Contour Integration: Dealing With Poles

  • Context: Graduate 
  • Thread starter Thread starter pivoxa15
  • Start date Start date
  • Tags Tags
    Integration
Click For Summary
SUMMARY

Contour integration requires careful consideration when poles are present on the contour itself. The contour integral becomes undefined in such cases. To compute a real integral effectively, one must select a contour that circumvents the poles, ensuring the integral remains valid and computable. This approach is essential for accurate results in complex analysis.

PREREQUISITES
  • Understanding of complex analysis concepts
  • Familiarity with contour integration techniques
  • Knowledge of poles and their implications in integrals
  • Basic proficiency in evaluating real integrals
NEXT STEPS
  • Research methods for selecting appropriate contours in complex analysis
  • Study the residue theorem and its applications
  • Learn about singularities and their impact on integrals
  • Explore advanced techniques in evaluating contour integrals
USEFUL FOR

Students and professionals in mathematics, particularly those focusing on complex analysis, as well as physicists and engineers dealing with integrals in their work.

pivoxa15
Messages
2,250
Reaction score
1
If you have poles on the contour, what do you do about them?
 
Physics news on Phys.org
Why wouldn't you be completely free to make a new contour that goes around the old one and cuts around the point(s).

Maybe I am missing something about the question ;x
 
pivoxa15 said:
If you have poles on the contour, what do you do about them?

The contour integral is not defined if you have poles on the contour itself. But if you are trying to compute some real integral chose a contour which avoids this.
 

Similar threads

Graduate A question about a complex integral
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad Drawing the contour with a branch cut
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad What is the value of the integral for higher order poles in the real axis?
  • · Replies 9 ·
Replies
9
Views
3K
Undergrad Integration above or below axis
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Evaluate two complex integrals along a parabolic contour
  • · Replies 2 ·
Replies
2
Views
1K
Graduate Contour integral with poles on contour
  • · Replies 8 ·
Replies
8
Views
6K
Graduate Contour integral with a pole on contour - justification?
  • · Replies 2 ·
Replies
2
Views
6K
Graduate Why can't I use contour integration for this integral?
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Integrating a function of which poles appear on the branch cut
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Antiderivative and contour integration
  • · Replies 3 ·
Replies
3
Views
2K