Question

Why is $ I = \int_\Omega \frac{1}{z-\zeta}\Delta u(\zeta) d\zeta = -2i \int_{\partial \Omega} \frac{1}{z-\zeta}\partial u(\zeta) d\zeta. $?

score 61 · Answer 1 · 2018-11-15 08:04:00

61

Views

Why is $ I = \int_\Omega \frac{1}{z-\zeta}\Delta u(\zeta) d\zeta = -2i \int_{\partial \Omega} \frac{1}{z-\zeta}\partial u(\zeta) d\zeta. $?

Published on 15 Nov 2018 - 8:04

score 78 · Answer 2 · 2018-11-16 17:33:24

78

Views

Calculate $\int_CPdx+Qdy$ where $P(x,y)=xe^{-y^2}$ and $Q(x,y)=-x^2ye^{-y^2}+\frac{1}{x^2+y^2+1}$, $C$ is the boundary of the square determined

Published on 16 Nov 2018 - 17:33

score 2.7k · Answer 3 · 2018-11-16 18:30:54

2.7k

Views

Find the work done by the force field $F(x,y)=(x^2+xy)\bar{i}+(xy^2)\bar{j}$ along a path

Published on 16 Nov 2018 - 18:30

score 177 · Answer 4 · 2018-11-16 19:10:15

177

Views

Calculate the line integral on the negatively oriented unit circumference (like the hands of the clock) under the $F(x,y)=(e^x+x^2y,e^y-xy^2)$ field

Published on 16 Nov 2018 - 19:10

score 6.9k · Answer 5 · 2018-11-23 00:01:32

6.9k

Views

Area of a simple closed curve

Published on 23 Nov 2018 - 0:01

score 20 · Answer 6 · 2018-11-28 12:18:08

20

Views

green theorem statement's meaning

Published on 28 Nov 2018 - 12:18

score 284 · Answer 7 · 2018-11-28 16:47:24

284

Views

Verifying Green's theorem for a function

Published on 28 Nov 2018 - 16:47

score 370 · Answer 8 · 2018-12-01 21:19:24

370

Views

Using Green's Theorem to find the flux

Published on 01 Dec 2018 - 21:19

score 103 · Answer 9 · 2018-12-02 12:26:18

103

Views

Trouble calculating line integral using Green's theorem, complicated integral.

Published on 02 Dec 2018 - 12:26

score 94 · Answer 10 · 2018-12-14 02:25:21

94

Views

Show that $F_x(x,y) = P(x,y), \ F_y(x,y) = Q(x,y)$.

Published on 14 Dec 2018 - 2:25

score 94 · Answer 11 · 2018-12-22 18:54:05

94

Views

Line integral in proof of Green's theorem

Published on 22 Dec 2018 - 18:54

score 55 · Answer 12 · 2019-01-04 21:48:11

55

Views

Integral of a differential form along a non-defined path

Published on 04 Jan 2019 - 21:48

score 95 · Answer 13 · 2019-01-07 22:11:57

95

Views

how to calculate $\int_C \frac{2xy^2dx-2yx^2dy}{x^2+y^2}$ using green theorm or directly

Published on 07 Jan 2019 - 22:11

score 165 · Answer 14 · 2019-01-08 14:21:33

165

Views

how to calculate $\int_{C}(2x^2+1)e^{x^2+y^2}dx+(2xy)e^{x^2+y^2}dy$ using Green theorem

Published on 08 Jan 2019 - 14:21

score 47 · Answer 15 · 2019-01-08 15:02:07

47

Views

Finding the maximum value of the integral $\int_{C}x^2y-2y^2-5y{dx} +(2xy-y^2x){dy}$

Published on 08 Jan 2019 - 15:02

List Question

Why is $ I = \int_\Omega \frac{1}{z-\zeta}\Delta u(\zeta) d\zeta = -2i \int_{\partial \Omega} \frac{1}{z-\zeta}\partial u(\zeta) d\zeta. $?

Calculate $\int_CPdx+Qdy$ where $P(x,y)=xe^{-y^2}$ and $Q(x,y)=-x^2ye^{-y^2}+\frac{1}{x^2+y^2+1}$, $C$ is the boundary of the square determined

Find the work done by the force field $F(x,y)=(x^2+xy)\bar{i}+(xy^2)\bar{j}$ along a path

Calculate the line integral on the negatively oriented unit circumference (like the hands of the clock) under the $F(x,y)=(e^x+x^2y,e^y-xy^2)$ field

Area of a simple closed curve

green theorem statement's meaning

Verifying Green's theorem for a function

Using Green's Theorem to find the flux

Trouble calculating line integral using Green's theorem, complicated integral.

Show that $F_x(x,y) = P(x,y), \ F_y(x,y) = Q(x,y)$.

Line integral in proof of Green's theorem

Integral of a differential form along a non-defined path

how to calculate $\int_C \frac{2xy^2dx-2yx^2dy}{x^2+y^2}$ using green theorm or directly

how to calculate $\int_{C}(2x^2+1)e^{x^2+y^2}dx+(2xy)e^{x^2+y^2}dy$ using Green theorem

Finding the maximum value of the integral $\int_{C}x^2y-2y^2-5y{dx} +(2xy-y^2x){dy}$

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