Question

Computing the contour integral of a complex function

score 211 · Answer 1 · 2017-10-20 11:11:32

211

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Computing the contour integral of a complex function

Published on 20 Oct 2017 - 11:11

score 233 · Answer 2 · 2017-10-22 18:36:19

233

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Primitive existence of a rational function outside disk containing its poles

Published on 22 Oct 2017 - 18:36

score 669 · Answer 3 · 2017-10-25 08:10:50

669

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Cauchy integral theorem involving branch cut

Published on 25 Oct 2017 - 8:10

score 48 · Answer 4 · 2017-10-30 19:15:57

48

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What steps do we usually perform to calculate integrals using Cauchy's theorem?

Published on 30 Oct 2017 - 19:15

score 58 · Answer 5 · 2017-10-31 01:45:27

58

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Integral involving Cauchy Int Formula

Published on 31 Oct 2017 - 1:45

score 73 · Answer 6 · 2017-10-31 04:12:03

73

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Satisfying the Cauchy-Riemann theorem

Published on 31 Oct 2017 - 4:12

score 93 · Answer 7 · 2017-11-01 04:21:02

93

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$f = u+iv$ holomorphic on $D(0, 1)$ and $f(0)=0$, prove $\int_{0}^{2\pi}u(e^{it})^{4}dt \leq 36\int_{0}^{2\pi}v(e^{it})^{4}dt$

Published on 01 Nov 2017 - 4:21

score 537 · Answer 8 · 2017-11-03 09:28:04

537

Views

A question about the inhomogeneous Cauchy-Riemann equations

Published on 03 Nov 2017 - 9:28

score 4.5k · Answer 9 · 2017-11-04 03:22:59

4.5k

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Evaluate: $\int_{\mathcal{C}}\frac{1}{z^3(z+4)}dz$

Published on 04 Nov 2017 - 3:22

score 113 · Answer 10 · 2017-11-05 02:12:35

113

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With the local Cauchy Integral formula find $\int_{|z-2|=2}\frac{\tan^{-1}(z)}{z^2-1}dz$ and $\int_{|z|=2}\frac{e^z}{(z+1)^2}dz$.

Published on 05 Nov 2017 - 2:12

score 66 · Answer 11 · 2017-11-05 02:46:56

66

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Let $\gamma=[-1, 1+i]+\beta+[-1+i,1]$, where $\beta(t)=i+e^{it}$ for $0\leq t\leq 3\pi.$ Compute: $\int_{\gamma}(z^2+1)^{-1}dz$

Published on 05 Nov 2017 - 2:46

score 88 · Answer 12 · 2017-11-06 22:42:34

88

Views

Evaluating $\int ^{2\pi} _{0} e^{-it} e^{( e^{it})} dt $

Published on 06 Nov 2017 - 22:42

score 551 · Answer 13 · 2017-11-07 02:37:57

551

Views

Let $\sum_{n=-\infty}^{\infty}a_{n}(z+1)^n$ be the laurent's series expansion of $f(z)=\sin(\frac{z}{z+1})$. Then $a_{-2}$ is

Published on 07 Nov 2017 - 2:37

score 2.2k · Answer 14 · 2017-11-07 20:40:19

2.2k

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$\int _{C} (z^3 + 2z +{\bf Re} z)\,dz$ where C is a triangle of vertices $z=0$, $z=1+2i $ and $z=1$.

Published on 07 Nov 2017 - 20:40

score 117 · Answer 15 · 2017-11-07 22:03:22

117

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Compute $ \int _{|z|=1} z^{-1+i} dz$ using the branch of log defined in {${z:0 <\arg (z) < 2\pi}$}

Published on 07 Nov 2017 - 22:03

List Question

Computing the contour integral of a complex function

Primitive existence of a rational function outside disk containing its poles

Cauchy integral theorem involving branch cut

What steps do we usually perform to calculate integrals using Cauchy's theorem?

Integral involving Cauchy Int Formula

Satisfying the Cauchy-Riemann theorem

$f = u+iv$ holomorphic on $D(0, 1)$ and $f(0)=0$, prove $\int_{0}^{2\pi}u(e^{it})^{4}dt \leq 36\int_{0}^{2\pi}v(e^{it})^{4}dt$

A question about the inhomogeneous Cauchy-Riemann equations

Evaluate: $\int_{\mathcal{C}}\frac{1}{z^3(z+4)}dz$

With the local Cauchy Integral formula find $\int_{|z-2|=2}\frac{\tan^{-1}(z)}{z^2-1}dz$ and $\int_{|z|=2}\frac{e^z}{(z+1)^2}dz$.

Let $\gamma=[-1, 1+i]+\beta+[-1+i,1]$, where $\beta(t)=i+e^{it}$ for $0\leq t\leq 3\pi.$ Compute: $\int_{\gamma}(z^2+1)^{-1}dz$

Evaluating $\int ^{2\pi} _{0} e^{-it} e^{( e^{it})} dt $

Let $\sum_{n=-\infty}^{\infty}a_{n}(z+1)^n$ be the laurent's series expansion of $f(z)=\sin(\frac{z}{z+1})$. Then $a_{-2}$ is

$\int _{C} (z^3 + 2z +{\bf Re} z)\,dz$ where C is a triangle of vertices $z=0$, $z=1+2i $ and $z=1$.

Compute $ \int _{|z|=1} z^{-1+i} dz$ using the branch of log defined in {${z:0 <\arg (z) < 2\pi}$}

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