in curvilinear coordinates, applications to cylindrically and spherically symmetric physical problems. Properties of the covariant derivative, higher covariant derivatives, Riemann curvature tensor, Einstein tensor, parallel displacement of vectors.
Method:
Lecture course with predominant use of the blackboard, opportunity for questions and discussion. Several examples are mentioned, where the subject matter of the lecture course can be autonomously applied by the students.

Assessment and permitted materials

Oral single examinations. The students should be able to explain important terms, definitions and relations, comment on their significance and properties and give descriptive interpretations where possible. Paper and pen will be available during the examination.

Minimum requirements and assessment criteria

Understanding of basic terms, their definitions and significance.

Examination topics

Corresponding to the contents of the lecture course.

Reading list

Wird am Beginn der Lehrveranstaltung vereinbart.

Association in the course directory

ERGB, ERG 3, P 3

Last modified: Tu 14.11.2023 00:23