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Author : Donald W. Kahn
Publisher : Courier Corporation
Page : 352 pages
File Size : 46,9 Mb
Release : 2013-11-07
Category : Mathematics
ISBN : 0486152294
This text introduces the methods of mathematical analysis as applied to manifolds, including the roles of differentiation and integration, infinite dimensions, Morse theory, Lie groups, and dynamical systems. 1980 edition.
Author : Demeter Krupka,David Saunders
Publisher : Elsevier
Page : 1243 pages
File Size : 40,7 Mb
Release : 2011-08-11
Category : Mathematics
ISBN : 9780080556734
This is a comprehensive exposition of topics covered by the American Mathematical Society’s 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
Author : S. Ramanan
Publisher : American Mathematical Soc.
Page : 330 pages
File Size : 47,8 Mb
Release : 2005
Category : Analytic spaces
ISBN : 9780821837023
The power that analysis, topology and algebra bring to geometry has revolutionised the way geometers and physicists look at conceptual problems. Some of the key ingredients in this interplay are sheaves, cohomology, Lie groups, connections and differential operators. In Global Calculus, the appropriate formalism for these topics is laid out with numerous examples and applications by one of the experts in differential and algebraic geometry. Ramanan has chosen an uncommon but natural path through the subject. In this almost completely self-contained account, these topics are developed from scratch. The basics of Fourier transforms, Sobolev theory and interior regularity are proved at the same time as symbol calculus, culminating in beautiful results in global analysis, real and complex. Many new perspectives on traditional and modern questions of differential analysis and geometry are the hallmarks of the book. The book is suitable for a first year graduate course on Global Analysis.
Author : Andreas Kriegl,Peter W. Michor
Publisher : American Mathematical Soc.
Page : 631 pages
File Size : 49,6 Mb
Release : 1997
Category : Global analysis (Mathematics).
ISBN : 9780821807804
For graduate students and research mathematicians interested in global analysis and the analysis of manifolds, lays the foundations for a differential calculus in infinite dimensions and discusses applications in infinite-dimension differential geometry and global analysis not involving Sobolev completions and fixed-point theory. Shows how the notion of smoothness as mapping smooth curves to smooth curves coincides with all known reasonable concepts up to Frechet spaces. Then develops a calculus of holomorphic mappings, and another of real analytical mapping. Emphasizes regular infinite dimensional Lie groups. Annotation copyrighted by Book News, Inc., Portland, OR
Author : Ilka Agricola,Thomas Friedrich
Publisher : American Mathematical Soc.
Page : 362 pages
File Size : 49,8 Mb
Release : 2002
Category : Differential forms
ISBN : 9780821829516
The final third of the book applies the mathematical ideas to important areas of physics: Hamiltonian mechanics, statistical mechanics, and electrodynamics." "There are many classroom-tested exercises and examples with excellent figures throughout. The book is ideal as a text for a first course in differential geometry, suitable for advanced undergraduates or graduate students in mathematics or physics."--BOOK JACKET.
Author : Anonim
Publisher : Bookboon
Page : 78 pages
File Size : 53,8 Mb
Release : 2024-06-25
Category : Electronic
ISBN : 9788776815332
Author : Calvin C. Moore,Claude Schochet
Publisher : Springer Science & Business Media
Page : 337 pages
File Size : 41,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461395928
Global analysis has as its primary focus the interplay between the local analysis and the global geometry and topology of a manifold. This is seen classicallv in the Gauss-Bonnet theorem and its generalizations. which culminate in the Ativah-Singer Index Theorem [ASI] which places constraints on the solutions of elliptic systems of partial differential equations in terms of the Fredholm index of the associated elliptic operator and characteristic differential forms which are related to global topologie al properties of the manifold. The Ativah-Singer Index Theorem has been generalized in several directions. notably by Atiyah-Singer to an index theorem for families [AS4]. The typical setting here is given by a family of elliptic operators (Pb) on the total space of a fibre bundle P = F_M_B. where is defined the Hilbert space on Pb 2 L 1p -llbl.dvollFll. In this case there is an abstract index class indlPI E ROIBI. Once the problem is properly formulated it turns out that no further deep analvtic information is needed in order to identify the class. These theorems and their equivariant counterparts have been enormously useful in topology. geometry. physics. and in representation theory.
Author : Shiing-Shen Chern,Stephen Smale
Publisher : American Mathematical Soc.
Page : 250 pages
File Size : 54,5 Mb
Release : 1970
Category : Analyse globale (Mathematiques)
ISBN : 9780821814161
Author : M. Grmela,J. E. Marsden
Publisher : Springer
Page : 386 pages
File Size : 40,9 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540384625
Author : Felix E. Browder
Publisher : American Mathematical Soc.
Page : 644 pages
File Size : 52,8 Mb
Release : 1992
Category : Mathematics
ISBN : 0821888544
This volume contains a number of research-expository articles that appeared in the Bulletin of the AMS between 1979 and 1984 and that address the general area of nonlinear functional analysis and global analysis and their applications. The central theme concerns qualitative methods in the study of nonlinear problems arising in applied mathematics, mathematical physics, and geometry. Since these articles first appeared, the methods and ideas they describe have been applied in an ever-widening array of applications. Readers will find this collection useful, as it brings together a range of influential papers by some of the leading researchers in the field.
Author : M. Kohno
Publisher : Springer Science & Business Media
Page : 539 pages
File Size : 42,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401146050
Since the initiative works for global analysis of linear differential equations by G.G. Stokes and B. Riemann in 1857, the Airy function and the Gauss hypergeometric function became the most important and the greatest practical special functions, which have a variety of applications to mathematical science, physics and engineering. The cffcctivity of these functions is essentially due to their "behavior in the large" . For instance, the Airy function plays a basic role in the asymptotic analysis of many functions arising as solutions of differential equations in several problems of applied math ematics. In case of the employment of its behavior, one should always pay attention to the Stokes phenomenon. On the other hand, as is well-known, the Gauss hypergeometric function arises in all fields of mathematics, e.g., in number theory, in the theory of groups and in analysis itself. It is not too much to say that all power series are special or extended cases of the hypergeometric series. For the full use of its properties, one needs connection formulas or contiguous relations.
Author : Yuri Gliklikh
Publisher : Springer Science & Business Media
Page : 221 pages
File Size : 46,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461218661
The first edition of this book entitled Analysis on Riemannian Manifolds and Some Problems of Mathematical Physics was published by Voronezh Univer sity Press in 1989. For its English edition, the book has been substantially revised and expanded. In particular, new material has been added to Sections 19 and 20. I am grateful to Viktor L. Ginzburg for his hard work on the transla tion and for writing Appendix F, and to Tomasz Zastawniak for his numerous suggestions. My special thanks go to the referee for his valuable remarks on the theory of stochastic processes. Finally, I would like to acknowledge the support of the AMS fSU Aid Fund and the International Science Foundation (Grant NZBOOO), which made possible my work on some of the new results included in the English edition of the book. Voronezh, Russia Yuri Gliklikh September, 1995 Preface to the Russian Edition The present book is apparently the first in monographic literature in which a common treatment is given to three areas of global analysis previously consid ered quite distant from each other, namely, differential geometry and classical mechanics, stochastic differential geometry and statistical and quantum me chanics, and infinite-dimensional differential geometry of groups of diffeomor phisms and hydrodynamics. The unification of these topics under the cover of one book appears, however, quite natural, since the exposition is based on a geometrically invariant form of the Newton equation and its analogs taken as a fundamental law of motion.
Author : Y.G. Borisovich,Y.E. Gliklikh
Publisher : Springer
Page : 308 pages
File Size : 46,5 Mb
Release : 2006-12-08
Category : Mathematics
ISBN : 9783540391326
This volume (a sequel to LNM 1108, 1214, 1334 and 1453) continues the presentation to English speaking readers of the Voronezh University press series on Global Analysis and Its Applications. The papers are selected fromtwo Russian issues entitled "Algebraic questions of Analysis and Topology" and "Nonlinear Operators in Global Analysis". CONTENTS: YuE. Gliklikh: Stochastic analysis, groups of diffeomorphisms and Lagrangian description of viscous incompressible fluid.- A. Ya. Helemskii: From topological homology: algebras with different properties of homological triviality.- V.V. Lychagin, L.V. Zil'bergleit: Duality in stable Spencer cohomologies.- O.R. Musin: On some problems of computational geometry and topology.- V.E. Nazaikinskii, B. Yu. Sternin, V.E. Shatalov: Introduction to Maslov's operational method (non-commutative analysis and differential equations).- Yu. B. Rudyak: The problem of realization of homology classes from Poincare up to the present.- V.G. Zvyagin, N.M. Ratiner: Oriented degree of Fredholm maps of non-negativeindex and its applications to global bifurcation of solutions.- A.A. Bolibruch: Fuchsian systems with reducible monodromy and the Riemann-Hilbert problem.- I.V. Bronstein, A. Ya. Kopanskii: Finitely smooth normal forms of vector fields in the vicinity of a rest point.- B.D. Gel'man: Generalized degree of multi-valued mappings.- G.N. Khimshiashvili: On Fredholmian aspects of linear transmission problems.- A.S. Mishchenko: Stationary solutions of nonlinear stochastic equations.- B. Yu. Sternin, V.E. Shatalov: Continuation of solutions to elliptic equations and localisation of singularities.- V.G. Zvyagin, V.T. Dmitrienko: Properness of nonlinear elliptic differential operators in H
Author : Yurii G. Borisovich,A.M. Vershik,Yurii E. Gliklikh
Publisher : Springer
Page : 338 pages
File Size : 44,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540458944
Author : Canadian Mathematical Society. Summer Meeting
Publisher : American Mathematical Soc.
Page : 198 pages
File Size : 42,8 Mb
Release : 1992
Category : Mathematics
ISBN : 0821860178
This book contains the proceedings of a special session held during the Summer Meeting of the Canadian Mathematical Society in 1990. The articles collected here reflect the diverse interests of the participants but are united by the common theme of the interplay among geometry, global analysis, and topology. The topics covered include applications to low dimensional manifolds, control theory, integrable systems, Lie algebras of operators, and algebraic geometry and provide an insight into some recent trends in these areas.