Evaluating Complex Integration I_c |z^2|

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Discussion Overview

The discussion revolves around evaluating the complex integral I_c |z^2| over a square contour defined by vertices at (0, 0), (1, 0), (1, 1), and (0, 1), with an anti-clockwise traversal. Participants explore the necessary steps for computation and the mathematical formulation required for the path integral.

Discussion Character

  • Exploratory, Technical explanation, Homework-related

Main Points Raised

  • One participant asks how to evaluate the integral I_c |z^2| over the specified square contour.
  • Another participant inquires about the need for a parametrization of the square to compute the path integral.
  • A subsequent post questions the utility of the parametrization in the evaluation process.
  • It is mentioned that a parametrization is necessary for computing the path integral.
  • Participants express uncertainty about how to proceed with the evaluation and seek guidance on the next steps.
  • There is a question regarding the equations of the four lines that define the square and the values between which these lines are defined.
  • One participant suggests a mathematical expression, max(x^2,y^2), in relation to the sides of the square being of length 1.

Areas of Agreement / Disagreement

The discussion remains unresolved, with participants expressing uncertainty about the steps to take and the formulation needed for the integral evaluation.

Contextual Notes

There are limitations regarding the assumptions needed for parametrization and the specific mathematical steps required for the integral evaluation, which remain unresolved.

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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