### Final Degree Project

 dc.contributor.advisor Freniche Ibáñez, Francisco José es dc.creator Castaño Muñoz, José Carlos es dc.date.accessioned 2018-07-23T09:49:31Z dc.date.available 2018-07-23T09:49:31Z dc.date.issued 2018 dc.identifier.citation Castaño Muñoz, J.C. (2018). El teorema de la función implícita. (Trabajo Fin de Grado Inédito). Universidad de Sevilla, Sevilla. dc.identifier.uri https://hdl.handle.net/11441/77506 dc.description.abstract In this work we study several proofs of the classical implicit function theorem, es which gives sufficient conditions for a vector equation to define a function. The first proof is the most elementary. It is obtained by induction on the number of dependent variables. The second proof is also based on calculus, by looking directly at the linear approximation of the mapping. Finally, Banach fixed point theorem is used in the more abstract functional analytic third proof. In the second part we show an application of the implicit function theorem. We give four different definitions of a smooth surface and prove all of them are equivalent using the range theorem, an important consequence of the implicit function theorem. We finish the work showing an alternative proof of the implicit function theorem using a classical existence theorem of solutions in ordinary differential equations. dc.format application/pdf es dc.language.iso spa es dc.rights Attribution-NonCommercial-NoDerivatives 4.0 Internacional * dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/4.0/ * dc.subject Teorema de la función implícita es dc.title El teorema de la función implícita es dc.type info:eu-repo/semantics/bachelorThesis es dc.type.version info:eu-repo/semantics/publishedVersion es dc.rights.accessRights info:eu-repo/semantics/openAccess es dc.contributor.affiliation Universidad de Sevilla. Departamento de Análisis Matemático es dc.description.degree Universidad de Sevilla. Grado en Matemáticas es idus.format.extent 61 p. es
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