Smooth curves, parameterizations, regular points, reparameterizations, length, tangent vector.
Curvature, torsion, Frenet frame, evolutes and involutes, envelopes, fundamental theorem of curves).
Simple surfaces, coordinate patches, maps, smooth surfaces, parameterizations, parametric curves,
tangent planes).
First fundamental form, orientation, length of a surface curve, surface area
Second fundamental form, normal curvature, principal directions and curvatures, mean
Curvature and Gauss curvature.
Geodesic curves, rotational surfaces, developable surfaces.
Local isometries, isometries, conformal mappings, equiareal mappings.
- Teacher: Δημήτριος Κοντοκώστας
- Teacher: Γεράσιμος Μανουσάκης
ECTS : 4
Language : el
Learning Outcomes : Upon successful completion of the course, students will be able to: o possess mathematical knowledge in the most advanced mathematical field with direct applications in topography. At the same time, have the ability at a theoretical level to sharpen their mathematical thinking and enrich their geometric background. o be able to understand the connection between the mathematical knowledge of differential geometry on the one hand and the representations of technical drawings and objects in space in general on the other. o be able to understand the application of the above knowledge for handling various technical issues related to the science of surveying via computer. o have the ability to mathematically analyze and describe existing topographic problems, propose mathematical solutions, conduct their mathematical investigation, transfer results to colleagues, predict the results of their actions without constructing true models for experimentation. Perform mathematical measurements of measurable properties on real objects. o have the ability to undertake future postgraduate studies in subjects of the surveying field or related fields, where a solid geometric foundation is essential.