Is paramitric Equation Correct?

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Homework Help Overview

The discussion revolves around the correctness of parametric equations representing a contour in complex analysis. Participants are examining the definitions and representations of these equations, particularly in the context of integrals over contours.

Discussion Character

  • Conceptual clarification, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are identifying potential mistakes in the parametric equations, such as the number of segments and the labeling of contours. There are questions regarding the implications of different contour representations in integrals.

Discussion Status

The discussion is active, with participants providing feedback on each other's attempts. Some have pointed out errors in the original post's equations, while others are seeking clarification on the implications of contour definitions. There is no explicit consensus yet, but guidance has been offered regarding the identification of mistakes.

Contextual Notes

Participants are working within the constraints of homework guidelines, which may limit the resources they can consult. There are indications of confusion regarding the notation and definitions used in the context of contour integrals.

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Homework Statement



http://up5.m5zn.com/photos/00017/t4x1262r70cu.jpg[/URL]
http://up5.m5zn.com/photos/00017/rpbn4bsfcace.jpg[/URL]

Homework Equations





The Attempt at a Solution


C1:z(t)=t , 0<t<5
C1:z(t)=5+it , 0<t<5
C2:z(t)=1-t+5i , 0<t<5
C3:z(t)=5-t+5i , 0<t<5
C4:z(t)=i(1-t) , 0<t<5
Is paramitric Equation Correct?
 
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1) Not really any difference as far as I know. They both indicate integral over the contour C. 2) The parametric form for the contour has several mistakes. Can you find one? I'll get you started. The contour has 4 segments, you've listed 5. Two of them labelled C1. What's up with that?
 
Dear
Dick
مرحبا
سعيد يرؤيتك
1)
I can not find an answer in books,In books sometimes use pattern,Sometimes using type IIusing
In your answer:
They both indicate integral over the contour
Do you clarify if possible
2)

C1:z(t)=t , 0=<t=<5
C2:z(t)=5-t+5i , 0=<t=<5
C3:z(t)=5-t+5i , 0=<t=<5
C4:z(t)=i(5-t) , 0=<t=<5
Sorry for error
I will try again.
Thanks
See you
 
For (1), IF "C" represents the same contour in both integrals, then, as Dick said, they are the same. However, I suspect that the question did not mean to imply that. If the two different "C"s may mean different contours, then the first form implies that C is a closed contour while the second does not.


For (2), now you've got C2 and C3 exactly the same! (Your second "C1" in your first answer should have been "C2".)
 
Hi king:smile:
O.K.
used (I) for Contour = sum of Curves , and Closed
and used (II) for any Curve

Q.2
Now
z1(t)=t , 0=<t=<5
z2(t)=5+it , 0=<t=<5
z3(t)= t+5i , 5=<t=<0
z4(t)=it , 5=<t=<0


 

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