Introduction to Curves and Surfaces
Code  Completion  Credits  Range 

02UKP1  Z  2  1P+1C 
 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 twodimensional 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:
 Syllabus of lectures:

Outline of the lecture:
1. Examples and definition of curves
2. Plane curves, natural equation of a curve
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. Transformation properties of the first fundamental form
Outline of the exercises:
1. Curvature and length of the curve
2. Curvature and area of a surface
3. Metric tensor
 Syllabus of tutorials:

Outline of the exercises:
1. Curvature and length of the curve
2. Curvature and area of a surface
3. Metric tensor
 Study Objective:

Knowledge:
To provide the simplest examples of manifolds and their properties.
Acquired skills:
Solve mathematical problems defined on manifolds.
 Study materials:

Key references:
[1] L. Hlavatý, Úvod do křivek a ploch (in Czech)
www.fjfi.cvut.cz > katedra fyziky > studentský servis > Doprovod přednášek > Úvod do křivek a ploch
Recommended references:
[2] B. Hostinský, Diferenciální geometrie křivek a ploch, Přírodovědecké nakladatelství v Praze, 1949 (in Czech)
[3] W. Kuehnel, Diferential Geometry, AMS2006
[4] T. Banchoff, S Lovett , Diferential Geometry of Curves and Surfaces, CRC Press 2016
 Note:
 Timetable for winter semester 2020/2021:
 Timetable is not available yet
 Timetable for summer semester 2020/2021:
 Timetable is not available yet
 The course is a part of the following study plans: