Evaluating Complex Integration I_c |z^2|

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SUMMARY

The discussion focuses on evaluating the integral I_c |z^2| over a square contour defined by the vertices (0, 0), (1, 0), (1, 1), and (0, 1), traversed anti-clockwise. Participants emphasize the necessity of parametrizing the square to compute the path integral effectively. The parametrization will facilitate the evaluation of the integral by defining the equations of the four lines that form the square and the corresponding limits for integration. The integral involves the function max(x^2, y^2) with sides of length 1.

PREREQUISITES
  • Complex analysis fundamentals
  • Path integrals in complex functions
  • Parametrization techniques for contours
  • Understanding of the max function in two dimensions
NEXT STEPS
  • Study complex contour integration methods
  • Learn about parametrizing curves in the complex plane
  • Explore the properties of the max function in multivariable calculus
  • Investigate the application of Green's Theorem in evaluating integrals over regions
USEFUL FOR

Mathematicians, physics students, and anyone involved in complex analysis or evaluating integrals over defined geometric shapes.

AkilMAI
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How can I evaluate I_c |z^2|,where I is the integral and c is the square with vertices at (0, 0), (1, 0), (1, 1), (0, 1) traversed anti-clockwise...?
 
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Did you write a parametrization of this square?
 
how will that help?
 
It's needed to compute a path integral.
 
ok ...how should I proceed?
 
James said:
ok ...how should I proceed?

What would be the equation of the four lines that make the square, and between which values are these lines defined?
 
max(x^2,y^2) with sides of 1?
 

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