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Cartan for Beginners: Differential Geometry Via Moving Frames and Exterior Differential Systems (Graduate Studies in Mathematics, 175, Band 175) - Hardcover
Buch 45 von 190: Graduate Studies in Mathematics
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This graduate text introduces exterior differential systems, their application to partial differential equations, and the use of moving frames in algebraic geometry. Three chapters on the Cartan-Kahler theorem derive Cartan’s test for constant coefficient homogeneous systems, linear Pfaffian systems, and non-Pfaffian systems arising in submanifold geometry. The second edition adds three chapters on Riemannian geometry, Darboux-integrable exterior differential systems, and conformal differential geometry. Appendices review linear algebra, representation theory, differential forms, complex manifolds, and the Cauchy-Kowalevski theorem. Annotation ©2017 Ringgold, Inc., Portland, OR (protoview.com)
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Über die Autorin bzw. den Autor
Thomas A. Ivey, College of Charleston, SC.
Joseph M. Landsberg, Texas A&M University, College Station, TX.
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Cartan for Beginners: Differential Geometry via Moving Frames and Exterior Differential Systems (eng)
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Cartan for Beginners: Differential Geometry via Moving Frames and Exterior Differential Systems
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Zustand: New. Two central aspects of Cartan's approach to differential geometry are the theory of exterior differential systems (EDS) and the method of moving frames. This book presents thorough and modern treatments of both subjects, including their applications to both classic and contemporary problems in geometry. Series: Graduate Studies in Mathematics. Num Pages: 455 pages. BIC Classification: PBM; PBP. Category: (G) General (US: Trade). Dimension: 188 x 266 x 28. Weight in Grams: 976. . 2016. 2nd Edition. Hardcover. . . . . Bestandsnummer des Verkäufers V9781470409869
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Hardcover. Zustand: new. Hardcover. Two central aspects of Cartan's approach to differential geometry are the theory of exterior differential systems (EDS) and the method of moving frames. This book presents thorough and modern treatments of both subjects, including their applications to both classic and contemporary problems in geometry. It begins with the classical differential geometry of surfaces and basic Riemannian geometry in the language of moving frames, along with an elementary introduction to exterior differential systems. Key concepts are developed incrementally, with motivating examples leading to definitions, theorems, and proofs.Once the basics of the methods are established, the authors develop applications and advanced topics. One notable application is to complex algebraic geometry, where they expand and update important results from projective differential geometry. As well, the book features an introduction to $G$-structures and a treatment of the theory of connections. The techniques of EDS are also applied to obtain explicit solutions of PDEs via Darboux's method, the method of characteristics, and Cartan's method of equivalence.This text is suitable for a one-year graduate course in differential geometry, and parts of it can be used for a one-semester course. It has numerous exercises and examples throughout. It will also be useful to experts in areas such as geometry of PDE systems and complex algebraic geometry who want to learn how moving frames and exterior differential systems apply to their fields.The second edition features three new chapters: on Riemannian geometry, emphasizing the use of representation theory; on the latest developments in the study of Darboux-integrable systems; and on conformal geometry, written in a manner to introduce readers to the related parabolic geometry perspective. Two central aspects of Cartan's approach to differential geometry are the theory of exterior differential systems (EDS) and the method of moving frames. This book presents thorough and modern treatments of both subjects, including their applications to both classic and contemporary problems in geometry. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Bestandsnummer des Verkäufers 9781470409869
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Cartan for Beginners
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Hardback. Zustand: New. Second Edition. Two central aspects of Cartan's approach to differential geometry are the theory of exterior differential systems (EDS) and the method of moving frames. This book presents thorough and modern treatments of both subjects, including their applications to both classic and contemporary problems in geometry. It begins with the classical differential geometry of surfaces and basic Riemannian geometry in the language of moving frames, along with an elementary introduction to exterior differential systems. Key concepts are developed incrementally, with motivating examples leading to definitions, theorems, and proofs.Once the basics of the methods are established, the authors develop applications and advanced topics. One notable application is to complex algebraic geometry, where they expand and update important results from projective differential geometry. As well, the book features an introduction to $G$-structures and a treatment of the theory of connections. The techniques of EDS are also applied to obtain explicit solutions of PDEs via Darboux's method, the method of characteristics, and Cartan's method of equivalence.This text is suitable for a one-year graduate course in differential geometry, and parts of it can be used for a one-semester course. It has numerous exercises and examples throughout. It will also be useful to experts in areas such as geometry of PDE systems and complex algebraic geometry who want to learn how moving frames and exterior differential systems apply to their fields.The second edition features three new chapters: on Riemannian geometry, emphasizing the use of representation theory; on the latest developments in the study of Darboux-integrable systems; and on conformal geometry, written in a manner to introduce readers to the related parabolic geometry perspective. Bestandsnummer des Verkäufers LU-9781470409869
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Cartan for Beginners: Differential Geometry via Moving Frames and Exterior Differential Systems
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ISBN 13: 9781470409869
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Zustand: New. Two central aspects of Cartan's approach to differential geometry are the theory of exterior differential systems (EDS) and the method of moving frames. This book presents thorough and modern treatments of both subjects, including their applications to both classic and contemporary problems in geometry. Series: Graduate Studies in Mathematics. Num Pages: 455 pages. BIC Classification: PBM; PBP. Category: (G) General (US: Trade). Dimension: 188 x 266 x 28. Weight in Grams: 976. . 2016. 2nd Edition. Hardcover. . . . . Books ship from the US and Ireland. Bestandsnummer des Verkäufers V9781470409869
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Cartan for Beginners: Differential Geometry Via Moving Frames and Exterior Differential Systems (Graduate Studies in Mathematics)
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