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# Order of approximation

In science, engineering, and other quantitative disciplines, orders of approximation refer to formal or informal terms for how precise an approximation is, and to indicate progressively more refined approximations: in increasing order of precision, a zeroth-order approximation, a first-order approximation, a second-order approximation, and so forth. [1]

## Approximation

An approximation is anything that is similar but not exactly equal to something else.

## Big O notation

Big O notation is a mathematical notation that describes the limiting behaviour of a function when the argument tends towards a particular value or infinity.

## Constant (mathematics)

In mathematics, the adjective constant means non-varying.

## Convexity (finance)

In mathematical finance, convexity refers to non-linearities in a financial model.

## Degree of a polynomial

The degree of a polynomial is the highest degree of its monomials (individual terms) with non-zero coefficients.

## Engineering

Engineering is the creative application of science, mathematical methods, and empirical evidence to the innovation, design, construction, operation and maintenance of structures, machines, materials, devices, systems, processes, and organizations.

## Formula

In science, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a chemical formula.

## Function (mathematics)

In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.

## Line (geometry)

The notion of line or straight line was introduced by ancient mathematicians to represent straight objects (i.e., having no curvature) with negligible width and depth.

## Linear approximation

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

## Linearization

In mathematics, linearization is finding the linear approximation to a function at a given point.

## Mathematical finance

Mathematical finance, also known as quantitative finance, is a field of applied mathematics, concerned with mathematical modeling of financial markets.

## Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

## Order of magnitude

An order of magnitude is an approximate measure of the number of digits that a number has in the commonly-used base-ten number system.

## Parabola

In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.

## Perturbation theory

Perturbation theory comprises mathematical methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem.

## Polynomial

In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

## Polynomial interpolation

In numerical analysis, polynomial interpolation is the interpolation of a given data set by the polynomial of lowest possible degree that passes through the points of the dataset.

In algebra, a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic, is a polynomial function in one or more variables in which the highest-degree term is of the second degree.

## Science

R. P. Feynman, The Feynman Lectures on Physics, Vol.1, Chaps.1,2,&3.

## Scientist

A scientist is a person engaging in a systematic activity to acquire knowledge that describes and predicts the natural world.

## Significant figures

The significant figures (also known as the significant digits) of a number are digits that carry meaning contributing to its measurement resolution.

## Slope

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.

## Smoothness

In mathematical analysis, the smoothness of a function is a property measured by the number of derivatives it has that are continuous.

## Taylor series

In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point.

## Unit of observation

In statistics, a unit of observation is the unit described by the data that one analyzes.

## References

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