## Conformal Map

A Transformation which preserves Angles is known as conformal. For a transformation to be conformal, it must be an Analytic Function and have a Nonzero Derivative. Let and be the tangents to the curves and at and ,

 (1)

 (2)

Then as and ,
 (3)

 (4)

References

Arfken, G. Conformal Mapping.'' §6.7 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 392-394, 1985.

Bergman, S. The Kernel Function and Conformal Mapping. New York: Amer. Math. Soc., 1950.

Katznelson, Y. An Introduction to Harmonic Analysis. New York: Dover, 1976.

Morse, P. M. and Feshbach, H. Conformal Mapping.'' §4.7 in Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 358-362 and 443-453, 1953.

Nehari, Z. Conformal Map. New York: Dover, 1982.