## Module Handbook

• Dynamischer Default-Fachbereich geändert auf MAT

# Course MAT-12-27-K-3

## Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
- K Lecture with exercise classes (V/U) 4.5 CP 93 h
2 V Lecture 28 h
1 U Exercise class (in small groups) 14 h
(2V+1U) 4.5 CP 42 h 93 h

## Basedata

SWS 2V+1U 4.5 CP = 135 h 1 Sem. in SuSe [3] Bachelor (Core) [DE] German Klar, Axel, Prof. Dr. (PROF | DEPT: MAT) Pinnau, René, Prof. Dr. (PROF | DEPT: MAT) Simeon, Bernd, Prof. Dr. (PROF | DEPT: MAT) Surulescu, Christina, Prof. Dr. (PROF | DEPT: MAT) [MAT-GRU] Mathematics (B.Sc. year 1 and 2) [NORM] Active

## Possible Study achievement

• Verification of study performance: proof of successful participation in the exercise classes (ungraded)
• Examination number (Study achievement): 83160 ("Exercise Class Vector Analysis")
• Details of the examination (type, duration, criteria) will be announced at the beginning of the course.

## Contents

• parametrisation of curves and surfaces in ℝn,
• calculation of surface and (scalar and vectorial) curve integrals in ℝn,
• tangent spaces and the differential of differentiable mappings,
• classic operators on vector fields: div, rot, grad,
• Gauss's divergence theorem, Stokes' theorem, Green's formulas,
• applications in ℝ3.

## Competencies / intended learning achievements

The students know the basic terms, statements and methods of vector analysis. Building on the knowledge from the lectures of the first year of a mathematical study programme, they have learned to apply techniques and fundamental propositions of the integration of scalar and vector-valued functions over surfaces and curves and to prove their correctness.

## Literature

• K. Burg, H. Haf, F. Wille, A. Meister: Vektoranalysis,
• K. Jänich: Vektoranalysis,
• D.E. Bourne, P.C. Kendall: Vektoranalysis,
• F.E. Marsden, A.J. Tromba: Vektoranalysis.

## Materials

Further literature will be announced in the lecture(s); exercise material is provided.

## Registration

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

## Requirements for attendance (informal)

Knowledge in multidimensional analysis, e.g. from the courses [MAT-10-12-K-2] "Fundamentals of Mathematics II" or [MAT-10-12L-K-2] "Fundamentals of Mathematics II (for Students of Teacher Training Programmes)".

None

## References to Course [MAT-12-27-K-3]

Module Name Context
[MAT-12-10P-M-3] Build-Up Module Mathematics (for Students of Physics) WP: Obligation to choose 2V+1U, 5.0 LP
[MAT-14-10L-M-3] Topic Module B: Mathematics as an Interdisciplinary Cross-Sectional Science WP: Obligation to choose 2V+1U, 4.5 LP
Course-Pool Name
[MAT-10-KPOOL-3] Pure Mathematics (B.Sc. Mathematics)
[PHY-M2-KPOOL-3] Höhere Analysis (für Studierende der Physik)