In mathematics, an integral curve is a parametric curve that represents a specific solution to an ordinary differential equation or system of equations.
mathematics, a line integral is an integral where the function to be integrated is evaluated along a curve. The terms path integral, curveintegral, and curvilinear...
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...
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...
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...
is called nonautonomous by definition. An integralcurve of the equation above (also called an integralcurve of X) is a map α : I ⊂ R ⟶ M {\displaystyle...
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...
differential calculus and integral calculus. The former concerns instantaneous rates of change, and the slopes of curves, while the latter concerns accumulation...
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...
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...
functions on closed bounded intervals—the area under the curve could be defined as the integral, and computed using approximation techniques on the region...
of the tangent to the graph of the differential equation's solution (integralcurve) at each point (x, y) as a function of the point coordinates. It can...
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...
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...
visual aid for visualizing vector fields. It consists of an imaginary integralcurve which is tangent to the field vector at each point along its length...
then θ defined as above is 0, and hence the curve is easily verified to be a solution (i.e. an integralcurve) for the above Pfaffian system for any nonzero...
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...
Cauchy integral formula for the winding number, it can be seen that the winding number is constant on connected components of the complement of the curve, is...
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...
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...
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