Osnove diferencialne geometrije in uvod v vektorsko analizo - Kosi Ulbl, Irena (2017)
Bases of Differential Geometry and Introduction to Vector Analysis. Some fields of higher education mathematics are a part of fundamental knowledge of future mechanical engineer. The textbook covers some areas of differential geometry and vector analysis. At the beginning the vector function is introduced. We continue with a curve consideration. We learn about different types of equations that represent curves and we find out how to calculate the arc length. We introduce three special lines for a curve such as tangent line, normal line and binormal line. There are also two special scalars which can be calculated for each point of the curve: a curvature and a torsion. Intuitively, the first one measures how the curve deviates from being the line and the second one measures how the curve deviates from being planar. We proceed with the consideration of another important geometrical object: a surface. As well as curves, surfaces can also be presented with different kinds of equations. Some well-known surfaces such as cylindrical surfaces, conical surfaces, ellipsoids, hyperboloids and paraboloids are described.
Keywords: curve; surface; gradient; divergence; curl