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:
M5130/01: Mon 17. 9. to Fri 14. 12. Wed 17:00–17:50 M3,01023, 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
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
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2010 - only for the accreditation, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2018/M5130