Suchergebnisse
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Vor einem Tag · where the integration limits indicate integration along a contour that can be chosen as follows: from −∞ to 0 along the negative real axis, from 0 to ± π i along the imaginary axis, and from ± π i to +∞ ± π i along a contour parallel to the real axis.
Vor 2 Tagen · More precisely, the divergence theorem states that the surface integral of a vector field over a closed surface, which is called the "flux" through the surface, is equal to the volume integral of the divergence over the region enclosed by the surface. Intuitively, it states that "the sum of all sources of the field in a region (with ...
Vor 3 Tagen · Die Integralrechnung ist ein Zweig der Infinitesimalrechnung und bildet mit der Differentialrechnung die mathematische Analysis. Sie ist aus der Aufgabe entstanden, Flächeninhalte oder Volumina zu berechnen, die durch gekrümmte Linien bzw. Flächen begrenzt sind.
Vor 3 Tagen · These types of integrals seem first to have attracted Laplace's attention in 1782, where he was following in the spirit of Euler in using the integrals themselves as solutions of equations. However, in 1785, Laplace took the critical step forward when, rather than simply looking for a solution in the form of an integral, he started to apply the transforms in the sense that was later to become ...
Vor 3 Tagen · Topics include:the topology of the complex plane; convergence of complex sequences and series; holomorphic functions, the Cauchy-Riemann equations, harmonic functions and applications; contour integrals and the Cauchy Integral Theorem; singularities, Laurent series, the Residue Theorem, evaluation of integrals using contour ...
Vor 3 Tagen · contour integrals (or the Master Theorem equivalent) to obtain identities valid for σ = 1/2. This will be found in Section 2. In Section 3, we then examine cases with general values of σ following the same methods. Acknowledging that we are dealing with functions on the very
Vor 2 Tagen · We extend the notion of a leading singularity to include any full dimensional compact contour integral of a scattering amplitude. By focusing on the massive double box integrand we find that the maximal co-dimension residue results in the inverse of the square root of a quartic, which defines an elliptic curve. Choosing to integrate the elliptic curve, (over one of its cycles) yields what we ...
