SubjectsSubjects(version: 849)
Course, academic year 2019/2020
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Differential Geometry - NMUM301
Title in English: Diferenciální geometrie
Guaranteed by: Department of Mathematics Education (32-KDM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2016
Semester: winter
E-Credits: 5
Hours per week, examination: winter s.:2/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Guarantor: doc. RNDr. Antonín Slavík, Ph.D.
Class: M Bc. MZV
M Bc. MZV > Povinné
Classification: Mathematics > Mathematics, Algebra, Differential Equations, Potential Theory, Didactics of Mathematics, Discrete Mathematics, Math. Econ. and Econometrics, External Subjects, Financial and Insurance Math., Functional Analysis, Geometry, General Subjects, , Real and Complex Analysis, Mathematics General, Mathematical Modeling in Physics, Numerical Analysis, Optimization, Probability and Statistics, Topology and Category
Incompatibility : NMUM816, NUMP014
Interchangeability : NMUM816, NUMP014
Annotation -
Last update: T_KDM (05.10.2016)
An introductory course in differential geometry of curves and surfaces.
Aim of the course -
Last update: T_KDM (14.04.2014)

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

Course completion requirements - Czech
Last update: doc. RNDr. Antonín Slavík, Ph.D. (02.10.2017)

Podmínkou získání zápočtu je úspěšné napsání dvou zápočtových písemek.

Literature -
Last update: T_KDM (24.04.2017)
  • K. Tapp: Differential Geometry of Curves and Surfaces, Springer, 2016
  • F. Borceux: A Differential Approach to Geometry (Geometric Trilogy III), Springer, 2014
  • A. Pressley: Elementary Differential Geometry, Springer, 2010

Teaching methods -
Last update: T_KDM (14.04.2014)

Lectures and exercises.

Requirements to the exam - Czech
Last update: doc. RNDr. Antonín Slavík, Ph.D. (06.10.2017)

Zkouška z předmětu je písemná. Požadavky odpovídají sylabu předmětu v rozsahu prezentovaném na přednášce.

Syllabus -
Last update: T_KDM (24.04.2017)
  • Plane and space curves, examples. Arclength parametrization, Frenet frame, Frenet formulas, curvature and torsion, evolutes and involutes.
  • Parametrized surfaces, examples. Curves on surfaces. First fundamental form and its applications. Surfaces mappings (isometries, conformal mappings). Normal curvature and second fundamental form. Principal directions and principal curvatures. Mean and Gaussian curvature. Gauss and Weingarten equations, Theorema egregium.

 
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