# conformal maps

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## 1—10 of 15 matching pages

##### 1: 4.3 Graphics
###### §4.3(ii) Complex Arguments: ConformalMaps
Figure 4.3.2 illustrates the conformal mapping of the strip $-\pi<\Im z<\pi$ onto the whole $w$-plane cut along the negative real axis, where $w=e^{z}$ and $z=\ln w$ (principal value). … Figure 4.3.2: Conformal mapping of exponential and logarithm. … Magnify
##### 3: 16.23 Mathematical Applications
###### §16.23(iii) ConformalMapping
The Bieberbach conjecture states that if $\sum_{n=0}^{\infty}a_{n}z^{n}$ is a conformal map of the unit disk to any complex domain, then $|a_{n}|\leq n|a_{1}|$. …
##### 4: 19.32 Conformal Map onto a Rectangle
###### §19.32 ConformalMap onto a Rectangle
For further connections between elliptic integrals and conformal maps, see Bowman (1953, pp. 44–85).
##### 5: 4.29 Graphics
###### §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). …
##### 6: 4.15 Graphics
###### §4.15(ii) Complex Arguments: ConformalMaps
Figure 4.15.7 illustrates the conformal mapping of the strip $-\tfrac{1}{2}\pi<\Re z<\tfrac{1}{2}\pi$ onto the whole $w$-plane cut along the real axis from $-\infty$ to $-1$ and $1$ to $\infty$, where $w=\sin z$ and $z=\operatorname{arcsin}w$ (principal value). … Figure 4.15.7: Conformal mapping of sine and inverse sine. … Magnify
##### 7: 23.20 Mathematical Applications
###### §23.20(i) ConformalMappings
For examples of conformal mappings of the function $\wp\left(z\right)$, see Abramowitz and Stegun (1964, pp. 642–648, 654–655, and 659–60). For conformal mappings via modular functions see Apostol (1990, §2.7). …
##### 8: 22.18 Mathematical Applications
###### §22.18(ii) ConformalMapping
With $k\in[0,1]$ the mapping $z\to w=\operatorname{sn}\left(z,k\right)$ gives a conformal map of the closed rectangle $[-K,K]\times[0,K^{\prime}]$ onto the half-plane $\Im w\geq 0$, with $0,\pm K,\pm K+iK^{\prime},iK^{\prime}$ mapping to $0,\pm 1,\pm k^{-2},\infty$ respectively. …Bowman (1953, Chapters V–VI) gives an overview of the use of Jacobian elliptic functions in conformal maps for engineering applications. …
##### 9: 29.18 Mathematical Applications
###### §29.18(iv) Other Applications
Triebel (1965) gives applications of Lamé functions to the theory of conformal mappings. …
##### 10: Bibliography H
• P. Henrici (1974) Applied and Computational Complex Analysis. Vol. 1: Power Series—Integration—Conformal Mapping—Location of Zeros. Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York.
• P. Henrici (1986) Applied and Computational Complex Analysis. Vol. 3: Discrete Fourier Analysis—Cauchy Integrals—Construction of Conformal Maps—Univalent Functions. Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons Inc.], New York.