Geometry
Code  Completion  Credits  Range  Language 

11GIEE  KZ  3  2P+2C+12B  English 
 Course guarantor:
 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
 Timetable for winter semester 2024/2025:

06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon Tue Wed Thu Fri  Timetable for summer semester 2024/2025:
 Timetable is not available yet
 The course is a part of the following study plans: