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Initial condition. In mathematics and particularly in dynamic systems, an initial condition, in some contexts called a seed value, [1]: pp. 160 is a value of an evolving variable at some point in time designated as the initial time (typically denoted t = 0). For a system of order k (the number of time lags in discrete time, or the order of the ...
Initial value problem. In multivariable calculus, an initial value problem[a] (IVP) is an ordinary differential equation together with an initial condition which specifies the value of the unknown function at a given point in the domain. Modeling a system in physics or other sciences frequently amounts to solving an initial value problem.
Boundary value problems are similar to initial value problems.A boundary value problem has conditions specified at the extremes ("boundaries") of the independent variable in the equation whereas an initial value problem has all of the conditions specified at the same value of the independent variable (and that value is at the lower boundary of the domain, thus the term "initial" value).
The statement being tested in a test of statistical significance is called the null hypothesis. The test of significance is designed to assess the strength of the evidence against the null hypothesis, or a statement of 'no effect' or 'no difference'. [ 2 ] It is often symbolized as H0. The statement that is being tested against the null ...
Phase (waves) Plot of one cycle of a sinusoidal function. The phase for each argument value, relative to the start of the cycle, is shown at the bottom, in degrees from 0° to 360° and in radians from 0 to 2π. In physics and mathematics, the phase (symbol φ or ϕ) of a wave or other periodic function of some real variable (such as time) is ...
v. t. e. In geometry and mechanics, a displacement is a vector whose length is the shortest distance from the initial to the final position of a point P undergoing motion. [1] It quantifies both the distance and direction of the net or total motion along a straight line from the initial position to the final position of the point trajectory.
Showing wall boundary condition. The most common boundary that comes upon in confined fluid flow problems is the wall of the conduit. The appropriate requirement is called the no-slip boundary condition, wherein the normal component of velocity is fixed at zero, and the tangential component is set equal to the velocity of the wall. [1]
ℵ 0 (aleph-nought, aleph-zero, or aleph-null) is the cardinality of the set of all natural numbers, and is an infinite cardinal. The set of all finite ordinals, called ω or ω0 (where ω is the lowercase Greek letter omega), has cardinality ℵ 0. A set has cardinality ℵ 0 if and only if it is countably infinite, that is, there is a ...