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Author : Theodor Bröcker,L. Lander
Publisher : Cambridge University Press
Page : 189 pages
File Size : 42,7 Mb
Release : 1975-07-17
Category : Mathematics
ISBN : 9780521206815
This book gives a fairly elementary introduction to the local theory of differentiable mappings and is suitable as a text for courses to graduates and advanced undergraduates.
Author : Theodor Bröcker,L. Lander,Theodor Br Cker
Publisher : Unknown
Page : 190 pages
File Size : 41,5 Mb
Release : 2014-05-14
Category : MATHEMATICS
ISBN : 1107087058
This book gives a fairly elementary introduction to the local theory of differentiable mappings and is suitable as a text for courses to graduates and advanced undergraduates.
Author : James Montaldi
Publisher : Cambridge University Press
Page : 449 pages
File Size : 52,7 Mb
Release : 2021-06-24
Category : Mathematics
ISBN : 9781107151642
This textbook gives a contemporary account of singularity theory and its principal application, bifurcation theory.
Author : Michel Demazure
Publisher : Springer Science & Business Media
Page : 304 pages
File Size : 42,7 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783642571343
Based on a lecture course, this text gives a rigorous introduction to nonlinear analysis, dynamical systems and bifurcation theory including catastrophe theory. Wherever appropriate it emphasizes a geometrical or coordinate-free approach allowing a clear focus on the essential mathematical structures. It brings out features common to different branches of the subject while giving ample references for more advanced or technical developments.
Author : A. Okninski
Publisher : Elsevier
Page : 284 pages
File Size : 47,6 Mb
Release : 1992-06-12
Category : Science
ISBN : 0080868274
This book aims to provide a straightforward introduction to chemical applications of the catastrophe theory. It is primarily intended for chemists interested in placing chemical reactions in the broader context of non-linear science, but it has a practical relevance for scientists in general. Catastrophe theory deals with those non-linear phenomena in which a continuous change in the control parameters results in a discontinuous alteration of a characteristic quantity of the system. The author discusses the origins of catastrophe theory, giving examples of occurrences in the areas of physics, chemistry and biology. Elementary theory and non-chemical applications are also described. The chemical kinetics and methods of analysis of chemical kinetic equations arising from elementary and generalized catastrophe theories are reviewed. Finally, the theory is applied to analyse and classify phenomena associated with the stability loss that may occur in chemical reactions. The book contains over 100 figures and an extensive subject index.
Author : Tim Poston,Ian Stewart
Publisher : Courier Corporation
Page : 514 pages
File Size : 51,9 Mb
Release : 2014-05-05
Category : Mathematics
ISBN : 9780486143781
First integrated treatment of main ideas behind René Thom's theory of catastrophes stresses detailed applications in the physical sciences. Mathematics of theory explained with a minimum of technicalities. Over 200 illustrations clarify text designed for researchers and postgraduate students in engineering, mathematics, physics and biology. 1978 edition. Bibliography.
Author : Domencio Castrigiano
Publisher : CRC Press
Page : 223 pages
File Size : 42,7 Mb
Release : 2019-06-03
Category : Mathematics
ISBN : 9780429981432
Catastrophe Theory was introduced in the 1960s by the renowned Fields Medal mathematician René Thom as a part of the general theory of local singularities. Since then it has found applications across many areas, including biology, economics, and chemical kinetics. By investigating the phenomena of bifurcation and chaos, Catastrophe Theory proved to
Author : Wolfgang Wildgen
Publisher : John Benjamins Publishing
Page : 130 pages
File Size : 48,9 Mb
Release : 1982-01-01
Category : Language Arts & Disciplines
ISBN : 9789027280602
René Thom, the famous French mathematician and founder of catastrophe theory, considered linguistics an exemplary field for the application of his general morphology. It is surprising that physicists, chemists, biologists, psychologists and sociologists are all engaged in the field of catastrophe theory, but that there has been almost no echo from linguistics. Meanwhile linguistics has evolved in the direction of René Thom’s intuitions about an integrated science of language and it has become a necessary task to review, update and elaborate the proposals made by Thom and to embed them in the framework of modern semantic theory.
Author : Vladimir I. Arnol'd
Publisher : Springer Science & Business Media
Page : 161 pages
File Size : 51,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642581243
The new edition of this non-mathematical review of catastrophe theory contains updated results and many new or expanded topics including delayed loss of stability, shock waves, and interior scattering. Three new sections offer the history of singularity and its applications from da Vinci to today, a discussion of perestroika in terms of the theory of metamorphosis, and a list of 93 problems touching on most of the subject matter in the book.
Author : Robert A. Meyers
Publisher : Springer Science & Business Media
Page : 1885 pages
File Size : 41,5 Mb
Release : 2011-10-05
Category : Mathematics
ISBN : 9781461418054
Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.
Author : Peter Orlik,American Mathematical Society
Publisher : American Mathematical Soc.
Page : 704 pages
File Size : 46,7 Mb
Release : 1983
Category : Mathematics
ISBN : 9780821814505
On April 7-10, 1980, the American Mathematical Society sponsored a Symposium on the Mathematical Heritage of Henri Poincari, held at Indiana University, Bloomington, Indiana. This title presents the written versions this Symposium. It contains two papers by invited speakers who were not able to attend, S S Chern and L Nirenberg.
Author : J. Margalef-Roig,E. Outerelo Dominguez
Publisher : Elsevier
Page : 602 pages
File Size : 40,6 Mb
Release : 1992-06-02
Category : Mathematics
ISBN : 9780080872841
...there are reasons enough to warrant a coherent treatment of the main body of differential topology in the realm of Banach manifolds, which is at the same time correct and complete. This book fills the gap: whenever possible the manifolds treated are Banach manifolds with corners. Corners add to the complications and the authors have carefully fathomed the validity of all main results at corners. Even in finite dimensions some results at corners are more complete and better thought out here than elsewhere in the literature. The proofs are correct and with all details. I see this book as a reliable monograph of a well-defined subject; the possibility to fall back to it adds to the feeling of security when climbing in the more dangerous realms of infinite dimensional differential geometry. Peter W. Michor
Author : Marta Bunge,Felipe Gago Couso,Ana María San Luis,Ana María San Luis Fernández
Publisher : Cambridge University Press
Page : 234 pages
File Size : 50,9 Mb
Release : 2018-03-29
Category : Mathematics
ISBN : 9781108447232
Represents the state of the art in the new field of synthetic differential topology.
Author : Demeter Krupka,David Saunders
Publisher : Elsevier
Page : 1243 pages
File Size : 44,5 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 : Elsa Abbena,Simon Salamon,Alfred Gray
Publisher : CRC Press
Page : 1024 pages
File Size : 54,7 Mb
Release : 2006-06-21
Category : Mathematics
ISBN : 1584884487
Presenting theory while using Mathematica in a complementary way, Modern Differential Geometry of Curves and Surfaces with Mathematica, the third edition of Alfred Gray’s famous textbook, covers how to define and compute standard geometric functions using Mathematica for constructing new curves and surfaces from existing ones. Since Gray’s death, authors Abbena and Salamon have stepped in to bring the book up to date. While maintaining Gray's intuitive approach, they reorganized the material to provide a clearer division between the text and the Mathematica code and added a Mathematica notebook as an appendix to each chapter. They also address important new topics, such as quaternions. The approach of this book is at times more computational than is usual for a book on the subject. For example, Brioshi’s formula for the Gaussian curvature in terms of the first fundamental form can be too complicated for use in hand calculations, but Mathematica handles it easily, either through computations or through graphing curvature. Another part of Mathematica that can be used effectively in differential geometry is its special function library, where nonstandard spaces of constant curvature can be defined in terms of elliptic functions and then plotted. Using the techniques described in this book, readers will understand concepts geometrically, plotting curves and surfaces on a monitor and then printing them. Containing more than 300 illustrations, the book demonstrates how to use Mathematica to plot many interesting curves and surfaces. Including as many topics of the classical differential geometry and surfaces as possible, it highlights important theorems with many examples. It includes 300 miniprograms for computing and plotting various geometric objects, alleviating the drudgery of computing things such as the curvature and torsion of a curve in space.