Question

A continuous function $f$ is analytic everywhere except along a simple closed contour $C$ in domain $D$, then $f$ is analytic everywhere in $D$.

score 693 · Answer 1 · 2020-04-05 10:40:42

A continuous function $f$ is analytic everywhere except along a simple closed contour $C$ in domain $D$, then $f$ is analytic everywhere in $D$.

score 190 · Answer 2 · 2020-04-06 09:09:47

190

Views

Methods to solve $\int _0^{\infty }\frac{x^{\frac{4}{5}}-x^{\frac{2}{3}}}{\ln \left(x\right)\left(x^2+1\right)}\:dx$

Published on 06 Apr 2020 - 9:09

score 97 · Answer 3 · 2020-04-06 12:39:54

97

Views

Evaluate the integral using contour integration

Published on 06 Apr 2020 - 12:39

score 91 · Answer 4 · 2026-03-30 04:00:22

91

Views

Calculate the contour integral of a complex trigonometric function (sinz)

Published on 30 Mar 2026 - 4:00

score 99 · Answer 5 · 2020-04-07 16:39:34

99

Views

Estimating the integral $\int_{- \pi}^\pi e^{i \lambda (x^2 -1)^2} \sin(x)^4$ for large $\lambda$

Published on 07 Apr 2020 - 16:39

score 750 · Answer 6 · 2026-03-30 04:41:55

750

Views

Formula for the area of the interior of a closed contour in the complex plane

Published on 30 Mar 2026 - 4:41

score 150 · Answer 7 · 2026-03-25 15:12:13

150

Views

Calculate the integral $\int_0^{2\pi}\sum_{k=n}^{\infty}\frac{e^{i(k-m)\theta}}{k+1}d\theta$

Published on 25 Mar 2026 - 15:12

score 143 · Answer 8 · 2026-03-30 03:54:04

143

Views

Tricky contours in the method of steepest descent

Published on 30 Mar 2026 - 3:54

score 47 · Answer 9 · 2020-04-09 15:25:08

47

Views

Complex Contour Integral $\int_C e^{5z-1}$

Published on 09 Apr 2020 - 15:25

score 35 · Answer 10 · 2026-03-26 12:08:29

35

Views

Complex Contour Integral $\oint_{C(-i, 1)} \left(\frac 1 {(z+i)^3} - \frac 5 {z+i} +8\right)\,dz$

Published on 26 Mar 2026 - 12:08

score 61 · Answer 11 · 2020-04-10 09:27:03

61

Views

Evaluate an integral using contour integration

Published on 10 Apr 2020 - 9:27

score 259 · Answer 12 · 2020-04-11 14:48:07

259

Views

Contour integral: $ \oint_{C}\frac{e^{\frac{1}{z}}}{z-1}dz $ where $C: |z-1|=\frac{3}{2}$.

Published on 11 Apr 2020 - 14:48

score 56 · Answer 13 · 2026-03-30 05:26:28

56

Views

Definite integral to Contour integral

Published on 30 Mar 2026 - 5:26

score 110 · Answer 14 · 2020-04-12 17:49:19

110

Views

What mistakes were made in evaluating $\int_0^{2\pi}e^{2it}\ln(a^2-2a \cos(t) + 1)dt$

Published on 12 Apr 2020 - 17:49

score 63 · Answer 15 · 2020-04-13 15:33:43

63

Views

Show that $ \lim_{R \rightarrow \infty } \oint_ {|z|=R} \frac{ 2z - 1 }{ z^{3} - 2z^{2} + 3z} = 0$

Published on 13 Apr 2020 - 15:33

List Question

A continuous function $f$ is analytic everywhere except along a simple closed contour $C$ in domain $D$, then $f$ is analytic everywhere in $D$.

Methods to solve $\int _0^{\infty }\frac{x^{\frac{4}{5}}-x^{\frac{2}{3}}}{\ln \left(x\right)\left(x^2+1\right)}\:dx$

Evaluate the integral using contour integration

Calculate the contour integral of a complex trigonometric function (sinz)

Estimating the integral $\int_{- \pi}^\pi e^{i \lambda (x^2 -1)^2} \sin(x)^4$ for large $\lambda$

Formula for the area of the interior of a closed contour in the complex plane

Calculate the integral $\int_0^{2\pi}\sum_{k=n}^{\infty}\frac{e^{i(k-m)\theta}}{k+1}d\theta$

Tricky contours in the method of steepest descent

Complex Contour Integral $\int_C e^{5z-1}$

Complex Contour Integral $\oint_{C(-i, 1)} \left(\frac 1 {(z+i)^3} - \frac 5 {z+i} +8\right)\,dz$

Evaluate an integral using contour integration

Contour integral: $ \oint_{C}\frac{e^{\frac{1}{z}}}{z-1}dz $ where $C: |z-1|=\frac{3}{2}$.

Definite integral to Contour integral

What mistakes were made in evaluating $\int_0^{2\pi}e^{2it}\ln(a^2-2a \cos(t) + 1)dt$

Show that $ \lim_{R \rightarrow \infty } \oint_ {|z|=R} \frac{ 2z - 1 }{ z^{3} - 2z^{2} + 3z} = 0$

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