List questions from contour-integration

Published on 09 Nov 2015 - 7:44

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2 ways for $\int_{|z|=r} x^2dz$

Published on 10 Nov 2015 - 18:28

709

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Complex Integral Over an Ellipse

Published on 11 Nov 2015 - 14:56

1.5k

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Complex Laurent Series and Contour Integral

Published on 31 Mar 2026 - 8:07

315

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Integrate: $\int_0^{2\pi} \frac{d\theta}{1+\cos^2\theta}$

Published on 03 Apr 2026 - 17:32

361

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Schwarz Function of an Ellipse

Published on 13 Nov 2015 - 0:56

393

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Show $\frac {1}{2\pi i}\int_\gamma\frac {f'(z)}{f(z)}$ is sum of poles and zeroes times their order

Published on 28 Mar 2026 - 12:15

388

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Determine the complex contour integral $\oint \limits_{C} \frac{2}{z^3+z}dz$ without using Residue Theorems

Published on 18 Mar 2026 - 23:56

920

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Evaluate improper integral $\int_0^\infty \frac{x\sin x}{x^2+1}dx$

Published on 16 Nov 2015 - 12:14

133

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Computing the integral using cauchy's theorem

Published on 17 Nov 2015 - 3:51

47

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Limit of contour integrals over semi-circles

Published on 17 Nov 2015 - 8:48

726

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Show $\int_{0}^{\infty} \frac{x^{-z}}{(1 + x)^{2}} ~ \mathrm{d}{x} = \frac{\pi z}{sin(\pi z)}$

Published on 04 Apr 2026 - 3:57

419

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Show that $\int_{0}^{+\infty} \frac{\sin(x)}{x(x^2+1)} dx = \frac{\pi}{2}\left(1-\frac{1}{e}\right) $

Published on 03 Apr 2026 - 19:03

324

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Application of Green's Theorem leading to different solutions of area integral

Published on 19 Nov 2015 - 11:47

3.2k

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Calculating convolution integral analytically

Published on 31 Mar 2026 - 12:10

List Question

An inequality from complex contour integral on page 81 of Stein and Shakarchi's Complex Analysis

2 ways for $\int_{|z|=r} x^2dz$

Complex Integral Over an Ellipse

Complex Laurent Series and Contour Integral

Integrate: $\int_0^{2\pi} \frac{d\theta}{1+\cos^2\theta}$

Schwarz Function of an Ellipse

Show $\frac {1}{2\pi i}\int_\gamma\frac {f'(z)}{f(z)}$ is sum of poles and zeroes times their order

Determine the complex contour integral $\oint \limits_{C} \frac{2}{z^3+z}dz$ without using Residue Theorems

Evaluate improper integral $\int_0^\infty \frac{x\sin x}{x^2+1}dx$

Computing the integral using cauchy's theorem

Limit of contour integrals over semi-circles

Show $\int_{0}^{\infty} \frac{x^{-z}}{(1 + x)^{2}} ~ \mathrm{d}{x} = \frac{\pi z}{sin(\pi z)}$

Show that $\int_{0}^{+\infty} \frac{\sin(x)}{x(x^2+1)} dx = \frac{\pi}{2}\left(1-\frac{1}{e}\right) $

Application of Green's Theorem leading to different solutions of area integral

Calculating convolution integral analytically

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