contour integration

Contours are the class of curves on which we define contour integration.

This path independence is very useful in contour integration.

Several methods exist to do this; see methods of contour integration.

This information is often exploited in contour integration.

The theory of contour integration comprises a major part of complex analysis.

A more transparent solution is provided by Wittig using contour integration.

This appendix does the integral by contour integration.

Contour integration Alternate methods exist to compute more complex integrals.

This may be evaluated using contour integration.

Hall and Heck give a related and possibly more intuitive proof that avoids contour integration.

Contour integration is closely related to the calculus of residues, a methodology of complex analysis.

In contour integration, contours provide a precise definition of the curves on which an integral may be suitably defined.

Contour integration depends on a subject's ability to link representations of separate visual stimuli into a coherent percept.

Use of Hankel contours is one of the methods of contour integration.

The second one can be addressed by calculus techniques, but also in some cases by contour integration, Fourier transforms and other more advanced methods.

The first nonfaithful Burau representations are found without the use of computer, using a notion of winding number or contour integration.

In the mathematical field of complex analysis, contour integration is a method of evaluating certain integrals along paths in the complex plane.

In mathematics, the Pochhammer contour, introduced by and , is a contour in the complex plane with two points removed, used for contour integration.

Path integrals in the complex plane are often used to determine complicated real integrals, and here the theory of residues among others is useful (see methods of contour integration).

However, path integrals in the sense of this article are important in quantum mechanics; for example, complex contour integration is often used in evaluating probability amplitudes in quantum scattering theory.

It has been proposed that weaker lateral excitation due to deficient NMDA-receptor functioning could disrupt neural processing, and that this might underlie problems with contour integration in schizophrenia.

There is a straightforward derivation using complex analysis and contour integration (the complex formal power series version is clearly a consequence of knowing the formula for polynomials, so the theory of analytic functions may be applied).

Subjects with schizophrenia have been shown to perform worse than healthy adults on tasks that depend on contour integration, and these deficits may be related to factors such as illness severity, chronicity, and degree of disorganized symptoms.

The estimation lemma is most commonly used as part of the methods of contour integration with the intent to show that the integral over part of a contour goes to zero as goes to infinity.

In fact by contour integration it can be shown that the main term on the right hand side of the equation is the value of the integral on the left hand side, extended over the range [ , ].