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TFG_Amer_Cerda_MariaDelMar.pdf (1.59 MB)

Document type

Bachelor thesis

Publication date

2025-06-09

Publication license

cc-by-nc-nd (c) Maria del Mar Amer Cerdà, 2025
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/227178

Conformal Mapping and Physical Modelling

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Abstract

This project presents a study of conformal mappings and some of their applications. We emphasize Möbius transformations and their algebraic and geometric properties. These transformations, which preserve angles and the structure of circles, serve as foundational tools in the broader theory of conformal maps. The Schwarz-Christoffel formula is introduced to construct conformal mappings from the upper half-plane to polygonal regions. Applications are explored in two main areas: fluid dynamics, where harmonic and conformal functions model ideal flows, and cartography, where classical projections such as the Mercator and stereographic projections are interpreted through conformal methods. This study demonstrates the powerful interplay between abstract complex analysis and its concrete applications in physics and geometry.

Description

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2025, Director: Xavier Massaneda Clares

Subject

Geometria conforme, Grups de transformacions, Dinàmica de fluids, Geografia matemàtica, Treballs de fi de grau, Maria del Mar Amer Cerdà

Subject (English)

Conformal geometry, Transformation groups, Fluid dynamics, Mathematical geography, Bachelor's theses

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Treballs Finals de Grau (TFG) - Matemàtiques

Citation

AMER CERDÀ, Maria del Mar. Conformal Mapping and Physical Modelling. [consulted: 8 of June of 2026]. Available at: https://hdl.handle.net/2445/227178

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