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Título : An Introduction to Manifolds Tipo de documento: documento electrónico Autores: Loring W. Tu ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2011 Colección: Universitext, ISSN 0172-5939 Número de páginas: XVIII, 410 p. 124 illus., 1 illus. in color Il.: online resource ISBN/ISSN/DL: 978-1-4419-7400-6 Idioma : Inglés (eng) Palabras clave: Mathematics Global analysis (Mathematics) Manifolds Differential geometry Complex manifolds and Cell Complexes (incl. Diff.Topology) Analysis on Geometry Clasificación: 51 Matemáticas Resumen: Manifolds, the higher-dimensional analogues of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way the reader acquires the knowledge and skills necessary for further study of geometry and topology. The second edition contains fifty pages of new material. Many passages have been rewritten, proofs simplified, and new examples and exercises added. This work may be used as a textbook for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. The requisite point-set topology is included in an appendix of twenty-five pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. Requiring only minimal undergraduate prerequisites, "An Introduction to Manifolds" is also an excellent foundation for the author's publication with Raoul Bott, "Differential Forms in Algebraic Topology." Nota de contenido: Preface to the Second Edition -- Preface to the First Edition -- Chapter 1. Euclidean Spaces -- Chapter 2. Manifolds -- Chapter 3. The Tangent Space -- Chapter 4. Lie Groups and Lie Algebras.-Chapter 5. Differential Forms -- Chapter 6. Integration.-Chapter 7. De Rham Theory -- Appendices -- A. Point-Set Topology -- B. The Inverse Function Theorem on R(N) and Related Results -- C. Existence of a Partition of Unity in General -- D. Linear Algebra -- E. Quaternions and the Symplectic Group -- Solutions to Selected Exercises -- Hints and Solutions to Selected End-of-Section Problems -- List of Symbols -- References -- Index En línea: http://dx.doi.org/10.1007/978-1-4419-7400-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33161 An Introduction to Manifolds [documento electrónico] / Loring W. Tu ; SpringerLink (Online service) . - New York, NY : Springer New York, 2011 . - XVIII, 410 p. 124 illus., 1 illus. in color : online resource. - (Universitext, ISSN 0172-5939) .
ISBN : 978-1-4419-7400-6
Idioma : Inglés (eng)
Palabras clave: Mathematics Global analysis (Mathematics) Manifolds Differential geometry Complex manifolds and Cell Complexes (incl. Diff.Topology) Analysis on Geometry Clasificación: 51 Matemáticas Resumen: Manifolds, the higher-dimensional analogues of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way the reader acquires the knowledge and skills necessary for further study of geometry and topology. The second edition contains fifty pages of new material. Many passages have been rewritten, proofs simplified, and new examples and exercises added. This work may be used as a textbook for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. The requisite point-set topology is included in an appendix of twenty-five pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. Requiring only minimal undergraduate prerequisites, "An Introduction to Manifolds" is also an excellent foundation for the author's publication with Raoul Bott, "Differential Forms in Algebraic Topology." Nota de contenido: Preface to the Second Edition -- Preface to the First Edition -- Chapter 1. Euclidean Spaces -- Chapter 2. Manifolds -- Chapter 3. The Tangent Space -- Chapter 4. Lie Groups and Lie Algebras.-Chapter 5. Differential Forms -- Chapter 6. Integration.-Chapter 7. De Rham Theory -- Appendices -- A. Point-Set Topology -- B. The Inverse Function Theorem on R(N) and Related Results -- C. Existence of a Partition of Unity in General -- D. Linear Algebra -- E. Quaternions and the Symplectic Group -- Solutions to Selected Exercises -- Hints and Solutions to Selected End-of-Section Problems -- List of Symbols -- References -- Index En línea: http://dx.doi.org/10.1007/978-1-4419-7400-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33161 Ejemplares
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Título : An Introduction to Manifolds Tipo de documento: documento electrónico Autores: Loring W. Tu ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2008 Colección: Universitext, ISSN 0172-5939 Número de páginas: XVI, 368 p. 104 illus Il.: online resource ISBN/ISSN/DL: 978-0-387-48101-2 Idioma : Inglés (eng) Palabras clave: Mathematics Global analysis (Mathematics) Manifolds Differential geometry Complex manifolds and Cell Complexes (incl. Diff.Topology) Analysis on Geometry Clasificación: 51 Matemáticas Resumen: Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, An Introduction to Manifolds is also an excellent foundation for Springer GTM 82, Differential Forms in Algebraic Topology. Nota de contenido: Euclidean Spaces -- Smooth Functions on a Euclidean Space -- Tangent Vectors in Rn as Derivations -- Alternating k-Linear Functions -- Differential Forms on Rn -- Manifolds -- Manifolds -- Smooth Maps on a Manifold -- Quotients -- Lie Groups and Lie Algebras -- The Tangent Space -- Submanifolds -- Categories and Functors -- The Rank of a Smooth Map -- The Tangent Bundle -- Bump Functions and Partitions of Unity -- Vector Fields -- Lie Groups and Lie Algebras -- Lie Groups -- Lie Algebras -- Differential Forms -- Differential 1-Forms -- Differential k-Forms -- The Exterior Derivative -- Integration -- Orientations -- Manifolds with Boundary -- Integration on a Manifold -- De Rham Theory -- De Rham Cohomology -- The Long Exact Sequence in Cohomology -- The Mayer–Vietoris Sequence -- Homotopy Invariance -- Computation of de Rham Cohomology -- Proof of Homotopy Invariance En línea: http://dx.doi.org/10.1007/978-0-387-48101-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34148 An Introduction to Manifolds [documento electrónico] / Loring W. Tu ; SpringerLink (Online service) . - New York, NY : Springer New York, 2008 . - XVI, 368 p. 104 illus : online resource. - (Universitext, ISSN 0172-5939) .
ISBN : 978-0-387-48101-2
Idioma : Inglés (eng)
Palabras clave: Mathematics Global analysis (Mathematics) Manifolds Differential geometry Complex manifolds and Cell Complexes (incl. Diff.Topology) Analysis on Geometry Clasificación: 51 Matemáticas Resumen: Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, An Introduction to Manifolds is also an excellent foundation for Springer GTM 82, Differential Forms in Algebraic Topology. Nota de contenido: Euclidean Spaces -- Smooth Functions on a Euclidean Space -- Tangent Vectors in Rn as Derivations -- Alternating k-Linear Functions -- Differential Forms on Rn -- Manifolds -- Manifolds -- Smooth Maps on a Manifold -- Quotients -- Lie Groups and Lie Algebras -- The Tangent Space -- Submanifolds -- Categories and Functors -- The Rank of a Smooth Map -- The Tangent Bundle -- Bump Functions and Partitions of Unity -- Vector Fields -- Lie Groups and Lie Algebras -- Lie Groups -- Lie Algebras -- Differential Forms -- Differential 1-Forms -- Differential k-Forms -- The Exterior Derivative -- Integration -- Orientations -- Manifolds with Boundary -- Integration on a Manifold -- De Rham Theory -- De Rham Cohomology -- The Long Exact Sequence in Cohomology -- The Mayer–Vietoris Sequence -- Homotopy Invariance -- Computation of de Rham Cohomology -- Proof of Homotopy Invariance En línea: http://dx.doi.org/10.1007/978-0-387-48101-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34148 Ejemplares
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Título : Differential Analysis on Complex Manifolds Tipo de documento: documento electrónico Autores: Raymond O. Wells ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2008 Colección: Graduate Texts in Mathematics, ISSN 0072-5285 num. 65 Número de páginas: XIV, 304 p Il.: online resource ISBN/ISSN/DL: 978-0-387-73892-5 Idioma : Inglés (eng) Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Global Manifolds and on Clasificación: 51 Matemáticas Resumen: In developing the tools necessary for the study of complex manifolds, this comprehensive, well-organized treatment presents in its opening chapters a detailed survey of recent progress in four areas: geometry (manifolds with vector bundles), algebraic topology, differential geometry, and partial differential equations. Subsequent chapters then develop such topics as Hermitian exterior algebra and the Hodge *-operator, harmonic theory on compact manifolds, differential operators on a Kahler manifold, the Hodge decomposition theorem on compact Kahler manifolds, the Hodge-Riemann bilinear relations on Kahler manifolds, Griffiths's period mapping, quadratic transformations, and Kodaira's vanishing and embedding theorems. The third edition of this standard reference contains a new appendix by Oscar Garcia-Prada which gives an overview of certain developments in the field during the decades since the book first appeared. From reviews of the 2nd Edition: "..the new edition of Professor Wells' book is timely and welcome...an excellent introduction for any mathematician who suspects that complex manifold techniques may be relevant to his work." - Nigel Hitchin, Bulletin of the London Mathematical Society "Its purpose is to present the basics of analysis and geometry on compact complex manifolds, and is already one of the standard sources for this material." - Daniel M. Burns, Jr., Mathematical Reviews Nota de contenido: Manifolds and Vector Bundles -- Sheaf Theory -- Differential Geometry -- Elliptic Operator Theory -- Compact Complex Manifolds -- Kodaira's Projective Embedding Theorem En línea: http://dx.doi.org/10.1007/978-0-387-73892-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34186 Differential Analysis on Complex Manifolds [documento electrónico] / Raymond O. Wells ; SpringerLink (Online service) . - New York, NY : Springer New York, 2008 . - XIV, 304 p : online resource. - (Graduate Texts in Mathematics, ISSN 0072-5285; 65) .
ISBN : 978-0-387-73892-5
Idioma : Inglés (eng)
Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Global Manifolds and on Clasificación: 51 Matemáticas Resumen: In developing the tools necessary for the study of complex manifolds, this comprehensive, well-organized treatment presents in its opening chapters a detailed survey of recent progress in four areas: geometry (manifolds with vector bundles), algebraic topology, differential geometry, and partial differential equations. Subsequent chapters then develop such topics as Hermitian exterior algebra and the Hodge *-operator, harmonic theory on compact manifolds, differential operators on a Kahler manifold, the Hodge decomposition theorem on compact Kahler manifolds, the Hodge-Riemann bilinear relations on Kahler manifolds, Griffiths's period mapping, quadratic transformations, and Kodaira's vanishing and embedding theorems. The third edition of this standard reference contains a new appendix by Oscar Garcia-Prada which gives an overview of certain developments in the field during the decades since the book first appeared. From reviews of the 2nd Edition: "..the new edition of Professor Wells' book is timely and welcome...an excellent introduction for any mathematician who suspects that complex manifold techniques may be relevant to his work." - Nigel Hitchin, Bulletin of the London Mathematical Society "Its purpose is to present the basics of analysis and geometry on compact complex manifolds, and is already one of the standard sources for this material." - Daniel M. Burns, Jr., Mathematical Reviews Nota de contenido: Manifolds and Vector Bundles -- Sheaf Theory -- Differential Geometry -- Elliptic Operator Theory -- Compact Complex Manifolds -- Kodaira's Projective Embedding Theorem En línea: http://dx.doi.org/10.1007/978-0-387-73892-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34186 Ejemplares
Signatura Medio Ubicación Sub-localización Sección Estado ningún ejemplar Complex, Contact and Symmetric Manifolds / SpringerLink (Online service) ; Oldrich Kowalski ; Emilio Musso ; Domenico Perrone (2005)
Título : Complex, Contact and Symmetric Manifolds : In Honor of L. Vanhecke Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Oldrich Kowalski ; Emilio Musso ; Domenico Perrone Editorial: Boston, MA : Birkhäuser Boston Fecha de publicación: 2005 Colección: Progress in Mathematics num. 234 Número de páginas: X, 278 p Il.: online resource ISBN/ISSN/DL: 978-0-8176-4424-6 Idioma : Inglés (eng) Palabras clave: Mathematics Topological groups Lie Global analysis (Mathematics) Manifolds Geometry Differential geometry Algebraic topology Complex manifolds Analysis and on Groups, Groups Topology Cell Complexes (incl. Diff.Topology) Clasificación: 51 Matemáticas Resumen: This volume contains research and survey articles by well known and respected mathematicians on differential geometry and topology that have been collected and dedicated in honor of Lieven Vanhecke, as a tribute to his many fruitful and inspiring contributions to these fields. The papers, all written with the necessary introductory and contextual material, describe recent developments and research trends in spectral geometry, the theory of geodesics and curvature, contact and symplectic geometry, complex geometry, algebraic topology, homogeneous and symmetric spaces, and various applications of partial differential equations and differential systems to geometry. One of the key strengths of these articles is their appeal to non-specialists, as well as researchers and differential geometers. Contributors: D.E. Blair; E. Boeckx; A.A. Borisenko; G. Calvaruso; V. Cortés; P. de Bartolomeis; J.C. Díaz-Ramos; M. Djoric; C. Dunn; M. Fernández; A. Fujiki; E. García-Río; P.B. Gilkey; O. Gil-Medrano; L. Hervella; O. Kowalski; V. Muñoz; M. Pontecorvo; A.M. Naveira; T. Oguro; L. Schäfer; K. Sekigawa; C-L. Terng; K. Tsukada; Z. Vlášek; E. Wang; and J.A. Wolf Nota de contenido: Curvature of Contact Metric Manifolds -- A Case for Curvature: the Unit Tangent Bundle -- Convex Hypersurfaces in Hadamard Manifolds -- Contact Metric Geometry of the Unit Tangent Sphere Bundle -- Topological-antitopological Fusion Equations, Pluriharmonic Maps and Special Kähler Manifolds -- ?2 and ?-Deformation Theory for Holomorphic and Symplectic Manifolds -- Commutative Condition on the Second Fundamental Form of CR-submanifolds of Maximal CR-dimension of a Kähler Manifold -- The Geography of Non-Formal Manifolds -- Total Scalar Curvatures of Geodesic Spheres and of Boundaries of Geodesic Disks -- Curvature Homogeneous Pseudo-Riemannian Manifolds which are not Locally Homogeneous -- On Hermitian Geometry of Complex Surfaces -- Unit Vector Fields that are Critical Points of the Volume and of the Energy: Characterization and Examples -- On 3D-Riemannian Manifolds with Prescribed Ricci Eigenvalues -- Two Problems in Real and Complex Integral Geometry -- Notes on the Goldberg Conjecture in Dimension Four -- Curved Flats, Exterior Differential Systems, and Conservation Laws -- Symmetric Submanifolds of Riemannian Symmetric Spaces and Symmetric R-spaces -- Complex Forms of Quaternionic Symmetric Spaces En línea: http://dx.doi.org/10.1007/b138831 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35181 Complex, Contact and Symmetric Manifolds : In Honor of L. Vanhecke [documento electrónico] / SpringerLink (Online service) ; Oldrich Kowalski ; Emilio Musso ; Domenico Perrone . - Boston, MA : Birkhäuser Boston, 2005 . - X, 278 p : online resource. - (Progress in Mathematics; 234) .
ISBN : 978-0-8176-4424-6
Idioma : Inglés (eng)
Palabras clave: Mathematics Topological groups Lie Global analysis (Mathematics) Manifolds Geometry Differential geometry Algebraic topology Complex manifolds Analysis and on Groups, Groups Topology Cell Complexes (incl. Diff.Topology) Clasificación: 51 Matemáticas Resumen: This volume contains research and survey articles by well known and respected mathematicians on differential geometry and topology that have been collected and dedicated in honor of Lieven Vanhecke, as a tribute to his many fruitful and inspiring contributions to these fields. The papers, all written with the necessary introductory and contextual material, describe recent developments and research trends in spectral geometry, the theory of geodesics and curvature, contact and symplectic geometry, complex geometry, algebraic topology, homogeneous and symmetric spaces, and various applications of partial differential equations and differential systems to geometry. One of the key strengths of these articles is their appeal to non-specialists, as well as researchers and differential geometers. Contributors: D.E. Blair; E. Boeckx; A.A. Borisenko; G. Calvaruso; V. Cortés; P. de Bartolomeis; J.C. Díaz-Ramos; M. Djoric; C. Dunn; M. Fernández; A. Fujiki; E. García-Río; P.B. Gilkey; O. Gil-Medrano; L. Hervella; O. Kowalski; V. Muñoz; M. Pontecorvo; A.M. Naveira; T. Oguro; L. Schäfer; K. Sekigawa; C-L. Terng; K. Tsukada; Z. Vlášek; E. Wang; and J.A. Wolf Nota de contenido: Curvature of Contact Metric Manifolds -- A Case for Curvature: the Unit Tangent Bundle -- Convex Hypersurfaces in Hadamard Manifolds -- Contact Metric Geometry of the Unit Tangent Sphere Bundle -- Topological-antitopological Fusion Equations, Pluriharmonic Maps and Special Kähler Manifolds -- ?2 and ?-Deformation Theory for Holomorphic and Symplectic Manifolds -- Commutative Condition on the Second Fundamental Form of CR-submanifolds of Maximal CR-dimension of a Kähler Manifold -- The Geography of Non-Formal Manifolds -- Total Scalar Curvatures of Geodesic Spheres and of Boundaries of Geodesic Disks -- Curvature Homogeneous Pseudo-Riemannian Manifolds which are not Locally Homogeneous -- On Hermitian Geometry of Complex Surfaces -- Unit Vector Fields that are Critical Points of the Volume and of the Energy: Characterization and Examples -- On 3D-Riemannian Manifolds with Prescribed Ricci Eigenvalues -- Two Problems in Real and Complex Integral Geometry -- Notes on the Goldberg Conjecture in Dimension Four -- Curved Flats, Exterior Differential Systems, and Conservation Laws -- Symmetric Submanifolds of Riemannian Symmetric Spaces and Symmetric R-spaces -- Complex Forms of Quaternionic Symmetric Spaces En línea: http://dx.doi.org/10.1007/b138831 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35181 Ejemplares
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Título : Differentiable Manifolds : A Theoretical Physics Approach Tipo de documento: documento electrónico Autores: Gerardo F. Torres del Castillo ; SpringerLink (Online service) Editorial: Boston : Birkhäuser Boston Fecha de publicación: 2012 Número de páginas: VIII, 275 p. 20 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-8271-2 Idioma : Inglés (eng) Palabras clave: Mathematics Topological groups Lie Manifolds (Mathematics) Complex manifolds Physics Mechanics and Cell Complexes (incl. Diff.Topology) Mathematical Methods in Groups, Groups Clasificación: 51 Matemáticas Resumen: This textbook gives a concise introduction to the theory of differentiable manifolds, focusing on their applications to differential equations, differential geometry, and Hamiltonian mechanics. The work’s first three chapters introduce the basic concepts of the theory, such as differentiable maps, tangent vectors, vector and tensor fields, differential forms, local one-parameter groups of diffeomorphisms, and Lie derivatives. These tools are subsequently employed in the study of differential equations (Chapter 4), connections (Chapter 5), Riemannian manifolds (Chapter 6), Lie groups (Chapter 7), and Hamiltonian mechanics (Chapter 8). Throughout, the book contains examples, worked out in detail, as well as exercises intended to show how the formalism is applied to actual computations and to emphasize the connections among various areas of mathematics. Differentiable Manifolds is addressed to advanced undergraduate or beginning graduate students in mathematics or physics. Prerequisites include multivariable calculus, linear algebra, differential equations, and (for the last chapter) a basic knowledge of analytical mechanics Nota de contenido: Preface.-1 Manifolds.- 2 Lie Derivatives -- 3 Differential Forms -- 4 Integral Manifolds -- 5 Connections -- 6. Riemannian Manifolds -- 7 Lie Groups -- 8 Hamiltonian Classical Mechanics -- References.-Index En línea: http://dx.doi.org/10.1007/978-0-8176-8271-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32680 Differentiable Manifolds : A Theoretical Physics Approach [documento electrónico] / Gerardo F. Torres del Castillo ; SpringerLink (Online service) . - Boston : Birkhäuser Boston, 2012 . - VIII, 275 p. 20 illus : online resource.
ISBN : 978-0-8176-8271-2
Idioma : Inglés (eng)
Palabras clave: Mathematics Topological groups Lie Manifolds (Mathematics) Complex manifolds Physics Mechanics and Cell Complexes (incl. Diff.Topology) Mathematical Methods in Groups, Groups Clasificación: 51 Matemáticas Resumen: This textbook gives a concise introduction to the theory of differentiable manifolds, focusing on their applications to differential equations, differential geometry, and Hamiltonian mechanics. The work’s first three chapters introduce the basic concepts of the theory, such as differentiable maps, tangent vectors, vector and tensor fields, differential forms, local one-parameter groups of diffeomorphisms, and Lie derivatives. These tools are subsequently employed in the study of differential equations (Chapter 4), connections (Chapter 5), Riemannian manifolds (Chapter 6), Lie groups (Chapter 7), and Hamiltonian mechanics (Chapter 8). Throughout, the book contains examples, worked out in detail, as well as exercises intended to show how the formalism is applied to actual computations and to emphasize the connections among various areas of mathematics. Differentiable Manifolds is addressed to advanced undergraduate or beginning graduate students in mathematics or physics. Prerequisites include multivariable calculus, linear algebra, differential equations, and (for the last chapter) a basic knowledge of analytical mechanics Nota de contenido: Preface.-1 Manifolds.- 2 Lie Derivatives -- 3 Differential Forms -- 4 Integral Manifolds -- 5 Connections -- 6. Riemannian Manifolds -- 7 Lie Groups -- 8 Hamiltonian Classical Mechanics -- References.-Index En línea: http://dx.doi.org/10.1007/978-0-8176-8271-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32680 Ejemplares
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