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11: Transformaciones conformes

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    En este tema veremos la noción geométrica de los mapas conformes. Resulta que las funciones analíticas son conformes automáticamente. Una vez entendida la noción general, veremos una familia específica de mapas conformales llamados transformaciones lineales fraccionarias y, en particular, sus propiedades geométricas. Como aplicación utilizaremos transformaciones lineales fraccionarias para resolver el problema de Dirichlet para funciones armónicas en el disco de la unidad con valores especificados en el círculo unitario. Al final volveremos a algunas preguntas de flujo de fluidos.

    Miniatura: Una cuadrícula rectangular bajo un mapa conforme. Se observa que mapea pares de líneas que se cruzan a 90° con pares de curvas que aún se cruzan a 90°. (Dominio público; Oleg Alexandrov vía Wikipedia)


    This page titled 11: Transformaciones conformes is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Jeremy Orloff (MIT OpenCourseWare) via source content that was edited to the style and standards of the LibreTexts platform.