Description:

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.

Contents:

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

Seminar contents:

Line, plane and conic sections
Linear algebra
Linear 2D transformations
Curve as a graph of a function
Differential geometry of curves
Geometry of surfaces

Recommended literature:

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

Keywords:

Conic section, linear mapping, parametric curves, invariants of curves, quadric surfaces.

Abbreviations used:

Semester:

• W ... winter semester (usually October - February)
• S ... spring semester (usually March - June)
• W,S ... both semesters

Mode of completion of the course:

• A ... Assessment (no grade is given to this course but credits are awarded. You will receive only P (Passed) of F (Failed) and number of credits)
• GA ... Graded Assessment (a grade is awarded for this course)
• EX ... Examination (a grade is awarded for this course)
• A, EX ... Examination (the award of Assessment is a precondition for taking the Examination in the given subject, a grade is awarded for this course)

Weekly load (hours per week):

• P ... lecture
• C ... seminar
• L ... laboratory
• R ... proseminar
• S ... seminar