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.

M5130 Global Analysis

Faculty of Science
autumn 2017
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. Lukáš Vokřínek, PhD. (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
Mon 18. 9. to Fri 15. 12. Tue 10:00–11:50 M6,01011
  • Timetable of Seminar Groups:
M5130/01: Mon 18. 9. to Fri 15. 12. Tue 12:00–12:50 M6,01011, L. Vokřínek
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
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 2018.

M5130 Global Analysis

Faculty of Science
Autumn 2016
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. Lukáš Vokřínek, PhD. (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
Mon 19. 9. to Sun 18. 12. Wed 13:00–14:50 MS1,01016
  • Timetable of Seminar Groups:
M5130/01: Mon 19. 9. to Sun 18. 12. Wed 15:00–15:50 MS1,01016, L. Vokřínek
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 2017, Autumn 2018.

M5130 Global Analysis

Faculty of Science
Autumn 2015
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. Lukáš Vokřínek, PhD. (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
Mon 14:00–15:50 M3,01023
  • Timetable of Seminar Groups:
M5130/01: Mon 16:00–16:50 M3,01023, L. Vokřínek
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
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 2016, autumn 2017, Autumn 2018.

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)
prof. 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.

M5130 Global Analysis

Faculty of Science
Autumn 2013
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)
prof. 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
Mon 12:00–13:50 MS1,01016
  • Timetable of Seminar Groups:
M5130/01: Mon 14:00–14:50 MS1,01016, A. Galaev
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
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 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018.

M5130 Global Analysis

Faculty of Science
Autumn 2012
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)
prof. 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
Thu 13:00–14:50 M6,01011
  • Timetable of Seminar Groups:
M5130/01: Thu 15:00–15:50 M6,01011, A. Galaev
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
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 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018.

M5130 Global Analysis

Faculty of Science
Autumn 2011
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)
prof. Anton Galaev, Dr. rer. nat. (lecturer)
Guaranteed by
prof. RNDr. Jan Slovák, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Wed 16:00–17:50 MS1,01016
  • Timetable of Seminar Groups:
M5130/01: Wed 18:00–18:50 MS1,01016, A. Galaev
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
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 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018.

M5130 Global Analysis

Faculty of Science
Autumn 2010
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)
prof. RNDr. Jan Slovák, DrSc. (lecturer)
Guaranteed by
prof. RNDr. Jan Slovák, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 13:00–14:50 M3,01023
  • Timetable of Seminar Groups:
M5130/01: Tue 15:00–15:50 M3,01023, 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 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
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 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018.

M5130 Global Analysis

Faculty of Science
Autumn 2009
Extent and Intensity
2/1. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Jan Slovák, DrSc. (lecturer)
Natalia Bezvitnaya, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Jan Slovák, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 13:00–14:50 MS2,01022
  • Timetable of Seminar Groups:
M5130/01: Mon 15:00–15:50 MS2,01022, 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 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
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 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018.

M5130 Global Analysis

Faculty of Science
Autumn 2008
Extent and Intensity
2/1. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Jan Slovák, DrSc. (lecturer)
Natalia Bezvitnaya, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Ivan Kolář, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 15:00–16:50 M3,01023
  • Timetable of Seminar Groups:
M5130/01: Mon 17:00–17:50 M3,01023, 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 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
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
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 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018.

M5130 Global Analysis

Faculty of Science
Autumn 2007
Extent and Intensity
2/1. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Jan Slovák, DrSc. (lecturer)
Guaranteed by
prof. RNDr. Ivan Kolář, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 17:00–18:50 UP1
  • Timetable of Seminar Groups:
M5130/01: Mon 19:00–19:50 UP1, 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 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
Course objectives
The course presents the foundations of the theory of smooth manifolds and tensor fields that are necessary for global analysis and global differential 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.
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 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018.

M5130 Global Analysis

Faculty of Science
Autumn 2006
Extent and Intensity
2/1. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Jan Slovák, DrSc. (lecturer)
Guaranteed by
prof. RNDr. Ivan Kolář, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Jan Slovák, DrSc.
Timetable
Mon 17:00–18:50 N41
  • Timetable of Seminar Groups:
M5130/01: Mon 19:00–19:50 N41
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
Course objectives
The course presents the foundations of the theory of smooth manifolds and tensor fields that are necessary for global analysis and global differential 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.
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 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018.

M5130 Global Analysis

Faculty of Science
Autumn 2005
Extent and Intensity
2/1. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Jan Slovák, DrSc. (lecturer)
Guaranteed by
prof. RNDr. Ivan Kolář, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Jan Slovák, DrSc.
Timetable
Wed 10:00–11:50 N41
  • Timetable of Seminar Groups:
M5130/01: Wed 12:00–12:50 N41, 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 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
Course objectives
The course presents the foundations of the theory of smooth manifolds and tensor fields that are necessary for global analysis and global differential 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.
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 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, Autumn 2018.

M5130 Global Analysis

Faculty of Science
Autumn 2004
Extent and Intensity
2/1. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Jan Slovák, DrSc. (lecturer)
Guaranteed by
prof. RNDr. Ivan Kolář, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Jan Slovák, DrSc.
Timetable
Tue 15:00–16:50 N21
  • Timetable of Seminar Groups:
M5130/01: Tue 17:00–17:50 N21, 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 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
Course objectives
The course presents the foundations of the theory of smooth manifolds and tensor fields that are necessary for global analysis and global differential 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.
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 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, Autumn 2018.

M5130 Global Analysis

Faculty of Science
Autumn 2003
Extent and Intensity
2/1. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Jan Slovák, DrSc. (lecturer)
Guaranteed by
prof. RNDr. Ivan Kolář, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Jan Slovák, DrSc.
Timetable of Seminar Groups
M5130/01: No timetable has been entered into IS. 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 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
Course objectives
The course presents the foundations of the theory of smooth manifolds and tensor fields that are necessary for global analysis and global differential 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.
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 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, Autumn 2018.

M5130 Global Analysis

Faculty of Science
Autumn 2002
Extent and Intensity
2/1. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ivan Kolář, DrSc. (lecturer)
Guaranteed by
prof. RNDr. Ivan Kolář, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Ivan Kolář, DrSc.
Prerequisites
( M3100 Mathematical Analysis III && M3120 Geometry ) || 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
Course objectives
The course presents the foundations of the theory of smooth manifolds and tensor fields that are necessary for global analysis and global differential 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.
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 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, Autumn 2018.

M5130 Global Analysis

Faculty of Science
Autumn 2024

The course is not taught in Autumn 2024

Extent and Intensity
2/1. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
In-person direct teaching
Teacher(s)
prof. RNDr. Jan Slovák, DrSc. (lecturer)
doc. Lukáš Vokřínek, PhD. (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
Prerequisites
( M3100 Mathematical Analysis III && M4190 Curves and Surfaces ) || M6722 Diff. Geom. of Surfaces
Knowledge of the basics of calculus (in particular, derivative and integral for several variables), linear algebra (in particular, tensor product) and topology.
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
The goal is to develop the foundations of the theory of smooth manifolds and tensor fields on them. The basic concepts from calculus are explained in a coordinate free manner. The main topics of the course are vector fileds, flows, distributions, integration on manifolds and Riemann spaces.
Learning outcomes
At the end of this course students will:
- understand the foundations of the theory of smooth manifolds and tensor fields;
- be able to use elements of global analysis and global differential geometry such as distributions, integration on manifolds, Riemannian geometry;
- know and understand main theorems related to these notions.
Syllabus
  • Smooth maps between euclidean spaces, submanifolds. Smooth manifolds, tangent bundles and vector fields. Smooth distributions, Frobenius theorem. Tensors and tensor fields. The exterior differential, Stokes theorem. 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 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018.

M5130 Global Analysis

Faculty of Science
Autumn 2023

The course is not taught in Autumn 2023

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)
prof. RNDr. Jan Slovák, DrSc. (lecturer)
doc. Lukáš Vokřínek, PhD. (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
Prerequisites
( M3100 Mathematical Analysis III && M4190 Curves and Surfaces ) || M6722 Diff. Geom. of Surfaces
Knowledge of the basics of calculus (in particular, derivative and integral for several variables), linear algebra (in particular, tensor product) and topology.
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
The goal is to develop the foundations of the theory of smooth manifolds and tensor fields on them. The basic concepts from calculus are explained in a coordinate free manner. The main topics of the course are vector fileds, flows, distributions, integration on manifolds and Riemann spaces.
Learning outcomes
At the end of this course students will:
- understand the foundations of the theory of smooth manifolds and tensor fields;
- be able to use elements of global analysis and global differential geometry such as distributions, integration on manifolds, Riemannian geometry;
- know and understand main theorems related to these notions.
Syllabus
  • Smooth maps between euclidean spaces, submanifolds. Smooth manifolds, tangent bundles and vector fields. Smooth distributions, Frobenius theorem. Tensors and tensor fields. The exterior differential, Stokes theorem. 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 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018.

M5130 Global Analysis

Faculty of Science
Autumn 2022

The course is not taught in Autumn 2022

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)
prof. RNDr. Jan Slovák, DrSc. (lecturer)
doc. Lukáš Vokřínek, PhD. (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
Prerequisites
( M3100 Mathematical Analysis III && M4190 Curves and Surfaces ) || M6722 Diff. Geom. of Surfaces
Knowledge of the basics of calculus (in particular, derivative and integral for several variables), linear algebra (in particular, tensor product) and topology.
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
The goal is to develop the foundations of the theory of smooth manifolds and tensor fields on them. The basic concepts from calculus are explained in a coordinate free manner. The main topics of the course are vector fileds, flows, distributions, integration on manifolds and Riemann spaces.
Learning outcomes
At the end of this course students will:
- understand the foundations of the theory of smooth manifolds and tensor fields;
- be able to use elements of global analysis and global differential geometry such as distributions, integration on manifolds, Riemannian geometry;
- know and understand main theorems related to these notions.
Syllabus
  • Smooth maps between euclidean spaces, submanifolds. Smooth manifolds, tangent bundles and vector fields. Smooth distributions, Frobenius theorem. Tensors and tensor fields. The exterior differential, Stokes theorem. 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 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018.

M5130 Global Analysis

Faculty of Science
autumn 2021

The course is not taught in autumn 2021

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)
prof. RNDr. Jan Slovák, DrSc. (lecturer)
doc. Lukáš Vokřínek, PhD. (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
Prerequisites
( M3100 Mathematical Analysis III && M4190 Curves and Surfaces ) || M6722 Diff. Geom. of Surfaces
Knowledge of the basics of calculus (in particular, derivative and integral for several variables), linear algebra (in particular, tensor product) and topology.
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
The goal is to develop the foundations of the theory of smooth manifolds and tensor fields on them. The basic concepts from calculus are explained in a coordinate free manner. The main topics of the course are vector fileds, flows, distributions, integration on manifolds and Riemann spaces.
Learning outcomes
At the end of this course students will:
- understand the foundations of the theory of smooth manifolds and tensor fields;
- be able to use elements of global analysis and global differential geometry such as distributions, integration on manifolds, Riemannian geometry;
- know and understand main theorems related to these notions.
Syllabus
  • Smooth maps between euclidean spaces, submanifolds. Smooth manifolds, tangent bundles and vector fields. Smooth distributions, Frobenius theorem. Tensors and tensor fields. The exterior differential, Stokes theorem. 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 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018.

M5130 Global Analysis

Faculty of Science
Autumn 2020

The course is not taught in Autumn 2020

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)
prof. RNDr. Jan Slovák, DrSc. (lecturer)
doc. Lukáš Vokřínek, PhD. (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
Prerequisites
( M3100 Mathematical Analysis III && M4190 Curves and Surfaces ) || M6722 Diff. Geom. of Surfaces
Knowledge of the basics of calculus (in particular, derivative and integral for several variables), linear algebra (in particular, tensor product) and topology.
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
The goal is to develop the foundations of the theory of smooth manifolds and tensor fields on them. The basic concepts from calculus are explained in a coordinate free manner. The main topics of the course are vector fileds, flows, distributions, integration on manifolds and Riemann spaces.
Learning outcomes
At the end of this course students will:
- understand the foundations of the theory of smooth manifolds and tensor fields;
- be able to use elements of global analysis and global differential geometry such as distributions, integration on manifolds, Riemannian geometry;
- know and understand main theorems related to these notions.
Syllabus
  • Smooth maps between euclidean spaces, submanifolds. Smooth manifolds, tangent bundles and vector fields. Smooth distributions, Frobenius theorem. Tensors and tensor fields. The exterior differential, Stokes theorem. 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 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018.

M5130 Global Analysis

Faculty of Science
Autumn 2019

The course is not taught in Autumn 2019

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)
prof. RNDr. Jan Slovák, DrSc. (lecturer)
doc. Lukáš Vokřínek, PhD. (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
Prerequisites
( M3100 Mathematical Analysis III && M4190 Curves and Surfaces ) || M6722 Diff. Geom. of Surfaces
Knowledge of the basics of calculus (in particular, derivative and integral for several variables), linear algebra (in particular, tensor product) and topology.
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
The goal is to develop the foundations of the theory of smooth manifolds and tensor fields on them. The basic concepts from calculus are explained in a coordinate free manner. The main topics of the course are vector fileds, flows, distributions, integration on manifolds and Riemann spaces.
Learning outcomes
At the end of this course students will:
- understand the foundations of the theory of smooth manifolds and tensor fields;
- be able to use elements of global analysis and global differential geometry such as distributions, integration on manifolds, Riemannian geometry;
- know and understand main theorems related to these notions.
Syllabus
  • Smooth maps between euclidean spaces, submanifolds. Smooth manifolds, tangent bundles and vector fields. Smooth distributions, Frobenius theorem. Tensors and tensor fields. The exterior differential, Stokes theorem. 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 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018.

M5130 Global Analysis

Faculty of Science
Autumn 2011 - acreditation

The information about the term Autumn 2011 - acreditation is not made public

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)
prof. RNDr. Jan Slovák, DrSc. (lecturer)
Guaranteed by
prof. RNDr. Jan Slovák, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
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
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 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018.

M5130 Global Analysis

Faculty of Science
Autumn 2010 - only for the accreditation
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)
prof. RNDr. Jan Slovák, DrSc. (lecturer)
Guaranteed by
prof. RNDr. Jan Slovák, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
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
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 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, Autumn 2018.

M5130 Global Analysis

Faculty of Science
Autumn 2007 - for the purpose of the accreditation
Extent and Intensity
2/1. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Jan Slovák, DrSc. (lecturer)
Guaranteed by
prof. RNDr. Ivan Kolář, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Jan Slovák, DrSc.
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
Course objectives
The course presents the foundations of the theory of smooth manifolds and tensor fields that are necessary for global analysis and global differential 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.
Language of instruction
Czech
The course is also listed under the following terms 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, Autumn 2018.
  • Enrolment Statistics (recent)