Expression | Curve definition | Variables | Description |
Linear transformations |
| | | Derivative of nth order |
| Cartesian |
| Integral, area |
| | | Composition operator |
| | | Even component |
| | | Odd component |
| | | Difference operator |
| | | Backward difference (Nabla operator) |
| | | Indefinite sum operator (inverse operator of difference) |
| | | Sturm–Liouville operator |
Non-linear transformations |
| | | Inverse function |
| | | Legendre transformation |
| | | Left composition |
| | | Indefinite product |
| | | Logarithmic derivative |
| | | Elasticity |
| | | Schwarzian derivative |
| | | Total variation |
| | | Arithmetic mean |
| | | Geometric mean |
| Cartesian |
| Subtangent |
| Parametric Cartesian | |
| Polar | |
| Polar |
| Sector area |
| Cartesian |
| Arc length |
| Parametric Cartesian | |
| Polar | |
| Cartesian |
| Affine arc length |
| Parametric Cartesian | |
| Parametric Cartesian |
|
| Cartesian |
| Curvature |
| Parametric Cartesian | |
| Polar | |
| Parametric Cartesian |
|
| Cartesian |
| Affine curvature |
| Parametric Cartesian | |
| Parametric Cartesian |
| Torsion of curves |
| Parametric Cartesian |
| Dual curve (tangent coordinates) |
| Parametric Cartesian |
| Parallel curve |
| Parametric Cartesian |
| Evolute |
| Intrinsic | |
| Parametric Cartesian |
| Involute |
| Parametric Cartesian |
| Pedal curve with pedal point (0;0) |
| Parametric Cartesian |
| Negative pedal curve with pedal point (0;0) |
| Intrinsic |
| Intrinsic to Cartesian transformation |
Metric functionals |
| | | Norm |
| | | Inner product |
| | | Fubini–Study metric (inner angle) |
Distribution functionals |
| | | Convolution |
| | | Differential entropy |
| | | Expected value |
| | | Variance |