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Autor Jürgen Jost |
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Título : Compact Riemann Surfaces : An Introduction to Contemporary Mathematics Tipo de documento: documento electrónico Autores: Jürgen Jost ; SpringerLink (Online service) Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2006 Colección: Universitext, ISSN 0172-5939 Número de páginas: XVIII, 282 p. 23 illus Il.: online resource ISBN/ISSN/DL: 978-3-540-33067-7 Idioma : Inglés (eng) Palabras clave: Mathematics Differential geometry Geometry Clasificación: 51 Matemáticas Resumen: Although Riemann surfaces are a time-honoured field, this book is novel in its broad perspective that systematically explores the connection with other fields of mathematics. It can serve as an introduction to contemporary mathematics as a whole as it develops background material from algebraic topology, differential geometry, the calculus of variations, elliptic PDE, and algebraic geometry. It is unique among textbooks on Riemann surfaces in including an introduction to Teichmüller theory. For this new edition, the author has expanded and rewritten several sections to include additional material and to improve the presentation Nota de contenido: Topological Foundations -- Differential Geometry of Riemann Surfaces -- Harmonic Maps -- Teichmüller Spaces -- Geometric Structures on Riemann Surfaces -- Erratum to: Characterizing Programming Systems Allowing Program Self-reference En línea: http://dx.doi.org/10.1007/978-3-540-33067-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34950 Compact Riemann Surfaces : An Introduction to Contemporary Mathematics [documento electrónico] / Jürgen Jost ; SpringerLink (Online service) . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2006 . - XVIII, 282 p. 23 illus : online resource. - (Universitext, ISSN 0172-5939) .
ISBN : 978-3-540-33067-7
Idioma : Inglés (eng)
Palabras clave: Mathematics Differential geometry Geometry Clasificación: 51 Matemáticas Resumen: Although Riemann surfaces are a time-honoured field, this book is novel in its broad perspective that systematically explores the connection with other fields of mathematics. It can serve as an introduction to contemporary mathematics as a whole as it develops background material from algebraic topology, differential geometry, the calculus of variations, elliptic PDE, and algebraic geometry. It is unique among textbooks on Riemann surfaces in including an introduction to Teichmüller theory. For this new edition, the author has expanded and rewritten several sections to include additional material and to improve the presentation Nota de contenido: Topological Foundations -- Differential Geometry of Riemann Surfaces -- Harmonic Maps -- Teichmüller Spaces -- Geometric Structures on Riemann Surfaces -- Erratum to: Characterizing Programming Systems Allowing Program Self-reference En línea: http://dx.doi.org/10.1007/978-3-540-33067-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34950 Ejemplares
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Título : Dynamical Systems : Examples of Complex Behaviour Tipo de documento: documento electrónico Autores: Jürgen Jost ; SpringerLink (Online service) Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2005 Colección: Universitext, ISSN 0172-5939 Número de páginas: VIII, 190 p. 65 illus., 15 illus. in color Il.: online resource ISBN/ISSN/DL: 978-3-540-28889-3 Idioma : Inglés (eng) Palabras clave: Physics Operations research Decision making Mathematics Dynamics Ergodic theory Calculus of variations Economic Physics, general Mathematics, Dynamical Systems and Theory Operation Research/Decision Theory/Quantitative Economics/Mathematical Methods Variations Optimal Control; Optimization Clasificación: 51 Matemáticas Resumen: Our aim is to introduce, explain, and discuss the fundamental problems, ideas, concepts, results, and methods of the theory of dynamical systems and to show how they can be used in speci?c examples. We do not intend to give a comprehensive overview of the present state of research in the theory of dynamical systems, nor a detailed historical account of its development. We try to explain the important results, often neglecting technical re?nements 1 and, usually, we do not provide proofs. One of the basic questions in studying dynamical systems, i.e. systems that evolve in time, is the construction of invariants that allow us to classify qualitative types of dynamical evolution, to distinguish between qualitatively di?erent dynamics, and to studytransitions between di?erent types. Itis also important to ?nd out when a certain dynamic behavior is stable under small perturbations, as well as to understand the various scenarios of instability. Finally, an essential aspect of a dynamic evolution is the transformation of some given initial state into some ?nal or asymptotic state as time proceeds. Thetemporalevolutionofadynamicalsystemmaybecontinuousordiscrete, butitturnsoutthatmanyoftheconceptstobeintroducedareusefulineither case Nota de contenido: Stability of dynamical systems, bifurcations, and generic properties -- Discrete invariants of dynamical systems -- Entropy and topological aspects of dynamical systems -- Entropy and metric aspects of dynamical systems -- Entropy and measure theoretic aspects of dynamical systems -- Smooth dynamical systems -- Cellular automata and Boolean networks as examples of discrete dynamical systems En línea: http://dx.doi.org/10.1007/3-540-28889-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35303 Dynamical Systems : Examples of Complex Behaviour [documento electrónico] / Jürgen Jost ; SpringerLink (Online service) . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2005 . - VIII, 190 p. 65 illus., 15 illus. in color : online resource. - (Universitext, ISSN 0172-5939) .
ISBN : 978-3-540-28889-3
Idioma : Inglés (eng)
Palabras clave: Physics Operations research Decision making Mathematics Dynamics Ergodic theory Calculus of variations Economic Physics, general Mathematics, Dynamical Systems and Theory Operation Research/Decision Theory/Quantitative Economics/Mathematical Methods Variations Optimal Control; Optimization Clasificación: 51 Matemáticas Resumen: Our aim is to introduce, explain, and discuss the fundamental problems, ideas, concepts, results, and methods of the theory of dynamical systems and to show how they can be used in speci?c examples. We do not intend to give a comprehensive overview of the present state of research in the theory of dynamical systems, nor a detailed historical account of its development. We try to explain the important results, often neglecting technical re?nements 1 and, usually, we do not provide proofs. One of the basic questions in studying dynamical systems, i.e. systems that evolve in time, is the construction of invariants that allow us to classify qualitative types of dynamical evolution, to distinguish between qualitatively di?erent dynamics, and to studytransitions between di?erent types. Itis also important to ?nd out when a certain dynamic behavior is stable under small perturbations, as well as to understand the various scenarios of instability. Finally, an essential aspect of a dynamic evolution is the transformation of some given initial state into some ?nal or asymptotic state as time proceeds. Thetemporalevolutionofadynamicalsystemmaybecontinuousordiscrete, butitturnsoutthatmanyoftheconceptstobeintroducedareusefulineither case Nota de contenido: Stability of dynamical systems, bifurcations, and generic properties -- Discrete invariants of dynamical systems -- Entropy and topological aspects of dynamical systems -- Entropy and metric aspects of dynamical systems -- Entropy and measure theoretic aspects of dynamical systems -- Smooth dynamical systems -- Cellular automata and Boolean networks as examples of discrete dynamical systems En línea: http://dx.doi.org/10.1007/3-540-28889-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35303 Ejemplares
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Título : Geometry and Physics Tipo de documento: documento electrónico Autores: Jürgen Jost ; SpringerLink (Online service) Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2009 Número de páginas: XIV, 217 p Il.: online resource ISBN/ISSN/DL: 978-3-642-00541-1 Idioma : Inglés (eng) Palabras clave: Mathematics Geometry Differential geometry Calculus of variations Physics Variations and Optimal Control; Optimization Theoretical, Mathematical Computational Methods in Clasificación: 51 Matemáticas Resumen: "Geometry and Physics" addresses mathematicians wanting to understand modern physics, and physicists wanting to learn geometry. It gives an introduction to modern quantum field theory and related areas of theoretical high-energy physics from the perspective of Riemannian geometry, and an introduction to modern geometry as needed and utilized in modern physics. Jürgen Jost, a well-known research mathematician and advanced textbook author, also develops important geometric concepts and methods that can be used for the structures of physics. In particular, he discusses the Lagrangians of the standard model and its supersymmetric extensions from a geometric perspective Nota de contenido: 1.Geometry -- 1.1.Riemannian and Lorentzian manifolds -- 1.2.Bundles and connections -- 1.3.Tensors and spinors -- 1.4.Riemann surfaces and moduli spaces -- 1.5.Supermanifolds -- 2.Physics -- 2.1.Classical and quantum physics -- 2.2.Lagrangians.-2.3.Variational aspects -- 2.4.The sigma model -- 2.5.Functional integrals -- 2.6.Conformal field theory -- 2.7.String theory -- Bibliography -- Index En línea: http://dx.doi.org/10.1007/978-3-642-00541-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34060 Geometry and Physics [documento electrónico] / Jürgen Jost ; SpringerLink (Online service) . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2009 . - XIV, 217 p : online resource.
ISBN : 978-3-642-00541-1
Idioma : Inglés (eng)
Palabras clave: Mathematics Geometry Differential geometry Calculus of variations Physics Variations and Optimal Control; Optimization Theoretical, Mathematical Computational Methods in Clasificación: 51 Matemáticas Resumen: "Geometry and Physics" addresses mathematicians wanting to understand modern physics, and physicists wanting to learn geometry. It gives an introduction to modern quantum field theory and related areas of theoretical high-energy physics from the perspective of Riemannian geometry, and an introduction to modern geometry as needed and utilized in modern physics. Jürgen Jost, a well-known research mathematician and advanced textbook author, also develops important geometric concepts and methods that can be used for the structures of physics. In particular, he discusses the Lagrangians of the standard model and its supersymmetric extensions from a geometric perspective Nota de contenido: 1.Geometry -- 1.1.Riemannian and Lorentzian manifolds -- 1.2.Bundles and connections -- 1.3.Tensors and spinors -- 1.4.Riemann surfaces and moduli spaces -- 1.5.Supermanifolds -- 2.Physics -- 2.1.Classical and quantum physics -- 2.2.Lagrangians.-2.3.Variational aspects -- 2.4.The sigma model -- 2.5.Functional integrals -- 2.6.Conformal field theory -- 2.7.String theory -- Bibliography -- Index En línea: http://dx.doi.org/10.1007/978-3-642-00541-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34060 Ejemplares
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Título : Partial Differential Equations Tipo de documento: documento electrónico Autores: Jürgen Jost ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2007 Colección: Graduate Texts in Mathematics, ISSN 0072-5285 num. 214 Número de páginas: XIV, 356 p. 10 illus Il.: online resource ISBN/ISSN/DL: 978-0-387-49319-0 Idioma : Inglés (eng) Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Partial differential equations Physics Theoretical, and Computational Differential Equations Numerical Clasificación: 51 Matemáticas Resumen: This book is intended for students who wish to get an introduction to the theory of partial differential equations. The author focuses on elliptic equations and systematically develops the relevant existence schemes, always with a view towards nonlinear problems. These are maximum principle methods (particularly important for numerical analysis schemes), parabolic equations, variational methods, and continuity methods. This book also develops the main methods for obtaining estimates for solutions of elliptic equations: Sobolev space theory, weak and strong solutions, Schauder estimates, and Moser iteration. Connections between elliptic, parabolic, and hyperbolic equations are explored, as well as the connection with Brownian motion and semigroups. This book can be utilized for a one-year course on partial differential equations. For the new edition the author has added a new chapter on reaction-diffusion equations and systems. There is also new material on Neumann boundary value problems, Poincaré inequalities, expansions, as well as a new proof of the Hölder regularity of solutions of the Poisson equation. Jürgen Jost is Co-Director of the Max Planck Institute for Mathematics in the Sciences and Professor of Mathematics at the University of Leipzig. He is the author of a number of Springer books, including Dynamical Systems (2005), Postmodern Analysis (3rd ed. 2005, also translated into Japanese), Compact Riemann Surfaces (3rd ed. 2006) and Riemannian Geometry and Geometric Analysis (4th ed., 2005). The present book is an expanded translation of the original German version, Partielle Differentialgleichungen (1998). About the first edition: Because of the nice global presentation, I recommend this book to students and young researchers who need the now classical properties of these second-order partial differential equations. Teachers will also find in this textbook the basis of an introductory course on second-order partial differential equations. - Alain Brillard, Mathematical Reviews Beautifully written and superbly well-organised, I strongly recommend this book to anyone seeking a stylish, balanced, up-to-date survey of this central area of mathematics. - Nick Lord, The Mathematical Gazette Nota de contenido: Introduction: What Are Partial Differential Equations? -- The Laplace Equation as the Prototype of an Elliptic Partial Differential Equation of Second Order -- The Maximum Principle -- Existence Techniques I: Methods Based on the Maximum Principle -- Existence Techniques II: Parabolic Methods. The Heat Equation -- Reaction-Diffusion Equations and Systems -- The Wave Equation and its Connections with the Laplace and Heat Equations -- The Heat Equation, Semigroups, and Brownian Motion -- The Dirichlet Principle. Variational Methods for the Solution of PDEs (Existence Techniques III) -- Sobolev Spaces and L2 Regularity Theory -- Strong Solutions -- The Regularity Theory of Schauder and the Continuity Method (Existence Techniques IV) -- The Moser Iteration Method and the Regularity Theorem of de Giorgi and Nash En línea: http://dx.doi.org/10.1007/978-0-387-49319-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34490 Partial Differential Equations [documento electrónico] / Jürgen Jost ; SpringerLink (Online service) . - New York, NY : Springer New York, 2007 . - XIV, 356 p. 10 illus : online resource. - (Graduate Texts in Mathematics, ISSN 0072-5285; 214) .
ISBN : 978-0-387-49319-0
Idioma : Inglés (eng)
Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Partial differential equations Physics Theoretical, and Computational Differential Equations Numerical Clasificación: 51 Matemáticas Resumen: This book is intended for students who wish to get an introduction to the theory of partial differential equations. The author focuses on elliptic equations and systematically develops the relevant existence schemes, always with a view towards nonlinear problems. These are maximum principle methods (particularly important for numerical analysis schemes), parabolic equations, variational methods, and continuity methods. This book also develops the main methods for obtaining estimates for solutions of elliptic equations: Sobolev space theory, weak and strong solutions, Schauder estimates, and Moser iteration. Connections between elliptic, parabolic, and hyperbolic equations are explored, as well as the connection with Brownian motion and semigroups. This book can be utilized for a one-year course on partial differential equations. For the new edition the author has added a new chapter on reaction-diffusion equations and systems. There is also new material on Neumann boundary value problems, Poincaré inequalities, expansions, as well as a new proof of the Hölder regularity of solutions of the Poisson equation. Jürgen Jost is Co-Director of the Max Planck Institute for Mathematics in the Sciences and Professor of Mathematics at the University of Leipzig. He is the author of a number of Springer books, including Dynamical Systems (2005), Postmodern Analysis (3rd ed. 2005, also translated into Japanese), Compact Riemann Surfaces (3rd ed. 2006) and Riemannian Geometry and Geometric Analysis (4th ed., 2005). The present book is an expanded translation of the original German version, Partielle Differentialgleichungen (1998). About the first edition: Because of the nice global presentation, I recommend this book to students and young researchers who need the now classical properties of these second-order partial differential equations. Teachers will also find in this textbook the basis of an introductory course on second-order partial differential equations. - Alain Brillard, Mathematical Reviews Beautifully written and superbly well-organised, I strongly recommend this book to anyone seeking a stylish, balanced, up-to-date survey of this central area of mathematics. - Nick Lord, The Mathematical Gazette Nota de contenido: Introduction: What Are Partial Differential Equations? -- The Laplace Equation as the Prototype of an Elliptic Partial Differential Equation of Second Order -- The Maximum Principle -- Existence Techniques I: Methods Based on the Maximum Principle -- Existence Techniques II: Parabolic Methods. The Heat Equation -- Reaction-Diffusion Equations and Systems -- The Wave Equation and its Connections with the Laplace and Heat Equations -- The Heat Equation, Semigroups, and Brownian Motion -- The Dirichlet Principle. Variational Methods for the Solution of PDEs (Existence Techniques III) -- Sobolev Spaces and L2 Regularity Theory -- Strong Solutions -- The Regularity Theory of Schauder and the Continuity Method (Existence Techniques IV) -- The Moser Iteration Method and the Regularity Theorem of de Giorgi and Nash En línea: http://dx.doi.org/10.1007/978-0-387-49319-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34490 Ejemplares
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Título : Partial Differential Equations Tipo de documento: documento electrónico Autores: Jürgen Jost ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2013 Otro editor: Imprint: Springer Colección: Graduate Texts in Mathematics, ISSN 0072-5285 num. 214 Número de páginas: XIV, 410 p Il.: online resource ISBN/ISSN/DL: 978-1-4614-4809-9 Idioma : Inglés (eng) Palabras clave: Mathematics Partial differential equations Physics Differential Equations Theoretical, Mathematical and Computational Clasificación: 51 Matemáticas Resumen: This book offers an ideal graduate-level introduction to the theory of partial differential equations. The first part of the book describes the basic mathematical problems and structures associated with elliptic, parabolic, and hyperbolic partial differential equations, and explores the connections between these fundamental types. Aspects of Brownian motion or pattern formation processes are also presented. The second part focuses on existence schemes and develops estimates for solutions of elliptic equations, such as Sobolev space theory, weak and strong solutions, Schauder estimates, and Moser iteration. In particular, the reader will learn the basic techniques underlying current research in elliptic partial differential equations. This revised and expanded third edition is enhanced with many additional examples that will help motivate the reader. New features include a reorganized and extended chapter on hyperbolic equations, as well as a new chapter on the relations between different types of partial differential equations, including first-order hyperbolic systems, Langevin and Fokker-Planck equations, viscosity solutions for elliptic PDEs, and much more. Also, the new edition contains additional material on systems of elliptic partial differential equations, and it explains in more detail how the Harnack inequality can be used for the regularity of solutions Nota de contenido: Preface -- Introduction: What are Partial Differential Equations? -- 1 The Laplace equation as the Prototype of an Elliptic Partial Differential Equation of Second Order -- 2 The Maximum Principle -- 3 Existence Techniques I: Methods Based on the Maximum Principle -- 4 Existence Techniques II: Parabolic Methods. The Heat Equation -- 5 Reaction-Diffusion Equations and Systems -- 6 Hyperbolic Equations -- 7 The Heat Equation, Semigroups, and Brownian Motion.- 8 Relationships between Different Partial Differential Equations -- 9 The Dirichlet Principle. Variational Methods for the Solutions of PDEs (Existence Techniques III) -- 10 Sobolev Spaces and L^2 Regularity theory -- 11 Strong solutions -- 12 The Regularity Theory of Schauder and the Continuity Method (Existence Techniques IV) -- 13The Moser Iteration Method and the Regularity Theorem of de Giorgi and Nash -- Appendix: Banach and Hilbert spaces. The L^p-Spaces -- References -- Index of Notation -- Index En línea: http://dx.doi.org/10.1007/978-1-4614-4809-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32229 Partial Differential Equations [documento electrónico] / Jürgen Jost ; SpringerLink (Online service) . - New York, NY : Springer New York : Imprint: Springer, 2013 . - XIV, 410 p : online resource. - (Graduate Texts in Mathematics, ISSN 0072-5285; 214) .
ISBN : 978-1-4614-4809-9
Idioma : Inglés (eng)
Palabras clave: Mathematics Partial differential equations Physics Differential Equations Theoretical, Mathematical and Computational Clasificación: 51 Matemáticas Resumen: This book offers an ideal graduate-level introduction to the theory of partial differential equations. The first part of the book describes the basic mathematical problems and structures associated with elliptic, parabolic, and hyperbolic partial differential equations, and explores the connections between these fundamental types. Aspects of Brownian motion or pattern formation processes are also presented. The second part focuses on existence schemes and develops estimates for solutions of elliptic equations, such as Sobolev space theory, weak and strong solutions, Schauder estimates, and Moser iteration. In particular, the reader will learn the basic techniques underlying current research in elliptic partial differential equations. This revised and expanded third edition is enhanced with many additional examples that will help motivate the reader. New features include a reorganized and extended chapter on hyperbolic equations, as well as a new chapter on the relations between different types of partial differential equations, including first-order hyperbolic systems, Langevin and Fokker-Planck equations, viscosity solutions for elliptic PDEs, and much more. Also, the new edition contains additional material on systems of elliptic partial differential equations, and it explains in more detail how the Harnack inequality can be used for the regularity of solutions Nota de contenido: Preface -- Introduction: What are Partial Differential Equations? -- 1 The Laplace equation as the Prototype of an Elliptic Partial Differential Equation of Second Order -- 2 The Maximum Principle -- 3 Existence Techniques I: Methods Based on the Maximum Principle -- 4 Existence Techniques II: Parabolic Methods. The Heat Equation -- 5 Reaction-Diffusion Equations and Systems -- 6 Hyperbolic Equations -- 7 The Heat Equation, Semigroups, and Brownian Motion.- 8 Relationships between Different Partial Differential Equations -- 9 The Dirichlet Principle. Variational Methods for the Solutions of PDEs (Existence Techniques III) -- 10 Sobolev Spaces and L^2 Regularity theory -- 11 Strong solutions -- 12 The Regularity Theory of Schauder and the Continuity Method (Existence Techniques IV) -- 13The Moser Iteration Method and the Regularity Theorem of de Giorgi and Nash -- Appendix: Banach and Hilbert spaces. The L^p-Spaces -- References -- Index of Notation -- Index En línea: http://dx.doi.org/10.1007/978-1-4614-4809-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32229 Ejemplares
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