M5130 Global Analysis

Faculty of Science
Autumn 2014
Extent and Intensity
2/1. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. Anton Galaev, Dr. rer. nat. (lecturer)
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
Tue 16:00–17:50 M4,01024
  • Timetable of Seminar Groups:
M5130/01: Tue 18:00–18:50 M4,01024, J. Slovák
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 offered to students of any study field.
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
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 2015, Autumn 2016, autumn 2017, Autumn 2018.
  • Enrolment Statistics (Autumn 2014, recent)
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