Contour integral

  • #1
elimenohpee
67
0

Homework Statement


Let C be a contour formed by the points O(0,0), A(1,0), B(1,1), with the direction OA->AB->BO. By using the definition of a contour integral, evaluate:

(integral) f(z)dz

Homework Equations



[tex]\int f[z(t)]z'(t)dt[/tex]

The Attempt at a Solution


I didn't include the work I've done, or even the function upon which I am integrating. I'm looking more for an understanding.

I perform the line integrals about each side of the triangle, and sum each value at the end. But I end up with 0, which I think makes sense since this is a closed region. But should the value equal zero?
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,263
621
It might be zero. But since you skipped telling us what the function f(z) is, it's hard to say. It also might not be zero. Is that what you wanted to know? What is f(z)?
 
  • #3
elimenohpee
67
0
f(z) = e^pi*z

Its a little too much to try and type all the work I did computing each integral.
 
  • #4
Dick
Science Advisor
Homework Helper
26,263
621
f(z) = e^pi*z

Its a little too much to try and type all the work I did computing each integral.

That's fine. Since e^(pi*z) doesn't have any poles, then you are ok. The integral should come out to be zero. It's analytic inside the triangle. That's Cauchy's integral theorem. There are other functions that don't satisfy that criterion.
 
  • #5
elimenohpee
67
0
That's fine. Since e^(pi*z) doesn't have any poles, then you are ok. The integral should come out to be zero. It's analytic inside the triangle. That's Cauchy's integral theorem.

Thank you, exactly what I figured and actually worked out. Just wanted to verify.

Thanks again!
 

Suggested for: Contour integral

Replies
4
Views
425
Replies
2
Views
771
Replies
4
Views
448
Replies
5
Views
312
Replies
3
Views
1K
  • Last Post
Replies
10
Views
942
Replies
7
Views
310
  • Last Post
Replies
26
Views
3K
Replies
1
Views
874
  • Last Post
Replies
12
Views
153
Top