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stefaneli
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I have a problem with choosing a contour for integration... Can someone explain to me when to use a keyhole contour and when a semi-circle? Thanks...:)
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stefaneli said:I have a problem with choosing a contour for integration... Can someone explain to me when to use a keyhole contour and when a semi-circle? Thanks...:)
Contour integration is a mathematical technique used to evaluate integrals of real functions by transforming them into integrals along a path, or contour, in the complex plane. It allows us to solve certain integrals that are difficult or impossible to evaluate using traditional methods.
Contour integration involves integrating a function along a specific path in the complex plane, while regular integration involves integrating over a range of real numbers. Contour integration also allows us to solve certain integrals that cannot be solved using regular integration techniques.
The Cauchy-Goursat theorem states that if a function is analytic (meaning it has a continuous derivative) inside a closed contour, then the integral of that function along the contour is equal to zero. This theorem is used to simplify contour integrals by breaking them up into smaller, easier to solve integrals.
No, contour integration can only be used for functions that are analytic (have a continuous derivative) in the region enclosed by the contour. If a function is not analytic, then contour integration cannot be used to solve its integral.
Contour integration has many applications in physics, engineering, and other fields. It can be used to solve problems involving electric fields, fluid dynamics, heat transfer, and more. It is also used in signal processing and image analysis to manipulate and analyze complex data.