Mixing
Evaluate $int_gamma frac{1+z}{1-cos z} dz$ where $gamma$ is origin centered circle with radius 7
$begingroup$
I am beginner at this topic, i need help to solve the following question for my exam preparation.
Evaluate $$int_gamma frac{1+z}{1-cos z} dz$$ where $gamma$ is origin centered circle with radius 7.
Any help would be really appreciated.
integration complex-analysis complex-integration
edited Jan 17 at 23:10
Larry
2,41331129
asked Jan 17 at 22:42
RenasRenas
122
$endgroup$
add a comment |
$begingroup$
I am beginner at this topic, i need help to solve the following question for my exam preparation.
Evaluate $$int_gamma frac{1+z}{1-cos z} dz$$ where $gamma$ is origin centered circle with radius 7.
Any help would be really appreciated.
integration complex-analysis complex-integration
edited Jan 17 at 23:10
Larry
2,41331129
asked Jan 17 at 22:42
RenasRenas
122
$endgroup$
2
$begingroup$
Do you know the residue theorem?
$endgroup$
– 0x539
Jan 17 at 22:46
1
$begingroup$
Where are the poles of your function located at? Which ones are located within your contour? Can you calculate the residue at each?
$endgroup$
– Brevan Ellefsen
Jan 17 at 22:56
add a comment |
$begingroup$
I am beginner at this topic, i need help to solve the following question for my exam preparation.
Evaluate $$int_gamma frac{1+z}{1-cos z} dz$$ where $gamma$ is origin centered circle with radius 7.
Any help would be really appreciated.
integration complex-analysis complex-integration
edited Jan 17 at 23:10
Larry
2,41331129
asked Jan 17 at 22:42
RenasRenas
122
$endgroup$
I am beginner at this topic, i need help to solve the following question for my exam preparation.
Evaluate $$int_gamma frac{1+z}{1-cos z} dz$$ where $gamma$ is origin centered circle with radius 7.
Any help would be really appreciated.
integration complex-analysis complex-integration
integration complex-analysis complex-integration
edited Jan 17 at 23:10
Larry
2,41331129
asked Jan 17 at 22:42
RenasRenas
122
edited Jan 17 at 23:10
Larry
2,41331129
asked Jan 17 at 22:42
RenasRenas
122
edited Jan 17 at 23:10
Larry
2,41331129
edited Jan 17 at 23:10
Larry
2,41331129
edited Jan 17 at 23:10
Larry
2,41331129
2,41331129
asked Jan 17 at 22:42
RenasRenas
122
asked Jan 17 at 22:42
RenasRenas
122
asked Jan 17 at 22:42
RenasRenas
122
122
2
$begingroup$
Do you know the residue theorem?
$endgroup$
– 0x539
Jan 17 at 22:46
1
$begingroup$
Where are the poles of your function located at? Which ones are located within your contour? Can you calculate the residue at each?
$endgroup$
– Brevan Ellefsen
Jan 17 at 22:56
add a comment |
2
$begingroup$
Do you know the residue theorem?
$endgroup$
– 0x539
Jan 17 at 22:46
1
$begingroup$
Where are the poles of your function located at? Which ones are located within your contour? Can you calculate the residue at each?
$endgroup$
– Brevan Ellefsen
Jan 17 at 22:56
2
2
$begingroup$
Do you know the residue theorem?
$endgroup$
– 0x539
Jan 17 at 22:46
$begingroup$
Do you know the residue theorem?
$endgroup$
– 0x539
Jan 17 at 22:46
1
1
$begingroup$
Where are the poles of your function located at? Which ones are located within your contour? Can you calculate the residue at each?
$endgroup$
– Brevan Ellefsen
Jan 17 at 22:56
$begingroup$
Where are the poles of your function located at? Which ones are located within your contour? Can you calculate the residue at each?
$endgroup$
– Brevan Ellefsen
Jan 17 at 22:56
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
If you have learned the Residue Theorem, you should be able to apply it; calculate the residues at each pole inside the contour.
If not, you can 1) plug in a suitable parameterization of the path, and use brute force to compute the resulting integral (with a real variable), or 2) obtain the indefinite integral away from the pole, it should contain branch cut(s), and your integral can be obtained by monodromy.
answered Jan 18 at 0:06
TreborTrebor
81013
$endgroup$
add a comment |
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1 Answer
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active
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votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
If you have learned the Residue Theorem, you should be able to apply it; calculate the residues at each pole inside the contour.
If not, you can 1) plug in a suitable parameterization of the path, and use brute force to compute the resulting integral (with a real variable), or 2) obtain the indefinite integral away from the pole, it should contain branch cut(s), and your integral can be obtained by monodromy.
answered Jan 18 at 0:06
TreborTrebor
81013
$endgroup$
add a comment |
$begingroup$
If you have learned the Residue Theorem, you should be able to apply it; calculate the residues at each pole inside the contour.
If not, you can 1) plug in a suitable parameterization of the path, and use brute force to compute the resulting integral (with a real variable), or 2) obtain the indefinite integral away from the pole, it should contain branch cut(s), and your integral can be obtained by monodromy.
answered Jan 18 at 0:06
TreborTrebor
81013
$endgroup$
add a comment |
$begingroup$
If you have learned the Residue Theorem, you should be able to apply it; calculate the residues at each pole inside the contour.
If not, you can 1) plug in a suitable parameterization of the path, and use brute force to compute the resulting integral (with a real variable), or 2) obtain the indefinite integral away from the pole, it should contain branch cut(s), and your integral can be obtained by monodromy.
answered Jan 18 at 0:06
TreborTrebor
81013
$endgroup$
If you have learned the Residue Theorem, you should be able to apply it; calculate the residues at each pole inside the contour.
If not, you can 1) plug in a suitable parameterization of the path, and use brute force to compute the resulting integral (with a real variable), or 2) obtain the indefinite integral away from the pole, it should contain branch cut(s), and your integral can be obtained by monodromy.
answered Jan 18 at 0:06
TreborTrebor
81013
answered Jan 18 at 0:06
TreborTrebor
81013
answered Jan 18 at 0:06
TreborTrebor
81013
answered Jan 18 at 0:06
TreborTrebor
81013
81013
add a comment |
add a comment |
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$begingroup$
Do you know the residue theorem?
$endgroup$
– 0x539
Jan 17 at 22:46
1
$begingroup$
Where are the poles of your function located at? Which ones are located within your contour? Can you calculate the residue at each?
$endgroup$
– Brevan Ellefsen
Jan 17 at 22:56