mathematics, a line integral is an integral where the function to be integrated is evaluated along a curve. The terms path integral, curve integral, and curvilinear...
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integral curve is a parametric curve that represents a specific solution to an ordinary differential equation or system of equations. Integral curves...
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For example, a line integral is defined for functions of two or more variables, and the interval of integration is replaced by a curve connecting two points...
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Fubini's theorem (redirect from An elegant rearrangement of a conditionally convergent iterated integral)
{1}{y^{2}+1}}\,\mathrm {d} y=\arctan(1)={\frac {\pi }{4}}} For the integral of the Gauss curve this value can be generated: ∫ 0 ∞ exp ( − x 2 ) d x = 1 2...
41 KB (7,893 words) - 01:54, 16 May 2024
Contour integration (redirect from Contour integral)
contours provide a precise definition of the curves on which an integral may be suitably defined. A curve in the complex plane is defined as a continuous...
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Gaussian function (redirect from Integral of a Gaussian function)
Gaussian is a characteristic symmetric "bell curve" shape. The parameter a is the height of the curve's peak, b is the position of the center of the peak...
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Arc length (redirect from Rectifiable curve)
curve. Determining the length of an irregular arc segment by approximating the arc segment as connected (straight) line segments is also called curve...
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tautochrone curve or isochrone curve (from Ancient Greek ταὐτό (tauto-) 'same', ἴσος (isos-) 'equal', and χρόνος (chronos) 'time') is the curve for which...
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In the following curve–surface integral theorems, S denotes a 2d open surface with a corresponding 1d boundary C = ∂S (a closed curve): ∮ ∂ S A ⋅ d ℓ ...
31 KB (4,999 words) - 11:41, 15 May 2024
has a holomorphic antiderivative F on U. Then for every curve γ : [a, b] → U, the curve integral can be computed as ∫ γ f ( z ) d z = F ( γ ( b ) ) − F...
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vector calculus, Green's theorem relates a line integral around a simple closed curve C to a double integral over the plane region D bounded by C. It is the...
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geometry of curves is the branch of geometry that deals with smooth curves in the plane and the Euclidean space by methods of differential and integral calculus...
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Path integral may refer to: Line integral, the integral of a function along a curve Contour integral, the integral of a complex function along a curve used...
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In mathematics, the Cauchy integral theorem (also known as the Cauchy–Goursat theorem) in complex analysis, named after Augustin-Louis Cauchy (and Édouard...
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Calculus (redirect from Differential and Integral Calculus)
differential calculus and integral calculus. The former concerns instantaneous rates of change, and the slopes of curves, while the latter concerns accumulation...
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Gradient theorem (redirect from Fundamental Theorem of Line Integrals)
integrals, says that a line integral through a gradient field can be evaluated by evaluating the original scalar field at the endpoints of the curve....
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Winding number (redirect from Index of the curve)
change in θ is equal to the integral of dθ. We can therefore express the winding number of a differentiable curve as a line integral: wind ( γ , 0 ) = 1 2 π...
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Lebesgue integration (redirect from Lebesgue integral)
functions on closed bounded intervals—the area under the curve could be defined as the integral, and computed using approximation techniques on the region...
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usually known as normalized Fresnel integrals. The Euler spiral, also known as Cornu spiral or clothoid, is the curve generated by a parametric plot of...
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modular group of integral 2×2 matrices SL(2, Z). The term modular curve can also be used to refer to the compactified modular curves X(Γ) which are compactifications...
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genus 1, i.e. an elliptic curve, such functions are the elliptic integrals. Logically speaking, therefore, an abelian integral should be a function such...
6 KB (848 words) - 21:37, 15 March 2022
In the field of pharmacokinetics, the area under the curve (AUC) is the definite integral of the concentration of a drug in blood plasma as a function...
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In calculus, the Leibniz integral rule for differentiation under the integral sign states that for an integral of the form ∫ a ( x ) b ( x ) f ( x , t...
52 KB (11,107 words) - 16:00, 13 May 2024
mathematics, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point O. An elliptic curve is defined over...
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along the water retention curve. Integral energy takes into the account the path or energy (characterised by water retention curve) required to dry a soil...
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In integral calculus, an elliptic integral is one of a number of related functions defined as the value of certain integrals, which were first studied...
39 KB (7,418 words) - 01:30, 5 March 2024
reduction of the 3-dimensional manifold integration formula to a double curve integral is that the current paths be filamentary circuits, i.e. thin wires where...
57 KB (8,469 words) - 02:36, 13 March 2024
Euler spiral (category Plane curves)
curve whose curvature changes linearly with its curve length (the curvature of a circular curve is equal to the reciprocal of the radius). This curve...
23 KB (2,965 words) - 11:32, 10 May 2024
mathematics (specifically multivariable calculus), a multiple integral is a definite integral of a function of several real variables, for instance, f(x...
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powerful tool to evaluate line integrals of analytic functions over closed curves; it can often be used to compute real integrals and infinite series as well...
13 KB (3,251 words) - 13:48, 29 March 2024