Università Roma Tre

Plane curves. Equation of a plane. Point-Plane distance. Plane sections. Parametric Curves in R². Arc length and curvature. Examples using Mathematica software: plot, symbolic and numerical commands. Modeling a curve profile of an image. Polar coordinates. Rigid transformations: translations, rotations and reflexions. Rotation and reflexion matrices. Curves defined by their curvature.
Space curves. Parametric Curves in R³. Curvature and torsion. Frenet frame: tangent, normal and binormal vectors. Rigid transformations in R³. Rotation and reflexion matrices. Curves on surfaces. Cylindrical and spherical coordinates.
Surfaces. Parametric surfaces in R³. Jacobian matrix. The gradient. Two variable function plot. Surface intersections. Domes and vaults. Tubes, conic and cylindric surfaces. 
Modeling a surface from an architectural example. Point cloud-Surface distance.

Alfred Gray, E. Abbena, S. Salamon Modern Differential Geometry of Curves and Surfaces with Mathematica, Third Edition Chapman & Hall/CRC (2006)
Lecture notes with examples on the use of the software Mathematica are at the link of the course http://www.formulas.it/sito/corsi/matematica-curve-e-superfici-falcolini/