What is Complex integration: Definition and 77 Discussions

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 method 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; and
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.

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  1. D

    Integral of g(z) around |z-i|=2: Cauchy Integral Formula

    Homework Statement Find the value of the integral of g(z) around the circle |z-i|=2 in the positive sense when g(z)=\frac{1}{z^2+4}. Answer: pi\2 Homework Equations Cauchy Integral Formula f(z_0)=\frac{1}{2\Pi i}\int \frac{f(z) dz}{z-z_0} The Attempt at a Solution I tried...
  2. C

    Complex integration: which path should i choose?

    Hi there, this is a problem I'm having since last year, and should be "very easy", and i guess it is. 3 long years ago i took the complex analysis course, and I've used so little of it until now, that i almost forgot everything of it. The problem is this, I have the following integration...
  3. U

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    Homework Statement I was told to post this kind of question on the homework help section by one of the mentors,even though I'm not sure it is appropiate. Anyway,I'm doing complex integration now,so I need to get some important concepts cleared. I'll post my doubts in points...
  4. M

    Complex integration, branch cuts

    Hi guys, I need to show that: \int_{0}^{\infty } \frac{x^{a}}{(x+1)^2} \dx = \frac{\pi a}{\sin(\pi a)} , where -1<a<1. The problem is, that although a hint is given,the path of integrating it, I have difficulty what they really mean with "cut line, branch points, multivalued functions" etc...
  5. M

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  6. G01

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  7. O

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    Homework Statement 1)a Let D = C\{-i,i} and let γ be a closed contour in D. Find all the possible values of : (∫(1/(1+z²))dz around γ) b) If σ is a contour from 0 to 1, determine all possible values of: (∫(1/(1+z²))dz ( around σ) Homework Equations The Attempt at a...
  8. L

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  9. K

    Need help in complex integration

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  10. K

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  11. N

    A physical meaning to complex integration

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  12. L

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  13. L

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  14. S

    Complex Integration by Parts Help. Please

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  15. G

    Maple Solving Complex Integration with Maple and Mathematica

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  16. C

    Parametrization in Complex Integration

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  17. S

    Complex Integration Homework: Compute Integrals w/ Principle Value of z^i

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  18. F

    Validating Complex Integration Using Polar Form and the Unit Circle

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  19. B

    Integrating Complex Variables - Types & Solutions

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  20. J

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  21. J

    Is Cosh(4z) Integrable Along Any Path Between -πi/8 and πi/8?

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  22. malawi_glenn

    How to Solve a Complex Integration Problem with a Unit Circle?

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  23. Reshma

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  24. S

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  25. Y

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  26. W

    Find dx in a Complex Integration Problem: Anti-Derivative of Cos(2x)

    how would i find the anti-derv. of (cos(2x)). I am really confused with sub. ok i'll use u-du u = 2x du = 2 dx dx = 1/2 du k so... cos(u)*dx since the dx is there, you plug in the dx that i found right? so... sin(2x)1/2 ok so that's a simple integration problem, can someone...
  27. E

    Solving a Complex Integration Problem: Finding the Work to Empty a Tank

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