克拉斯诺亚尔斯克国立师范大学学历认证办理【假证加微aptao168】mAp

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1: 15.17 Mathematical Applications

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§15.17(ii) Conformal Mappings

►The quotient of two solutions of (15.10.1) maps the closed upper half-plane $\mathrm{\Im }z\ge 0$ conformally onto a curvilinear triangle. …Hypergeometric functions, especially complete elliptic integrals, also play an important role in quasiconformal mapping. …

2: About Color Map

About Color Map

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Height Mapping

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Phase Mappings

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Four Color Phase Mapping

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Continuous Phase Mapping

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3: 4.3 Graphics

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§4.3(ii) Complex Arguments: Conformal Maps

►Figure 4.3.2 illustrates the conformal mapping of the strip onto the whole $w$-plane cut along the negative real axis, where $w={\mathrm{e}}^z$ and $z=\ln w$ (principal value). …Lines parallel to the real axis in the $z$-plane map onto rays in the $w$-plane, and lines parallel to the imaginary axis in the $z$-plane map onto circles centered at the origin in the $w$-plane. … ►

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Figure 4.3.2: Conformal mapping of exponential and logarithm. … Magnify

… ►See also About Color Map. …

4: Joyce E. Conlon

… ►From 1980–85 she worked as a computer programmer for the Defense Mapping Agency. …

5: 32.16 Physical Applications

§32.16 Physical Applications

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6: 4.29 Graphics

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§4.29(ii) Complex Arguments

►The conformal mapping $w=\sinh z$ is obtainable from Figure 4.15.7 by rotating both the $w$-plane and the $z$-plane through an angle $\frac{1}{2}\pi$, compare (4.28.8). …

7: 19.32 Conformal Map onto a Rectangle

§19.32 Conformal Map onto a Rectangle

… ►then $z(p)$ is a Schwartz–Christoffel mapping of the open upper-half $p$-plane onto the interior of the rectangle in the $z$-plane with vertices … ►For further connections between elliptic integrals and conformal maps, see Bowman (1953, pp. 44–85).

8: 4.15 Graphics

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§4.15(ii) Complex Arguments: Conformal Maps

►Figure 4.15.7 illustrates the conformal mapping of the strip onto the whole $w$-plane cut along the real axis from $-\mathrm{\infty }$ to $-1$ and $1$ to $\mathrm{\infty }$, where $w=\sin z$ and $z=\arcsin w$ (principal value). …Lines parallel to the real axis in the $z$-plane map onto ellipses in the $w$-plane with foci at $w=\pm 1$, and lines parallel to the imaginary axis in the $z$-plane map onto rectangular hyperbolas confocal with the ellipses. … ►

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Figure 4.15.7: Conformal mapping of sine and inverse sine. … Magnify

… ►See also About Color Map. …

9: 16.23 Mathematical Applications

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§16.23(iii) Conformal Mapping

►The Bieberbach conjecture states that if ${\sum }_{n=0}^{\mathrm{\infty }}{a}_n{z}^n$ is a conformal map of the unit disk to any complex domain, then $|a_n|\le n|a_1|$. …

10: 26.17 The Twelvefold Way

… ►The twelvefold way gives the number of mappings $f$ from set $N$ of $n$ objects to set $K$ of $k$ objects (putting balls from set $N$ into boxes in set $K$). …