SubjectsSubjects(version: 953)
Course, academic year 2023/2024
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Selected topics in differential geometry - NMUG404
Title: Vybrané kapitoly z diferenciální geometrie
Guaranteed by: Department of Mathematics Education (32-KDM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2021
Semester: summer
E-Credits: 5
Hours per week, examination: summer s.:2/2, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Guarantor: doc. RNDr. Antonín Slavík, Ph.D.
Classification: Mathematics > Geometry
Incompatibility : NDGE012, NMTD402
Interchangeability : NDGE012, NMTD402
Is incompatible with: NMTD402, NDGE012
Is interchangeable with: NMTD402, NDGE012
Annotation -
Advanced course in classical differential geometry, focuses on deeper properties of plane curves and surfaces in three dimensions.
Last update: T_KDM (24.04.2017)
Aim of the course -

This course helps to obtain theoretical background for teaching mathematics at high school.

Last update: T_KDM (04.05.2015)
Course completion requirements - Czech

Požadavky ke zkoušce odpovídají sylabu předmětu v rozsahu, který byl prezentován na přednášce.

Podmínkou získání zápočtu je vyřešení všech domácích úloh.

Last update: Slavík Antonín, doc. RNDr., Ph.D. (11.03.2021)
Literature -
  • K. Tapp: Differential Geometry of Curves and Surfaces, Springer, 2016
  • F. Borceux: A Differential Approach to Geometry (Geometric Trilogy III), Springer, 2014
  • M. P. do Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall, 1976.
  • P. M. H. Wilson, Curved Spaces (From Classical Geometries to Elementary Differential Geometry). Cambridge University Press, 2008.
  • E. Kreyszig, Differential Geometry, New York, 1991.
  • Ch. Bär, Elementary Differential Geometry, Cambridge University Press, 2010.
  • B. O'Neill, Elementary Differential Geometry (2nd edition), Elsevier, 2006.
  • A. Pressley, Elementary Differential Geometry (2nd edition), Springer, 2010.
  • M. Spivak, A comprehensive introduction to differential geometry vol. 1-5. Publish or Perish, Inc.
  • J. Oprea, Differential Geometry and Its Applications, The Mathematical Association of America, 2007.
  • C. G. Gibson, Elementary Geometry of Differentiable Curves, Cambridge University Press, 2001.

Last update: T_KDM (24.04.2017)
Teaching methods -

Lectures and exercises.

Last update: T_KDM (04.05.2015)
Syllabus -
  • Plane curves: envelopes, rotation index, winding number, four vertex theorem, areas of planar figures, isoperimetric problems.

  • Surfaces in three dimensions: Geodesic curves and their properties, geodesic polar coordinates and their applications, Minding's theorem.

Last update: Slavík Antonín, doc. RNDr., Ph.D. (22.05.2019)
 
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