CINXE.COM

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id="main" class="site-main" role="main"> <article id="post-137" class="post-137 page type-page status-publish hentry"> <header class="entry-header"> <h1 class="entry-title">Variedades diferenciables 23/24</h1> </header> <div class="entry-content"> <h2>Curso 2023/2024</h2> <h3>Horarios y Aulas</h3> <ul> <li>Lunes, Martes y Jueves: 17:00-18:00 (Teor铆a). Aula B-12.</li> <li>Mi茅rcoles: 17:00-18:00 (Pr谩cticas – Robert Cardona). Aula B-12.</li> </ul> <h3>Informaci贸n General</h3> <ul> <li><strong>Grado:</strong> Matem谩ticas.</li> <li><strong>Curso:</strong> Cuarto.</li> <li><strong>Cuatrimestre:</strong> Primero.</li> <li><strong>Cr茅ditos ECTS:</strong> 6.</li> <li><a class="a_white" href="https://www.ucm.es/estudios/grado-matematicasyestadistica-plan-800631" target="new"><strong>Ficha de la asignatura</strong></a></li> </ul> <h3>Contenido de la Asignatura</h3> <ol type="1"> <li>Variedades diferenciables. Definici贸n de variedad. Construcci贸n de variedades. Particiones diferenciables de la unidad. Variedades con borde.</li> <li>C谩lculo en variedades. Espacio tangente. Derivada de aplicaciones entre variedades. Derivaciones.</li> <li>Campos y ecuaciones diferenciales. Campos y flujos. Integraci贸n de campos. Derivada de Lie y campos coordenados.</li> <li>Formas diferenciales. Aplicaciones multilineales alternadas. Determinantes. Formas en variedades. Diferencial exterior.</li> <li>Integraci贸n en variedades. Orientaci贸n de variedades. Orientaci贸n de hipersuperficies. Aplicaci贸n de Gauss y curvatura. Integral de una forma diferencial. Teorema de Stokes.</li> </ol> <h3>Bibliograf铆a</h3> <ol type="1"> <li>J.M. Gamboa, J. M. Ruiz. Introducci贸n al estudio de las variedades diferenciables. Sanz y Torres, 2016.</li> <li>W. Boothby. An introduction to differentiable manifolds and riemannian geometry, Gulf Professional Publishing, 2003.</li> <li>M. P. do Carmo. Riemannian Geometry, Birkh盲user, 1992.</li> <li>M. Spivak. 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