Question

Definition of the Complex Derivative and Cauchy Riemann Equations

score 28 · Answer 1 · 2023-11-01 23:23:38

28

Views

Definition of the Complex Derivative and Cauchy Riemann Equations

Published on 01 Nov 2023 - 23:23

score 55 · Answer 2 · 2023-11-15 01:35:01

55

Views

How do you explain the following equations geometrically?

Published on 15 Nov 2023 - 1:35

score 71 · Answer 3 · 2023-11-19 01:36:05

71

Views

Where's $\dfrac{\sinh(\sin z)}{z^2+9}$ analytic?

Published on 19 Nov 2023 - 1:36

score 70 · Answer 4 · 2023-11-26 17:11:14

70

Views

Equivalence of Cauchy-Riemann equations

Published on 26 Nov 2023 - 17:11

score 61 · Answer 5 · 2023-11-28 19:02:37

61

Views

Find parameters such that $f(z)=\log(x^2+y^2)-a(\arg z)^2+ib\arg\bar z+\dfrac{c}{\bar z}$ is analytic

Published on 28 Nov 2023 - 19:02

score 81 · Answer 6 · 2023-12-04 17:26:17

81

Views

Find $f(z)=u+iv$ if $u=\frac{e^x( (x^2-y^2)\cos y+ 2xy\sin y)}{(x^2+y^2)^2}$

Published on 04 Dec 2023 - 17:26

score 26 · Answer 7 · 2023-12-13 11:52:33

26

Views

Determine all holomorphic functions $f :\mathbb{C} → \mathbb{C}$ with $Re(f(z))) = x^2 + axy + by^2$ for $x = Re(z), y = Im(z)$.

Published on 13 Dec 2023 - 11:52

score 91 · Answer 8 · 2023-12-26 12:44:28

91

Views

How do I show that the Cauchy-Riemann Equations hold for any polynomial?

Published on 26 Dec 2023 - 12:44

score 64 · Answer 9 · 2023-12-30 14:05:58

64

Views

To find the constants of a function which is analytic

Published on 30 Dec 2023 - 14:05

score 65 · Answer 10 · 2023-12-30 15:06:16

65

Views

Finding real constants of the function which are analytic

Published on 30 Dec 2023 - 15:06

score 52 · Answer 11 · 2024-01-29 22:10:58

52

Views

Confusions about proof of Cauchy-Riemann equations for $r$ and $\theta$

Published on 29 Jan 2024 - 22:10

score 94 · Answer 12 · 2024-03-24 21:12:17

94

Views

Derivative notation in section 1.2 of Stein-Shakarchi's Complex Analysis

Published on 24 Mar 2024 - 21:12

score 40 · Answer 13 · 2024-03-26 16:30:16

40

Views

$f(x + iy) = u(x,y) + iv(x,y)$ holomorphic implies that $F(x,y) = (u(x,y), v(x,y))$ is differentiable

Published on 26 Mar 2024 - 16:30

score 33 · Answer 14 · 2026-03-25 07:47:53

33

Views

Does anyone know how to demonstrate that the stereographic projection is antiholomorphic?

Published on 25 Mar 2026 - 7:47

score 399 · Answer 15 · 2015-01-08 23:24:44

399

Views

Cauchy-Riemann contradiction?

Published on 08 Jan 2015 - 23:24

List Question

Definition of the Complex Derivative and Cauchy Riemann Equations

How do you explain the following equations geometrically?

Where's $\dfrac{\sinh(\sin z)}{z^2+9}$ analytic?

Equivalence of Cauchy-Riemann equations

Find parameters such that $f(z)=\log(x^2+y^2)-a(\arg z)^2+ib\arg\bar z+\dfrac{c}{\bar z}$ is analytic

Find $f(z)=u+iv$ if $u=\frac{e^x( (x^2-y^2)\cos y+ 2xy\sin y)}{(x^2+y^2)^2}$

Determine all holomorphic functions $f :\mathbb{C} → \mathbb{C}$ with $Re(f(z))) = x^2 + axy + by^2$ for $x = Re(z), y = Im(z)$.

How do I show that the Cauchy-Riemann Equations hold for any polynomial?

To find the constants of a function which is analytic

Finding real constants of the function which are analytic

Confusions about proof of Cauchy-Riemann equations for $r$ and $\theta$

Derivative notation in section 1.2 of Stein-Shakarchi's Complex Analysis

$f(x + iy) = u(x,y) + iv(x,y)$ holomorphic implies that $F(x,y) = (u(x,y), v(x,y))$ is differentiable

Does anyone know how to demonstrate that the stereographic projection is antiholomorphic?

Cauchy-Riemann contradiction?

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