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Topic: Cotangent


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In the News (Wed 25 Nov 09)

  
  NationMaster - Encyclopedia: Cotangent space
All cotangent spaces have the same dimension, equal to the dimension of the manifold.
Note that since the tangent space and the cotangent space at a point are both real vector spaces of the same dimension, they are isomorphic to each other.
All the cotangent spaces of a manifold can be "glued together" to form a new differentiable manifold of twice the dimension, the cotangent bundle of the manifold.
www.nationmaster.com /encyclopedia/Cotangent-space   (828 words)

  
 Reference.com/Encyclopedia/Cotangent bundle
Because cotangent bundles can be thought of as symplectic manifolds, any real function on the cotangent bundle can be interpreted to be a Hamiltonian; thus the cotangent bundle can be understood to be a phase space on which Hamiltonian mechanics plays out.
That is: The one-form assigns to a vector in the tangent bundle of the cotangent bundle the application of the element in the cotangent bundle (a linear functional) to the projection of the vector into the tangent bundle (the differential of the projection of the cotangent bundle to the original manifold).
The cylinder is the cotangent bundle of the circle.
www.reference.com /browse/wiki/Cotangent_bundle   (834 words)

  
 Call That Jazz - Cotangent
Although the instrumentation is of the classic jazz quartet, the music spans many styles and has diverse global influences.
Cotangent is an exiting, fresh, world-class group, capable of awe-inspiring technique as well as beautifully sensitive moments.
Cotangent plays all original music composed by this amazing line up of musicians who have toured together since 1999.
www.callthatjazz.com /cotangent.html   (170 words)

  
  Mathwords: Inverse Cotangent
With inverse cotangent, we select the angle on the top half of the unit circle.
Note: arccot refers to "arc cotangent", or the radian measure of the arc on a circle corresponding to a given value of cotangent.
Technical note: Since none of the six trig functions sine, cosine, tangent, cosecant, secant, and cotangent are one-to-one, their inverses are not functions.
www.mathwords.com /c/cotangent_inverse.htm   (198 words)

  
 cotangent bundle
In differential geometry, the cotangent bundle of a manifold is the vector bundle of all the cotangent spaces at every point in the manifold.
The cotangent bundle has a canonical symplectic 2-form on it, as an exterior derivative of a one-form.
The one-form assigns to a vector in the tangent bundle of the cotangent bundle the application of the element in the cotangent bundle (a linear functional) to the projection of the vector into the tangent bundle (the differential of the projection of the cotangent bundle to the original manifold).
www.abacci.com /wikipedia/topic.aspx?cur_title=cotangent_bundle   (287 words)

  
 PlanetMath: cotangent bundle
The cotangent bundle to any manifold has a natural symplectic structure given in terms of the Poincaré 1-form, which is in some sense unique.
The existence of a symplectic structure implies that the cotangent bundle is always orientable, even if the original manifold is not.
This is version 14 of cotangent bundle, born on 2003-10-06, modified 2006-10-05.
www.planetmath.org /encyclopedia/CotangentBundle.html   (297 words)

  
 PlanetMath: complex tangent and cotangent   (Site not responding. Last check: )
Thus the properties of the tangent are easily derived from the corresponding properties of the cotangent.
As all meromorphic functions, the cotangent may be expressed as a series with the partial fraction terms of the form
This is version 5 of complex tangent and cotangent, born on 2007-03-14, modified 2007-03-23.
planetmath.org /encyclopedia/ComplexTangentAndCotangent.html   (293 words)

  
 Arc Cotangent - Search Results - MSN Encarta
Arc Cotangent, in trigonometry, the inverse of the cotangent function.
Cotangent, one of the six fundamental ratios of trigonometry, along with tangent, sine, cosine, secant, and cosecant.
An arc of a circle is often expressed in degrees and corresponds to the...
encarta.msn.com /Arc_Cotangent.html   (147 words)

  
 cotangent.vector   (Site not responding. Last check: )
One can present a cotangent vector by giving a function of which it is the gradient at the point in question.
You can associate to the cotangent vector the tangent vector which suggests moving in the direction of fastest increase of the function, and whose length is the rate of increase.
If you multiply the coordinates of all the points by 10, then the coordinates of a tangent vector also get multiplied by 10, but the coordinates of a cotangent vector are reduced by a factor of 10: the amount by which the function increases per "unit" change in a coordinate is less, not greater.
math.ucr.edu /home/baez/gr/cotangent.vector.html   (695 words)

  
 Calcute functions: logarithm, inverse hyperbolic cotangent, arc-cosecant, hyperbolic inverse cosecant, arc-cotangent, ...
Calcute functions: logarithm, inverse hyperbolic cotangent, arc-cosecant, hyperbolic inverse cosecant, arc-cotangent, inverse hyperbolic secant, arc-secant...
Arc-cotangent (arccotangent, inverse cotangent) value expressed using the currently-selected angle unit.
Cotangent of an angle in the currently-selected unit.
calcute.com /functions.html   (629 words)

  
 cotangent bundle - OneLook Dictionary Search
Tip: Click on the first link on a line below to go directly to a page where "cotangent bundle" is defined.
Cotangent Bundle : Eric Weisstein's World of Mathematics [home, info]
Phrases that include cotangent bundle: cotangent bundle is a bundle
www.onelook.com /?w=cotangent+bundle&ls=a   (91 words)

  
 Differentiation of trig functions
Derivative of the cotangent of a linear quantity
Derivative of the cotangent of a quadratic quantity
Derivative of the cotangent of a fractional power
www.jtaylor1142001.net /calcjat/Contents/CDTrig.htm   (300 words)

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