| Edition |
1st ed. |
| Description |
1 online resource (xii, 1229 pages) |
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text txt rdacontent |
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computer c rdamedia |
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online resource cr rdacarrier |
| Summary |
This is a comprehensive exposition of topics covered by the American Mathematical Societys classification Global Analysis, dealing with modern developments in calculus expressed using abstract terminology. It will be invaluable for graduate students and researchers embarking on advanced studies in mathematics and mathematical physics. This book provides a comprehensive coverage of modern global analysis and geometrical mathematical physics, dealing with topics such as; structures on manifolds, pseudogroups, Lie groupoids, and global Finsler geometry; the topology of manifolds and differentiable mappings; differential equations (including ODEs, differential systems and distributions, and spectral theory); variational theory on manifolds, with applications to physics; function spaces on manifolds; jets, natural bundles and generalizations; and non-commutative geometry. - Comprehensive coverage of modern global analysis and geometrical mathematical physics - Written by world-experts in the field - Up-to-date contents. |
| Contents |
Preface -- Contents -- 1. Global aspects of Finsler geometry (T. Aikou and L. Kozma) -- 2. Morse theory and nonlinear differential equations (T. Bartsch, A. Szulkin and M. Willem) -- 3. Index theory (D. Bleecker) -- 4. Partial differential equations on closed and open manifolds (J. Eichhorn) -- 5. Spectral geometry (P. Gilkey) -- 6. Lagrangian formalism on Grassmann manifolds (D.R. Grigore) -- 7. Sobolev spaces on manifolds (E. Hebey and F. Robert) -- 8. Harmonic maps (F. lein and J.C. Wood) -- 9. Topology of differentiable mappings (K. Houston) -- 10. Group actions and Hilbert's fifth problem (S. Illman) -- 11. Exterior differential systems (N. Kamran) -- 12. Weil bundles as generalized jet spaces (I. K`olr) -- 13. Distributions, vector distributions, and immersions of manifolds in Euclidean spaces (J. Korbas) -- 14. Geometry of differential equations (B. Kruglikov and V. Lychagin) -- 15. Global variational theory in fibred spaces (D. Krupka) -- 16. Second Order Ordinary Differential Equations in Jet Bundles and the Inverse Problem of the Calculus of Variations (O. Krupk`ov and G.E. Prince) -- 17. Elements of noncommutative geometry (G. Landi) -- 18. De Rham cohomology (M.A. Malakhaltsev) -- 19. Topology of manifolds with corners (J. Margalef-Roig and E. Outerelo Domnguez) -- 20. Jet manifolds and natural bundles (D.J. Saunders) -- 21. Some aspects of differential theories (J. Szilasi and R.L. Lovas) -- 22. Variational sequences (R. Vitolo) -- 23. The Oka-Grauert-Gromov principle for holomorphic bundles (P-M. Wong) -- A. Abstracts. |
| Bibliography |
Includes bibliographical references and index. |
| Contents |
Global aspects of Finsler geometry / T. Aikou and L. Kozma -- Morse theory and nonlinear differential equations / T. Bartsch, A. Szulkin and M. Willem -- Index theory / D. Bleecker -- Partial differential equations on closed and open manifolds / J. Eichhorn -- Spectral geometry / P. Gilkey -- Lagrangian formalism on Grassmann manifolds / D.R. Grigore -- Sobolev spaces on manifolds / E. Hebey and F. Robert -- Harmonic maps / F. Helein and J.C. Wood -- Topology of differentiable mappings / K. Houston -- Group actions and Hilbert's fifth problem / S. Illman -- Exterior differential systems / N. Kamran -- Weil bundles as generalized jet spaces / I. Kolar -- Distributions, vector distributions, and immersions of manifolds in Euclidean spaces / J. Korbas -- Geometry of differential equations / B. Kruglikov and V. Lychagin -- Global variational theory in fibred spaces / D. Krupka -- Second order ordinary differential equations in jet bundles and the inverse problem of the calculus of variations / O. Krupkova and G.E. Prince -- Elements of noncommutative geometry / G. Landi -- De Rham cohomology / M.A. Malakhaltsev -- Topology of manifolds with corners / J. Margalef-Roig and E. Outerelo Dominguez -- Jet manifolds and natural bundles / D.J. Saunders -- Some aspects of differential theories / J. Szilasi and R.L. Lovas -- Variational sequences / R. Vitolo -- The Oka-Grauert-Gromov principle for holomorphic bundles / P-M. Wong. |
| Note |
Print version record. |
| Subject |
Global analysis (Mathematics)
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Mathematical physics.
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Analyse globale (Mathématiques)
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Physique mathématique.
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MATHEMATICS -- Topology.
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Global analysis (Mathematics)
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Mathematical physics
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Differentialgeometrie
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Globale Analysis
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Mathematische Physik
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Analyse globale (mathématiques)
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Physique mathématique.
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| Added Author |
Krupka, D.
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Saunders, D. J.
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| Added Title |
Global analysis |
| Other Form: |
Print version: Handbook of global analysis. 1st ed. Amsterdam ; Boston : Elsevier, 2008 9780444528339 0444528334 (OCoLC)190776638 |
| ISBN |
9780444528339 |
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0444528334 |
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9780080556734 (electronic bk.) |
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0080556736 (electronic bk.) |
| Standard No. |
AU@ 000043178530 |
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CHNEW 001007583 |
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DEBBG BV036962168 |
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DEBBG BV042307029 |
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DEBSZ 305599038 |
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HEBIS 207975418 |
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NZ1 12541684 |
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AU@ 000075316785 |
|
