Subjects

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Differential Geometry I - NUMP014

Title:	Diferenciální geometrie I
Guaranteed by:	Department of Mathematics Education (32-KDM)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2016
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:	cancelled
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	doc. RNDr. Antonín Slavík, Ph.D.
Class:	M Bc. DGZV M Bc. DGZV > Povinné 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 :	NMUM301
Interchangeability :	NMUM301
Is incompatible with:	NMUM301, NMUM816
Is interchangeable with:	NMUM301, NMUM816

Annotation -

Last update: T_KDM (03.05.2011)

Basic course of classical differential geometry curves and surfaces.

Aim of the course -

Last update: T_KDM (19.05.2008)

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

Literature -

Last update: T_KDM (17.05.2011)

Teaching methods -

Last update: T_KDM (20.05.2008)

Lectures and exercises.

Syllabus -

Last update: T_KDM (17.05.2011)

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.