Geometry

Garant předmětu:

Šárka Voráčová

Lecturer:

Šárka Voráčová

Tutor:

Šárka Voráčová

Supervisor:

Department of Applied Mathematics

Synopsis:

Differential geometry of curves - parameterization, the arc of the curve, torsion and curvature, Frenet`s trihedron. Kinematics - a curve as a trajectory of the motion, the velocity, and acceleration of a particle moving on a curved path.

Requirements:

Plane and space geometry, analytic geometry

Syllabus of lectures:

Line, plane and conic sections

Linear algebra

Linear 2D transformations

Curve as a graph of a function

Differential geometry of curves

Differential geometry of surfaces

Syllabus of tutorials:

Line, plane and conic sections

Linear algebra

Linear 2D transformations

Curve as a graph of a function

Differential geometry of curves

Geometry of surfaces

Study Objective:

Basic methods of the descriptive geometry, sketch of a 3D geometric object. Matrix representation of linear mapping. Parametrization of the curve, torsion and curvature. Application of differential geometry in a road design.

Study materials:

M. Hohenwarten, J. Preiner: Introduction to GeoGebra 4.4, 2013

J. Stewart: Essential Calculus, Early transcendentals, 6ed. Chapters:

Review of Conic Section

Review of Analytic Geometry

Summary of Curve Sketching

Parametric Equations

Geometry of space

Vector function (Curves)

F. Hreinsdótir: Investigation 2 by 2 matrices, University of Iceland

Note:

Further information:

https://www.fd.cvut.cz/department/k611/PEDAGOG/K611GM_A.html

Time-table for winter semester 2023/2024:

Time-table is not available yet

Time-table for summer semester 2023/2024:

Time-table is not available yet

The course is a part of the following study plans:

• Prospectus-Bachelor (elective specialized course)