Tangent Map
If 
, then the tangent map 
associated to 
is a Vector Bundle Homeomorphism 
(i.e., a Map between the Tangent Bundles of 
and 
respectively). Thetangent map corresponds to Differentiation by the formula
 | (1) |
(i.e., 
is a curve passing through the base point to 
in 
at time 0 with velocity ).In this case, if and 
, then the Chain Rule is expressed as | (2) |
 | (3) |
, is more intuitive than the usual form of the Chain Rule.See also Diffeomorphism
References
Gray, A. ``Tangent Maps.'' §9.3 in Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, pp. 168-171, 1993.
- Polymorph
- Polynomial
- Polynomial Bar Norm
- Polynomial Bracket Norm
- Polynomial Curve
- Polynomial Factor
- Polynomial Norm
- Polynomial Remainder Theorem
- Polynomial Ring
- Polynomial Root
- Polynomial Series
- Polyomino
- Polyomino Tiling
- Polyplet
- Polytope
- Poncelet's Closure Theorem
- Poncelet's Continuity Principle
- Poncelet-Steiner Theorem
- Poncelet's Theorem
- Poncelet Transform
- Poncelet Transverse
- Pong Hau K'i
- Pons Asinorum
- Pontryagin Class
- Pontryagin Duality