Subjects

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Differential Geometry (CŽV) - NMUM816

Title:	Diferenciální geometrie (CŽV)
Guaranteed by:	Department of Mathematics Education (32-KDM)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2018
Semester:	winter
E-Credits:	5
Hours per week, examination:	winter 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
Is provided by:	NMUM301

Guarantor:	doc. RNDr. Antonín Slavík, Ph.D.
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 :	NUMP014
Interchangeability :	NUMP014
Is incompatible with:	NMUM301
Is interchangeable with:	NMUM301

Annotation -

Last update: JUDr. Dana Macharová (10.10.2012)

Basic course of classical differential geometry curves and surfaces.

Aim of the course -

Last update: JUDr. Dana Macharová (10.10.2012)

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

Literature -

Last update: T_KDM (14.04.2014)

F. Borceux: A Differential Approach to Geometry (Geometric Trilogy III), Springer, 2014

Teaching methods -

Last update: JUDr. Dana Macharová (10.10.2012)

Lectures and exercises.

Syllabus -

Last update: JUDr. Dana Macharová (10.10.2012)

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.