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PřF:M5130 Global Analysis - Course Information

## M5130 Global Analysis

**Faculty of Science**

Autumn 2018

**Extent and Intensity**- 2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
**Teacher(s)**- doc. Lukáš Vokřínek, PhD. (lecturer)

Mgr. Tomáš Svoboda (seminar tutor) **Guaranteed by**- prof. RNDr. Jan Slovák, DrSc.

Department of Mathematics and Statistics - Departments - Faculty of Science

Supplier department: Department of Mathematics and Statistics - Departments - Faculty of Science **Timetable**- Mon 17. 9. to Fri 14. 12. Mon 12:00–13:50 MS1,01016
- Timetable of Seminar Groups:

*T. Svoboda* **Prerequisites**- (
**M3100**Mathematical Analysis III &&**M4190**Curves and Surfaces ) ||**M6722**Diff. Geom. of Surfaces

Before enrolling this course the students should go through "Differential Geometry of Curves and Surfaces." **Course Enrolment Limitations**- The course is also offered to the students of the fields other than those the course is directly associated with.
**fields of study / plans the course is directly associated with**- there are 7 fields of study the course is directly associated with, display
**Course objectives**- Main objectives can be summarized as follows: to understand the foundations of the theory of smooth manifolds and tensor fields; to understand elements of global analysis and global differential geometry (distributions, integration on manifolds, connections, Riemannian geometry).
**Syllabus**- Smooth functions, Whitney theorem. Smooth maps of numerical spaces, submanifolds. Smooth manifolds, tangent bundles and vector fields. Smooth distributions, Frobenius theorem. Tensors and tensor fields. The exterior differential, Stokes theorem. Jets. Riemannian spaces.

**Literature**- KOLÁŘ, Ivan.
*Úvod do globální analýzy*. 1st ed. Brno: Masarykova univerzita, 2003. iv, 118 s. ISBN 80-210-3205-7. info

- KOLÁŘ, Ivan.
**Teaching methods**- Standard lectures aimed at the explanation of the theory, accompanied by practical tutorials and homework assignements.
**Assessment methods**- oral final exam
**Language of instruction**- Czech
**Further Comments**- Study Materials

- Enrolment Statistics (recent)

- Permalink: https://is.muni.cz/course/sci/autumn2018/M5130