Massaneda Clares, Francesc XavierAmer Cerdà, Maria del Mar2026-02-202026-02-202025-06-09https://hdl.handle.net/2445/227178Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2025, Director: Xavier Massaneda ClaresThis 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.51 p.application/pdfengcc-by-nc-nd (c) Maria del Mar Amer Cerdà, 2025http://creativecommons.org/licenses/by-nc-nd/3.0/esGeometria conformeGrups de transformacionsDinàmica de fluidsGeografia matemàticaTreballs de fi de grauMaria del Mar Amer CerdàConformal geometryTransformation groupsFluid dynamicsMathematical geographyBachelor's thesesinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess