To recognize the mathematical and numerical skills acquired within the theory of curves and surfaces in the field of study.
To use the mathematical and numerical skills acquired within the theory of curves and surfaces for solving problems in the field of study. Understand mathematical methods and physical laws applied in geodesy and geoinformatics.
-Apply knowledge of mathematics and physics for the purpose of recognizing, formulating and solving of problems in the field of geodesy and geoinformatics.
- Use information technology in solving geodetic and geoinformation tasks
-Exercise appropriate judgements on the basis of performed calculation processing and interpretation of data obtained by means of surveying and its results.
-Take responsibility for continuing academic development in the field of geodesy and geoinformatics, or related disciplines, and for the development of interest in lifelong learning and further identify various forms of curve equations, calculate arc length, curvature and determine the associated vector fields;
Identify and differentiate between types of second order surfaces; -analyze the second order surfaces with emphasis on the sphere and the ellipsoid of revolution: determine the parameter curves, the tangent plane and the normal vector to the surface;
-determine the first fundamental form of the surface and use it to calculate arc length, surface area and angle between two curves on a surface;
-determine the second fundamental form of the surface and use it for classifying points on the surface, calculating the normal, principal, Gaussian and mean curvature of the surface;
- detect some special curves on surfaces (lines of curvature, asymptotic lines);
-define the concept of the geodesic curvature along a curve on a surfaces and the term geodesic; calculate the geodesic curvature of parameter curves in order to identify whether it is a matter of geodesic coordinates;
- pronounce the Theorema Egregium of Gauss;
-distinguish and name types of mappings of surfaces according to the mapping invariants;
-use a variety of tools for visualizing and solving problems related to the theory