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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2019/2020

Introduction to Curves and Surfaces

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Code Completion Credits Range Language
02UKP Z 2 1+1 Czech
Lecturer:
Ladislav Hlavatý (guarantor)
Tutor:
Ladislav Hlavatý (guarantor)
Supervisor:
Department of Physics
Synopsis:

The goal of the lecture is an introduction to the differential geometry of simple manifolds - curves and two-dimensional surfaces. The basic concepts for the curves are introduced Frenets formulae are explained. In the surface theory we introduce first and second fundamental forms and mean and Gaussian curvature. Essential part of the lecture are the examples calculated by students

Requirements:

Differential calculus with several varaibles

Syllabus of lectures:

1.Examples and definition of curves

2.Plane curves, natural equation

3.Space curves, curvature, torsion

4.Frenet formulas

5.Examples and definition of surfaces

6.The first fundamental form, lenght of a curve on the surface

7.The second fundamental form

8.Mean and Gauss curvature of the surface

9.Gauss Weingarten equations

10.Codazzi equation

11.Gauss theorema egregium

Syllabus of tutorials:

Curvature and length of a curve

Curvature of a surface

Metric tensor

Study Objective:

Knowledge:

To provide the simplest examples of manifolds and their properties

Skills:

solve mathematical problems defined on manifolds

Study materials:

Key references:

[1] M.P. do Carmo, Differential Geometry of Curves and Surfaces,

New Jersey : Prentice - Hall, 1976

Recommended references:

[2] A. Gray Modern Differential Geometry, Boca Raton : CRC Press, c1998

Note:
Time-table for winter semester 2019/2020:
Time-table is not available yet
Time-table for summer semester 2019/2020:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2019-09-15
For updated information see http://bilakniha.cvut.cz/en/predmet12073605.html