Search results
Results from the WOW.Com Content Network
A time derivative is a derivative of a function with respect to time, usually interpreted as the rate of change of the value of the function. [1] The variable denoting time is usually written as t {\displaystyle t} .
The units of group-delay dispersion are [time] 2, often expressed in fs 2. The group-delay dispersion (GDD) of an optical element is the derivative of the group delay with respect to angular frequency, and also the second derivative of the optical phase:
The derivative of the delta function satisfies a number of basic properties, including: [50] ... and 4/10 of the time returns exactly the value 3.5 ...
The behavior of temperature when the sides of a 1D rod are at fixed temperatures (in this case, 0.8 and 0 with initial Gaussian distribution). The temperature approaches a linear function because that is the stable solution of the equation: wherever temperature has a nonzero second spatial derivative, the time derivative is nonzero as well.
Snap, [6] or jounce, [2] is the fourth derivative of the position vector with respect to time, or the rate of change of the jerk with respect to time. [4] Equivalently, it is the second derivative of acceleration or the third derivative of velocity, and is defined by any of the following equivalent expressions: = ȷ = = =.
The slope of the constant function is 0, because the tangent line to the constant function is horizontal and its angle is 0. In other words, the value of the constant function, , will not change as the value of increases or decreases.
The left-hand side consists of a "time decay" term, the change in derivative value with respect to time, called theta, and a term involving the second spatial derivative gamma, the convexity of the derivative value with respect to the underlying value.
For example, consider the ordinary differential equation ′ = + The Euler method for solving this equation uses the finite difference quotient (+) ′ to approximate the differential equation by first substituting it for u'(x) then applying a little algebra (multiplying both sides by h, and then adding u(x) to both sides) to get (+) + (() +).