quantitative disciplines, order of approximation refers to formal or informal expressions for how accurate an approximation is. In formal expressions...

An approximation is anything that is intentionally similar but not exactly equal to something else. The word approximation is derived from Latin approximatus...

geometric optics, the paraxial approximation is a small-angle approximation used in Gaussian optics and ray tracing of light through an optical system...

letter O was chosen by Bachmann to stand for Ordnung, meaning the order of approximation. In computer science, big O notation is used to classify algorithms...

series for each of the trigonometric functions. Depending on the order of the approximation, cos ⁡ θ {\displaystyle \textstyle \cos \theta } is approximated...

)\neq 0} . To begin, we use the mean value theorem (i.e.: the first order approximation of a Taylor series using Taylor's theorem): g ( X n ) = g ( θ ) + g...

pair of approximations to the system (a pair, because S0 can take two signs); the first-order WKB-approximation will be a linear combination of the two:...

In mathematics, a linear approximation is an approximation of a general function using a linear function (more precisely, an affine function). They are...

nearest order of magnitude for 3.7×108 is 9. An order-of-magnitude estimate is sometimes also called a zeroth order approximation. An order of magnitude...

series of the function. The first-order Taylor polynomial is the linear approximation of the function, and the second-order Taylor polynomial is often referred...

method Interval finite element Lyapunov stability Method of dominant balance Order of approximation Perturbation theory (quantum mechanics) Structural stability...

order-of-magnitude problem, is an estimation problem in physics or engineering education, designed to teach dimensional analysis or approximation of extreme...

Zeroth-order may refer to: Zeroth-order approximation, a rough approximation Zeroth-order logic, is first-order logic without variables or quantifiers...

mathematics, Stirling's approximation (or Stirling's formula) is an asymptotic approximation for factorials. It is a good approximation, leading to accurate...

In numerical analysis, order of accuracy quantifies the rate of convergence of a numerical approximation of a differential equation to the exact solution...

of change of concentration is independent of the concentrations Zeroth-order approximation, an approximation of a function by a constant Zeroth-order...

molecular physics, the Born–Oppenheimer (BO) approximation is the assumption that the wave functions of atomic nuclei and electrons in a molecule can...

constructing a second-order product approximation of a joint probability distribution, first described in a paper by Chow & Liu (1968). The goals of such a decomposition...

Approximations for the mathematical constant pi (π) in the history of mathematics reached an accuracy within 0.04% of the true value before the beginning...

particular in quantum mechanics, the Born approximation consists of taking the incident field in place of the total field as the driving field at each...

A successive-approximation ADC is a type of analog-to-digital converter (ADC) that digitizes each sample from a continuous analog waveform using a binary...

exists, is the slope of the tangent line to the graph of the function at that point. The tangent line is the best linear approximation of the function near...

The GW approximation (GWA) is an approximation made in order to calculate the self-energy of a many-body system of electrons. The approximation is that...

Padé approximant is the "best" approximation of a function near a specific point by a rational function of given order. Under this technique, the approximant's...

An order of magnitude is an approximation of the logarithm of a value relative to some contextually understood reference value. Orders of magnitude may...

pure exponential. Find a one pole approximation to the true frequency response. This is a first-order Padé approximation. There are many extensions to Elmore...

linear-elastic or Hookean. Hooke's law is only a first-order linear approximation to the real response of springs and other elastic bodies to applied forces...

introduced by the use of such approximations. If the Taylor series of a function is convergent, its sum is the limit of the infinite sequence of the Taylor polynomials...

values are given by the first-order (linear) approximation of their characteristic curve near the bias point. Many of the electrical components used...

certain order of approximation. There is, in general, an obstruction to continuing this extension past the critical order. The obstruction itself is of tensorial...