Frequently, physical systems exhibit special symmetries or structures that make a particular coordinate system especially useful. In a mathematically elegant solution to problems related to these systems, often the main step is choosing the correct coordinates. A variety of tools for doing calculus in various three‐dimensional coordinate systems are provided in this package.

SetCoordinates — set the default coordinate system

CoordinateSystem — default coordinate system

Coordinates — default variables in the default coordinate system

Coordinate Systems »

Bipolar  ▪  Bispherical  ▪  Cartesian  ▪  ...

Parameters

CoordinateRanges — interval over which the coordinate variables range

Parameters — default parameters of the coordinate system

ParameterRanges — range of values of the parameters of the coordinate system

Coordinate Transformations

CoordinatesToCartesian — transform coordinates to Cartesian coordinates

CoordinatesFromCartesian — transform coordinates from Cartesian coordinates

Vector Calculus

Div  ▪  Curl  ▪  Grad  ▪  Laplacian  ▪  Biharmonic

ArcLengthFactor — derivative of the arc length along parameterized curve

JacobianMatrix — derivative matrix of the coordinate transformation

JacobianDeterminant — determinant of the Jacobian matrix

ScaleFactors — list the scale factors

DotProduct  ▪  CrossProduct  ▪  ScalarTripleProduct