- #1
doey
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Homework Statement
evaluate contour integral ∫ Z dz from 0 to 1+21 in the curve of y=2x
doey said:Homework Statement
evaluate contour integral ∫ Z dz from 0 to 1+21 in the curve of y=2x
Dick said:So what exactly is your problem here? I can think of two ways to do this. Parametrize the curve or use the complex antiderivative. Both are easy. Do something!
doey said:ok,i try to solve for integrate z dz= x+iy(dx+idy) and get dy dx from y=2x.and i get the answer for integrate z dz,
how about the answer for integrate complex conjugate of z? since complex conjugate of z is not analytical .can i do it in the same way oso?
A contour integral is a type of line integral in complex analysis that is used to calculate the value of a function along a specific path or curve in the complex plane. It is represented by the symbol ∮ and is also known as a path integral.
The points 0 and 1+2i represent the start and end points of the curve or contour along which the integral is being calculated. They define the boundaries of the integral and determine the path over which the function will be integrated.
A contour integral is calculated by breaking the curve or contour into small segments, approximating each segment as a straight line, and then summing up the values of the function at each point along the contour. This sum is then multiplied by the length of each segment to get an accurate estimate of the integral.
A contour integral is a generalization of a regular integral in the complex plane. While a regular integral is calculated along a real axis, a contour integral is calculated along a curve or contour in the complex plane. In some cases, a contour integral can be reduced to a regular integral by choosing a specific path or curve in the complex plane.
Contour integrals have many practical applications in physics, engineering, and other fields. They are used, for example, in the calculation of electric and magnetic fields, fluid flow, and heat transfer. They are also used in signal processing, image processing, and control theory.