Difference quotientExpression in calculusIn single-variable calculus, the difference quotient is usually the name for the expression f(x+h)−f(x)h{\displaystyle {\frac {f(x+h)-f(x)}{h}}}which when taken to the limit as h approaches 0 gives the derivative of the functionf. The name of the expression stems from the fact that it is the quotient of the difference of values of the function by the difference of the corresponding values of its argument (the latter is (x + h) - x = h in this case).
Numerical differentiationUse of numerical analysis to estimate derivatives of functionsFinite difference estimation of derivativeIn numerical analysis, numerical differentiationalgorithms estimate the derivative of a mathematical function or subroutine using values of the function.
Recurrence relationIn mathematics and computer science, a recurrence relation is an equation according to which the n{\displaystyle n}th term of a sequence of numbers is equal to some combination of the previous terms. Often, only k{\displaystyle k} previous terms of the sequence appear in the equation, for a parameter k{\displaystyle k} that is independent of n{\displaystyle n}; this number k{\displaystyle k} is called the order of the relation.Differential equationIn mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two.
DerivativeInstantaneous rate of change (mathematics)The graph of a function, drawn in black, and a tangent line to that graph, drawn in red. The slope of the tangent line is equal to the derivative of the function at the marked point.The derivative at different points of a differentiable function. In this case, the derivative is equal to sin(x2)+2x2cos(x2){\displaystyle \sin \left(x^{2} ight)+2x^{2}\cos \left(x^{2} ight)}.
Numerical analysisNumerical analysis is the study of algorithms for the problems of continuous mathematics. These algorithms involve real or complex variables (in contrast to discrete mathematics), and typically use numerical approximation in addition to symbolic manipulation. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences like economics, medicine, business and even the arts.
Operator (mathematics)In mathematics, an operator is generally a mapping or function that acts on elements of a space to produce elements of another space (possibly and sometimes required to be the same space). There is no general definition of an operator, but the term is often used in place of function when the domain is a set of functions or other structured objects.Functional equationIn mathematics, a functional equation is, in the broadest meaning, an equation in which one or several functions appear as unknowns. So, differential equations and integral equations are functional equations. However, a more restricted meaning is often used, where a functional equation is an equation that relates several values of the same function.
Delta (letter)HistoryArchaic local variants Diacritics and other symbolsDiacriticsάὰᾶἀἁᾱᾰϊᾳσ̌LigaturesϗϛNumerals (Attic)ϛ (6)ϟ (90)ϡ (900) Related topicsUse as scientific symbolsOrthographyRomanizationCyrillizationDelta ( ; uppercase Δ, lowercase δ; Greek: δέλτα, délta, ) is the fourth letter of the Greek alphabet. In the system of Greek numerals, it has a value of four. It was derived from the Phoenician letterdalet 𐤃.
Brook TaylorBrook Taylor (18 August 1685 – 29 December 1731) was an English mathematician and barrister best known for several results in mathematical analysis. Taylor's most famous developments are Taylor's theorem and the Taylor series, essential in the infinitesimal approach of functions in specific points.*As an Amazon Associate I earn from qualifying purchases.