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...

integral curve is a parametric curve that represents a specific solution to an ordinary differential equation or system of equations. Integral curves...

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...

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...

{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...

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...

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  ...

curve. Determining the length of an irregular arc segment by approximating the arc segment as connected (straight) line segments is also called curve...

tautochrone curve or isochrone curve (from Ancient Greek ταὐτό (tauto-) 'same', ἴσος (isos-) 'equal', and χρόνος (chronos) 'time') is the curve for which...

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...

In mathematics, the Cauchy integral theorem (also known as the Cauchy–Goursat theorem) in complex analysis, named after Augustin-Louis Cauchy (and Édouard...

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...

differential calculus and integral calculus. The former concerns instantaneous rates of change, and the slopes of curves, while the latter concerns accumulation...

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...

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...

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...

functions on closed bounded intervals—the area under the curve could be defined as the integral, and computed using approximation techniques on the region...

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...

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...

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...

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...

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...

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...

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...

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...

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...

genus 1, i.e. an elliptic curve, such functions are the elliptic integrals. Logically speaking, therefore, an abelian integral should be a function such...

limit" we get exactly the area of S under the curve. When f(x) can take negative values, the integral equals the signed area between the graph of f and...

Riemann–Stieltjes integral is a generalization of the Riemann integral, named after Bernhard Riemann and Thomas Joannes Stieltjes. The definition of this integral was...

mathematics (specifically multivariable calculus), a multiple integral is a definite integral of a function of several real variables, for instance, f(x...