List questions from complex-integration

Published on 30 Mar 2016 - 8:43

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Find $\oint_\Gamma \frac{\cos z}{z(z^2+8)}dz$ where $\Gamma$ is a positevly oriented unit circle.

Published on 28 Mar 2026 - 2:44

359

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Indefinite integral

Published on 04 Apr 2026 - 6:01

59

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Under which conditions is $\int_\Gamma f=0$

Published on 31 Mar 2016 - 15:05

92

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Prove that $|R(z)| \leq \frac{e-1}{(n+1)!}$ if $|z| \leq 1$ Complex Variables

Published on 03 Apr 2016 - 18:36

847

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Using Cauchy's Integral Formula on a simple closed contour

Published on 28 Mar 2026 - 4:33

92

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Show that the Cauchy principal value of $ \int_{-\infty}^{\infty}\frac{P(x)}{Q(x)}dx$ exists when $\mbox{deg}(Q)=\mbox{deg}(P)+1$.

Published on 04 Apr 2016 - 14:53

933

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Show that Function is Path Dependent

Published on 28 Mar 2026 - 4:32

356

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$M\mathcal{l}$-inequality: Putting a bound on the integrand in $\int_{|z|=R}\frac{f(z)}{(z-a)(z-b)}dz$

Published on 28 Mar 2026 - 4:35

73

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Integration of complex exponential function over $\mathbb C$

Published on 05 Apr 2016 - 4:58

77

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How do I show the following modification of the Counting formula of zeros and poles?

Published on 05 Apr 2016 - 17:07

400

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Showing a complex integral has zero real part

Published on 06 Apr 2016 - 13:13

126

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Calculating a certain Laurent series (two parts)

Published on 31 Mar 2026 - 20:05

32

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Simplifying two complex integrals

Published on 09 Apr 2016 - 1:32

39

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Differentiate $v(x,y)=-\int_0^x u_y(t,0)dt+\int_0^y u_x (x,t) dt$ w.r.t. $x,y$ to prove complex differentiability

Published on 09 Apr 2016 - 16:06

List Question

Fourier transform with branchcuts

Find $\oint_\Gamma \frac{\cos z}{z(z^2+8)}dz$ where $\Gamma$ is a positevly oriented unit circle.

Indefinite integral

Under which conditions is $\int_\Gamma f=0$

Prove that $|R(z)| \leq \frac{e-1}{(n+1)!}$ if $|z| \leq 1$ Complex Variables

Using Cauchy's Integral Formula on a simple closed contour

Show that the Cauchy principal value of $ \int_{-\infty}^{\infty}\frac{P(x)}{Q(x)}dx$ exists when $\mbox{deg}(Q)=\mbox{deg}(P)+1$.

Show that Function is Path Dependent

$M\mathcal{l}$-inequality: Putting a bound on the integrand in $\int_{|z|=R}\frac{f(z)}{(z-a)(z-b)}dz$

Integration of complex exponential function over $\mathbb C$

How do I show the following modification of the Counting formula of zeros and poles?

Showing a complex integral has zero real part

Calculating a certain Laurent series (two parts)

Simplifying two complex integrals

Differentiate $v(x,y)=-\int_0^x u_y(t,0)dt+\int_0^y u_x (x,t) dt$ w.r.t. $x,y$ to prove complex differentiability

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