Gradient
In mathematics, the gradient is a generalization of the usual concept of derivative of a function in one dimension to a function in several dimensions. If f(x1, ..., xn) is a differentiable, scalar-valued function of standard Cartesian coordinates in Euclidean space, its gradient is the vector whose components are the n partial derivatives of f. It is thus a vector-valued function.
Similarly to the usual derivative, the gradient represents the slope of the tangent of the graph of the function. More precisely, the gradient points in the direction of the greatest rate of increase of the function, and its magnitude is the slope of the graph in that direction. The components of the gradient in coordinates are the coefficients of the variables in the equation of the tangent space to the graph. This characterizing property of the gradient allows it to be defined independently of a choice of coordinate system, as a vector field whose components in a coordinate system will transform when going from one coordinate system to another.
Gradient (disambiguation)
The Gradient is the rate of variation of a numerical quantity. It may refer to:
Mathematics
Biology
Fluid dynamics and earth science
See also
Four-gradient
In differential geometry, the four-gradient is the four-vector analogue of the gradient from Gibbs-Heaviside vector calculus.
Definition
The covariant components compactly written in index notation are:
The comma in the last part above 
implies the partial differentiation with respect to 
. This is not the same as a semi-colon, used for the covariant derivative.
The contravariant components are:
where gαβ is the metric tensor, which here has been chosen for flat spacetime with the metric signature (+,−,−,−).
Alternative symbols to 
are 
and D.
Usage
The 4-Gradient is used in a number of different ways in Special Relativity:
As a 4-Divergence
The 4-Divergence of the 4-Position 
gives the dimensionality of spacetime:
The 4-Divergence of the 4-CurrentDensity 
gives a conservation law - the conservation of charge:
This means that the time rate of change of the charge density must equal the negative spatial divergence of the current density 
. In other words, the charge inside a box cannot just change arbitrarily, it must enter and leave the box via a current. This is a continuity equation.
Podcasts:
Gradient
ALBUMS
- Wired Thoughts released: 2010
- Electronica 2.0 released: 2009
- Seashore released: 2009
Electronica 2.0
Released 2009- Photo
- Timeless
- Touch of Light
- Takatak
- Return to the Earth
- Funky Smiles
- The Hunter of Harmony
- Heim
- Thunderstorm
- Sleet
- Shum Belogo
- Indian Summer
- Through a Mango Shade
- Autumn Crosses
- Efemer
- Aerobic
- Hap
- One Day (Doyeq remix)
- November 19
- Mist
- Leneyes
- Soffto
- Smells Like Fall
- Plush
- Animalcule (remix)
- Supreme Soul
- Canoe
- Next
- Pimpa Leaves Home
- Hyposomnia
- Guli
- True
- Old-Cool Support
- Kara Melek
- Voodoo
- Biser
- Back to the Roots
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In Anger
by: CardiantWhy I thought I had it all
and why I wanted more
Could it be just there for while,
the while I need for myself
Never dared to seal my door
Never dared to look behind
Once again I was
As fool as I can be
Anger takes my mind at will
The will I never could lead
Feel this anxious rise
Got no chance to be myself
Maybe somewhere I´ll find
the place where I can just be
Let me allow this dawn
Before we´ll follow that star
I´m making my command
on this hazy unknown ground
(The) Pain and the anger is gone
I know my life is worth of this run
I won´t again put myself to burn my
Candle at both ends
Once we will break our time
And that shine in your eyes will be my guide
Looking into the stars
made me blindly believe
in the truth of the lighting star
It may be hard to tell in advance
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