List questions from rouches-theorem

Published on 29 Dec 2018 - 23:08

71

Views

Finding number of roots to an equation

Published on 20 Jan 2019 - 11:09

424

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Showing that, for $|a|>3$ and $n\geq1$, the function $f(z)=e^z-az^n$ has exactly $n$ roots (all simple and different) in the open unit disc

Published on 21 Jan 2019 - 11:15

398

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Using Rouché's theorem to bound zeroes of partial sums of $e^z$

Published on 23 Jan 2019 - 22:42

354

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Prove that $ze^{\lambda - z} - 1$ has a real root in the unit disk

Published on 29 Mar 2019 - 0:59

434

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Roots of $z \sin(z) =1$

Published on 01 Apr 2019 - 3:11

95

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Solving non-homogeneous system of equations with Rouche Capelli theorem

Published on 03 Apr 2019 - 16:04

77

Views

Confusion in the proof of Rouché's theorem (joint continuity part)

Published on 01 May 2019 - 16:31

285

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Number of zeros of $p(z)=z^5+10z-3$ on annulus $A(0,1,2)$

Published on 08 May 2019 - 17:14

82

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non-existence of a polynomial

Published on 06 Jun 2019 - 21:03

764

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Zeroes of $\sin(z)-z^2$

Published on 14 Jun 2019 - 6:08

396

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Show that $z^5 - z +16$ has two roots in the right half plane

Published on 14 Jun 2019 - 20:42

231

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Inverse statement to Rouché's theorem in complex analysis.

Published on 21 Jun 2019 - 10:06

112

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$Re(\frac{f}{g})\geq 0$ on the boundary of disk implies $f$ and $g$ have same number of zeros in the disk

Published on 24 Jun 2019 - 4:30

59

Views

Bound on constant in Polynomial so that zeros are bounded (Rouche)

Published on 25 Jun 2019 - 13:32

List Question

Rouché's Theorem/Argument Principle Application

Finding number of roots to an equation

Showing that, for $|a|>3$ and $n\geq1$, the function $f(z)=e^z-az^n$ has exactly $n$ roots (all simple and different) in the open unit disc

Using Rouché's theorem to bound zeroes of partial sums of $e^z$

Prove that $ze^{\lambda - z} - 1$ has a real root in the unit disk

Roots of $z \sin(z) =1$

Solving non-homogeneous system of equations with Rouche Capelli theorem

Confusion in the proof of Rouché's theorem (joint continuity part)

Number of zeros of $p(z)=z^5+10z-3$ on annulus $A(0,1,2)$

non-existence of a polynomial

Zeroes of $\sin(z)-z^2$

Show that $z^5 - z +16$ has two roots in the right half plane

Inverse statement to Rouché's theorem in complex analysis.

$Re(\frac{f}{g})\geq 0$ on the boundary of disk implies $f$ and $g$ have same number of zeros in the disk

Bound on constant in Polynomial so that zeros are bounded (Rouche)

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