Abstract
Let z(t) = x(t) + ≀y(t), a ≤ t ≤ b, be a path. We suppose throughout this chapter that z′(t) ≠ 0 for all t. Let f be defined in a neighborhood of a point z 0 ∈ ℂ. f is conformal at z 0 if f preserves angles at z 0, for any two paths P 1 and P 2 intersecting at z 0 the angle from P 1 to P 2 at z 0, the angle oriented counterclockwise from the tangent line of P 1 at z 0 to the tangent line of P 2 at z 0, is equal to angle between f(P 1) and f(P 2). The function f is conformal in a region O if it is conformal at all points from O.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Pap, E. (1999). Conformal mappings. In: Complex Analysis through Examples and Exercises. Kluwer Text in the Mathematical Sciences, vol 21. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1106-7_4
Download citation
DOI: https://doi.org/10.1007/978-94-017-1106-7_4
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5253-7
Online ISBN: 978-94-017-1106-7
eBook Packages: Springer Book Archive