Question

Proving the polynomial $P_t(z) = \sum_{j=0}^N a_j(t) z^j$ has exactly one zero if $P_0$ has a simple zero with $a_j(t)$ and $P_t(z)$ continuous in $t$

score 135 · Answer 1 · 2022-01-14 15:03:08

135

Views

Proving the polynomial $P_t(z) = \sum_{j=0}^N a_j(t) z^j$ has exactly one zero if $P_0$ has a simple zero with $a_j(t)$ and $P_t(z)$ continuous in $t$

Published on 14 Jan 2022 - 15:03

score 95 · Answer 2 · 2022-01-15 02:03:25

95

Views

Why is only the boundary considered when using Rouche's Theorem?

Published on 15 Jan 2022 - 2:03

score 46 · Answer 3 · 2022-01-29 13:50:26

46

Views

Show that $P(z)=a_kZ^k$ has $n$ zeros in $B(0,1)$.

Published on 29 Jan 2022 - 13:50

score 22 · Answer 4 · 2022-01-30 10:10:44

22

Views

Rouché for positive $n$, but what for negative $n$?

Published on 30 Jan 2022 - 10:10

score 134 · Answer 5 · 2022-02-07 13:41:57

134

Views

How can I show that $z^4-2z+3$ has no zeros within the unit circle in the complex plane?

Published on 07 Feb 2022 - 13:41

score 269 · Answer 6 · 2022-03-31 13:02:46

269

Views

Find out the number of zeroes of $f(z) = e^z -3z -2 =0$ , inside $|z|=1.$

Published on 31 Mar 2022 - 13:02

score 150 · Answer 7 · 2022-04-11 07:27:39

150

Views

$|f(z) - g(z)| < |f(z)|$ vs $|f(z) - g(z)| < |g(z)|$ in Rouche's theorem?

Published on 11 Apr 2022 - 7:27

score 50 · Answer 8 · 2022-05-13 02:17:54

50

Views

Computing the Number of Zeroes using Rouché + Argument Principle

Published on 13 May 2022 - 2:17

score 97 · Answer 9 · 2022-05-17 13:08:47

97

Views

Number of zeros of the complex function in the unit disk

Published on 17 May 2022 - 13:08

score 41 · Answer 10 · 2022-06-06 16:44:31

41

Views

Prove that an equation has only one complex solution

Published on 06 Jun 2022 - 16:44

score 54 · Answer 11 · 2022-06-06 23:21:14

54

Views

number of zeros/rouche's theorem

Published on 06 Jun 2022 - 23:21

score 137 · Answer 12 · 2022-06-16 15:01:55

137

Views

Rouche’s Theorem?

Published on 16 Jun 2022 - 15:01

score 141 · Answer 13 · 2022-06-17 09:00:23

141

Views

Number of zeros inside unit disk

Published on 17 Jun 2022 - 9:00

score 80 · Answer 14 · 2022-06-20 21:19:22

80

Views

Show $2z^5-6z^2+z+1$ has three zeroes in $\{z : 1<\vert z \vert < 2\}$

Published on 20 Jun 2022 - 21:19

score 80 · Answer 15 · 2022-06-21 18:50:09

80

Views

Find number of zeros of $z^{113}-180z^{23}+115z^{7}-32z^2-3z-10$ in annulus $1≤|z|≤2$

Published on 21 Jun 2022 - 18:50

List Question

Proving the polynomial $P_t(z) = \sum_{j=0}^N a_j(t) z^j$ has exactly one zero if $P_0$ has a simple zero with $a_j(t)$ and $P_t(z)$ continuous in $t$

Why is only the boundary considered when using Rouche's Theorem?

Show that $P(z)=a_kZ^k$ has $n$ zeros in $B(0,1)$.

Rouché for positive $n$, but what for negative $n$?

How can I show that $z^4-2z+3$ has no zeros within the unit circle in the complex plane?

Find out the number of zeroes of $f(z) = e^z -3z -2 =0$ , inside $|z|=1.$

$|f(z) - g(z)| < |f(z)|$ vs $|f(z) - g(z)| < |g(z)|$ in Rouche's theorem?

Computing the Number of Zeroes using Rouché + Argument Principle

Number of zeros of the complex function in the unit disk

Prove that an equation has only one complex solution

number of zeros/rouche's theorem

Rouche’s Theorem?

Number of zeros inside unit disk

Show $2z^5-6z^2+z+1$ has three zeroes in $\{z : 1<\vert z \vert < 2\}$

Find number of zeros of $z^{113}-180z^{23}+115z^{7}-32z^2-3z-10$ in annulus $1≤|z|≤2$

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