Methods Of Contour Integration
In the mathematical field of complex analysis, contour integration is a method of evaluating certain integrals along paths in the complex plane.
Contour integration is closely related to the calculus of residues, a methodology of complex analysis.
One use for contour integrals is the evaluation of integrals along the real line that are not readily found by using only real variable methods.
Contour integration methods include
- direct integration of a complex-valued function along a curve in the complex plane (a contour)
- application of the Cauchy integral formula
- application of the residue theorem.
One method can be used, or a combination of these methods, or various limiting processes, for the purpose of finding these integrals or sums.
Read more about Methods Of Contour Integration: Direct Methods, Applications of Integral Theorems
Famous quotes containing the words methods of, methods, contour and/or integration:
“If you want to know the taste of a pear, you must change the pear by eating it yourself.... If you want to know the theory and methods of revolution, you must take part in revolution. All genuine knowledge originates in direct experience.”
—Mao Zedong (1893–1976)
“I think it is a wise course for laborers to unite to defend their interests.... I think the employer who declines to deal with organized labor and to recognize it as a proper element in the settlement of wage controversies is behind the times.... Of course, when organized labor permits itself to sympathize with violent methods or undue duress, it is not entitled to our sympathy.”
—William Howard Taft (1857–1930)
“The living language is like a cowpath: it is the creation of the cows themselves, who, having created it, follow it or depart from it according to their whims or their needs. From daily use, the path undergoes change. A cow is under no obligation to stay in the narrow path she helped make, following the contour of the land, but she often profits by staying with it and she would be handicapped if she didn’t know where it was or where it led to.”
—E.B. (Elwyn Brooks)
“The more specific idea of evolution now reached is—a change from an indefinite, incoherent homogeneity to a definite, coherent heterogeneity, accompanying the dissipation of motion and integration of matter.”
—Herbert Spencer (1820–1903)