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The term "numerical integration" first appears in 1915 in the publication A Course in Interpolation and Numeric Integration for the Mathematical Laboratory by David Gibb. [2] "Quadrature" is a historical mathematical term that means calculating area. Quadrature problems have served as one of the main sources of mathematical analysis.
Nonelementary integral. In mathematics, a nonelementary antiderivative of a given elementary function is an antiderivative (or indefinite integral) that is, itself, not an elementary function (i.e. a function constructed from a finite number of quotients of constant, algebraic, exponential, trigonometric, and logarithmic functions using field ...
In mathematics, an integral is the continuous analog of a sum, which is used to calculate areas, volumes, and their generalizations. Integration, the process of computing an integral, is one of the two fundamental operations of calculus, [a] the other being differentiation. Integration was initially used to solve problems in mathematics and ...
Integer. The integers arranged on a number line. An integer is the number zero (0), a positive natural number (1, 2, 3, . . .), or the negation of a positive natural number (−1, −2, −3, . . .). [1] The negations or additive inverses of the positive natural numbers are referred to as negative integers. [2]
In calculus, the trapezoidal rule (also known as the trapezoid rule or trapezium rule) [a] is a technique for numerical integration, i.e., approximating the definite integral: The trapezoidal rule works by approximating the region under the graph of the function as a trapezoid and calculating its area. It follows that.
Linear: An integral equation is linear if the unknown function u (x) and its integrals appear linear in the equation. [ 1 ] Hence, an example of a linear equation would be: 1 As a note on naming convention: i) u (x) is called the unknown function, ii) f (x) is called a known function, iii) K (x,t) is a function of two variables and often called ...
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