Website owner:  James Miller

Vector Analysis

Basic concepts and conventions, vectors, scalars, operations on vectors, vector algebra, dot product, cross product, triple product

Scalar and vector functions, point functions, scalar point functions, vector point functions, scalar and vector fields

Vector differentiation

Space curves, tangent vector, principal normal, binormal, curvature, torsion, Frenet-Serret formulas

Vector integration, line integrals, surface integrals, volume integrals

Orthogonal projections of plane area regions

Surface integral representing a summation of flux passing through a closed surface

Gradient, del operator, directional derivative

Divergence

Curl (or rotation), circulation, circulation intensity

Formulas involving the del operator

Divergence theorem, Stokes' theorem, Green's theorem and related integral theorems

Simply connected regions, work, conservative force fields, scalar potential, irrotational vector

Concept of a tensor

Curvilinear coordinates

Tensors, contravariant and covariant components of a vector in a curvilinear coordinate system, notations and abbreviations