MU03036 Global Analysis I

Mathematical Institute in Opava
Winter 2012
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: z (credit).
Teacher(s)
doc. RNDr. Michal Marvan, CSc. (lecturer)
RNDr. Adam Hlaváč, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Michal Marvan, CSc.
Mathematical Institute in Opava
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
In this lecture, methods of Analysis are extended from open subsets of R^n to spaces of more complicated topology -- smooth manifolds. The first part of this two-semester course covers differential calculus on varieties in a coordinate-independent presentation.
Syllabus
  • Charts and atlases, smooth structure, smooth mapping, manifold; examples.
    Submanifolds, products of manifolds.
    The algebra of smooth functions.
    Tangent vectors to curves, tangent bundle, vector fields, differentiations of the algebra of smooth functions, Hadamard lemma.
    Trajectories and flows of vector fields, local 1-parameter groups of transformations.
    Lie bracket of vector fields, vector distributions, integral submanifolds, link to solution of systems of 1st order homogeneous linear equations in one unknown function.
    Projectable vector fields.
Literature
    recommended literature
  • L. Krump, V. Souček, J. A. Těšínský. Matematická analýza na varietách. Praha, Karolinum, 1998. info
  • D. Krupka. Úvod do analýzy na varietách. SPN, Praha, 1986. info
  • R. Narasimhan. Analysis on real and complex manifolds. North-Holland Publishing Company, Amsterdam, 1968. info
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
Teacher's information
Written and oral examination.
The course is also listed under the following terms Winter 1998, Winter 1999, Winter 2000, Winter 2001, Winter 2002, Winter 2003, Winter 2004, Winter 2005, Winter 2006, Winter 2007, Winter 2008, Winter 2009, Winter 2010, Winter 2011.
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