1. komponenta

Lecture type	Total
Lectures	30
Exercises	30

* Load is given in academic hour (1 academic hour = 45 minutes)

COURSE AIMS AND OBJECTIVES: Students will be introduced to the basic concepts of differential geometry of curves and surfaces in space in the local aspect. The geometric point of view will be emphasized. Mathematica/Maple software will be used to visualize introduced concepts.

COURSE DESCRIPTION AND SYLLABUS:
1. Curves in space. Regular curves. Arc length. Parametrization by the arc length. Frenet's moving frame. Frenet's formulas. Flexion and torsion. Fundamental theorem for space curves.
2. Surfaces in space. Regular surfaces. Tangent plane. Differential of a mapping. First fundamental form. Orientation of a surface. Shape operator (Weingarten map). Second fundamental form. Normal curvature. Principal curvatures and vectors. Gaussian and mean curvature.
3. Special curves on a surface: lines of curvatures, asymptotic lines, geodesics. Parallel transport. Local isometry of surfaces. Christoffel symbols. Gauss's Theorema Egregium. Fundamental theorem for surfaces in space.

Enrollment :
Passed : Differential calculus of functions of several variables

Izborni predmet 1, 2 - Regular study - Mathematics

Izborni predmet 1, 2 - Regular study - Mathematics