Vector Analysis

Building on the Wolfram Language's powerful capabilities in calculus and algebra, the Wolfram Language supports a variety of vector analysis operations. Vectors in any dimension are supported in common coordinate systems. By exploiting the Wolfram Language's efficient representation of arrays, operations can be performed on scalars, vectors, and higher-rank tensors in a uniform manner.

ReferenceReference

Vector Calculus

Grad (TemplateBox[{f, x}, Grad]) gradient

Div (TemplateBox[{f, x}, Div]) divergence

Curl (TemplateBox[{f, x}, Curl]) curl in any dimension

Laplacian (TemplateBox[{f, x}, Laplacian]) Laplacian

Coordinate Systems

CoordinateChartData properties of coordinate systems

CoordinateTransformData relationships between coordinate systems

TransformedField transform a scalar, vector, or tensor field between coordinate systems

CoordinateTransform re-express a point in a new coordinate system

Curves

ArcLength length

ArcCurvature curvature

FrenetSerretSystem generalized curvatures and associated basis

Visualization

StreamPlot  ▪  VectorPlot  ▪  ListVectorPlot  ▪  VectorPlot3D  ▪  ...