Subjects

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Differential Geometry - NMUM301

Title:	Diferenciální geometrie
Guaranteed by:	Department of Mathematics Education (32-KDM)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2023
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

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 :	NMTM301, NMUM816, NUMP014
Interchangeability :	NMTM301, NMUM816, NUMP014
Is incompatible with:	NMTM301, NUMP014
Is interchangeable with:	NMTM301, 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 -

Last update: doc. RNDr. Antonín Slavík, Ph.D. (28.10.2019)

It is necessary to pass two written tests during the term.

Literature -

Last update: T_KDM (24.04.2017)

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

Teaching methods -

Last update: T_KDM (14.04.2014)

Lectures and exercises.

Requirements to the exam -

Last update: doc. RNDr. Antonín Slavík, Ph.D. (28.10.2019)

A written exam following the syllabus of the subject in the scope of the lecture.

Syllabus -

Last update: doc. RNDr. Antonín Slavík, Ph.D. (01.10.2021)

Plane and space curves, examples. Arclenght parametrization, Frenet frame, Frenet formulas, curvature and torsion, evolutes and involutes.

Parametrized surfaces, examples. Curves on surfaces. First fundamental form and its applications. Surface mapping (isometries, conformal mappings). Normal curvatures and second fundamental form. Principal directions and principal curvatures. Mean and Gaussian curvature, Theorema egregium, geodesic curves.