Definition, Betydelse, Synonymer & Anagram | Engelska ordet INTEGRAND

Definition av INTEGRAND

1. (matematik) integrand; en funktion som ska integreras

Exempel på hur du använder INTEGRAND i en mening

• The trapezoidal rule approximates the function with a linear function that coincides with the integrand at the endpoints of the interval and is represented by an orange dashed line.
• In order to evaluate real integrals, the residue theorem is used in the following manner: the integrand is extended to the complex plane and its residues are computed (which is usually easy), and a part of the real axis is extended to a closed curve by attaching a half-circle in the upper or lower half-plane, forming a semicircle.
• In any event, the result should be verified by differentiating and comparing to the original integrand.
• The resulting integrands are of the same form as the original integrand, so these reduction formulas can be repeatedly applied to drive the exponents m and p toward 0.
• If it is possible to change the points at which the integrand is evaluated, then other methods such as Gaussian quadrature and Clenshaw–Curtis quadrature are probably more suitable.
• The Riemann–Stieltjes integral also generalizes to the case when either the integrand ƒ or the integrator g take values in a Banach space.
• If an integrand can be rewritten in a form which is approximately separable this will increase the efficiency of integration with VEGAS.
• That the integral is positive follows from the fact that the integrand is non-negative; the denominator is positive and the numerator is a product of nonnegative numbers.
• If it is possible to evaluate the integrand at unequally spaced points, then other methods such as Gaussian quadrature and Clenshaw–Curtis quadrature are generally more accurate.
• Also note that if the integrand is meromorphic, one may have to add residues corresponding to poles traversed while deforming the contour (see for example section 3 of Okounkov's paper Symmetric functions and random partitions).
• It is a good illustration of special techniques for evaluating definite integrals, particularly when it is not useful to directly apply the fundamental theorem of calculus due to the lack of an elementary antiderivative for the integrand, as the sine integral, an antiderivative of the sinc function, is not an elementary function.
• The discontinuities of the stochastic integral are given by the jumps of the integrator multiplied by the integrand.
• The technique approximates part of the integrand using radial basis functions (local interpolating functions) and converts the volume integral into boundary integral after collocating at selected points distributed throughout the volume domain (including the boundary).

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