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Complex line integrals
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Suppose we have an analytic function then Why complex integral of that function does not depend on the path of integration?
complex-analysis contour-integration line-integrals analytic-functions
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robin
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Suppose we have an analytic function then Why complex integral of that function does not depend on the path of integration?
complex-analysis contour-integration line-integrals analytic-functions
asked yesterday
robin
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Read about Cauchy's theorem.
– Richard Martin
yesterday
Because the integral around a closed loop is zero. This follows from Green's theorem in the plane. Look in any book on complex variables.
– saulspatz
yesterday
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up vote
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Suppose we have an analytic function then Why complex integral of that function does not depend on the path of integration?
complex-analysis contour-integration line-integrals analytic-functions
asked yesterday
robin
183
New contributor
robin is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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Suppose we have an analytic function then Why complex integral of that function does not depend on the path of integration?
complex-analysis contour-integration line-integrals analytic-functions
complex-analysis contour-integration line-integrals analytic-functions
asked yesterday
robin
183
New contributor
robin is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
robin
183
New contributor
robin is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
robin
183
New contributor
robin is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
robin
183
asked yesterday
robin
183
183
New contributor
robin is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
robin is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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Read about Cauchy's theorem.
– Richard Martin
yesterday
Because the integral around a closed loop is zero. This follows from Green's theorem in the plane. Look in any book on complex variables.
– saulspatz
yesterday
add a comment |
Read about Cauchy's theorem.
– Richard Martin
yesterday
Because the integral around a closed loop is zero. This follows from Green's theorem in the plane. Look in any book on complex variables.
– saulspatz
yesterday
Read about Cauchy's theorem.
– Richard Martin
yesterday
Read about Cauchy's theorem.
– Richard Martin
yesterday
Because the integral around a closed loop is zero. This follows from Green's theorem in the plane. Look in any book on complex variables.
– saulspatz
yesterday
Because the integral around a closed loop is zero. This follows from Green's theorem in the plane. Look in any book on complex variables.
– saulspatz
yesterday
add a comment |
1 Answer
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In general, the complex integral depends on the path of integration !
Example: $D= mathbb C setminus {0}, f(z)=1/z$ and $c(t)=e^{it}$ with $t in [0, 2m pi i]$ for some $m in mathbb N$.
Then we have $int_c f(z) dz = 2m pi i$.
answered yesterday
Fred
41.9k1642
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
In general, the complex integral depends on the path of integration !
Example: $D= mathbb C setminus {0}, f(z)=1/z$ and $c(t)=e^{it}$ with $t in [0, 2m pi i]$ for some $m in mathbb N$.
Then we have $int_c f(z) dz = 2m pi i$.
answered yesterday
Fred
41.9k1642
add a comment |
up vote
1
down vote
In general, the complex integral depends on the path of integration !
Example: $D= mathbb C setminus {0}, f(z)=1/z$ and $c(t)=e^{it}$ with $t in [0, 2m pi i]$ for some $m in mathbb N$.
Then we have $int_c f(z) dz = 2m pi i$.
answered yesterday
Fred
41.9k1642
add a comment |
up vote
1
down vote
up vote
1
down vote
In general, the complex integral depends on the path of integration !
Example: $D= mathbb C setminus {0}, f(z)=1/z$ and $c(t)=e^{it}$ with $t in [0, 2m pi i]$ for some $m in mathbb N$.
Then we have $int_c f(z) dz = 2m pi i$.
answered yesterday
Fred
41.9k1642
In general, the complex integral depends on the path of integration !
Example: $D= mathbb C setminus {0}, f(z)=1/z$ and $c(t)=e^{it}$ with $t in [0, 2m pi i]$ for some $m in mathbb N$.
Then we have $int_c f(z) dz = 2m pi i$.
answered yesterday
Fred
41.9k1642
answered yesterday
Fred
41.9k1642
answered yesterday
Fred
41.9k1642
answered yesterday
Fred
41.9k1642
41.9k1642
add a comment |
add a comment |
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Read about Cauchy's theorem.
– Richard Martin
yesterday
Because the integral around a closed loop is zero. This follows from Green's theorem in the plane. Look in any book on complex variables.
– saulspatz
yesterday