260203 VO Introduction to vector and tensor calculus II (2018S)

Description of curves and surfaces, tangential and normal vectors. Nonlinear coordinate systems, coordinate lines and coordinate surfaces, covariant and contravariant vector bases, transformation behavior. Length of curves, metric tensor, Riemann space, flat space, Euklidian space. Covariant derivative of scalars and vectors, vector differential operators in nonlinear coordinates, applications to cylindrically and spherically symmetric physical problems. Properties of the covariant derivative, higher covariant derivatives, Riemann curvature tensor, parallel displacement of vectors.