Singularity Theory and an Introduction to Catastrophe Theory PDF Download
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Author: Yung-Chen Lu
Publisher:
ISBN: 9781461299103
Category :
Languages : en
Pages : 199
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Book Description
Author: Yung-Chen Lu
Publisher:
ISBN: 9781461299103
Category :
Languages : en
Pages : 199
Get Book Here
Book Description
Author: Y.-C. Lu
Publisher: Springer Science & Business Media
ISBN: 1461299098
Category : Mathematics
Languages : en
Pages : 212
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Book Description
In April, 1975, I organised a conference at the Battelle Research Center, Seattle, Washington on the theme "Structural stability, catastrophe theory and their applications in the sciences". To this conference were invited a number of mathematicians concerned with the mathematical theories of structural stability and catastrophe theory, and other mathematicians whose principal interest lay in applications to various sciences - physical, biological, medical and social. Rene Thorn and Christopher Zeeman figured in the list of distinguished participants. The conference aroused considerable interest, and many mathematicians who were not specialists in the fields covered by the conference expressed their desire to attend the conference sessions; in addition, scientists from the Battelle laboratories came to Seattle to learn of developments in these areas and to consider possible applications to their own work. In view of the attendance of these mathematicians and scientists, and in order to enable the expositions of the experts to be intelligible to this wider audience, I invited Professor Yung Chen Lu, of Ohio State University, to come to Battelle Seattle in advance of the actual conference to deliver a series of informal lecture-seminars, explaining the background of the mathematical theory and indicating some of the actual and possible applications. In the event, Yung-Chen Lu delivered his lectures in the week preceding and the week following the actual conference, so that the first half of his course was preparatory and the second half explanatory and evaluative. These lecture notes constitute an expanded version of the course.
Author: Yung-Chen Lu
Publisher:
ISBN: 9783540902218
Category : Catastrophes (Mathematics)
Languages : en
Pages : 199
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Book Description
Author: Vladimir I. Arnol'd
Publisher: Springer Science & Business Media
ISBN: 3642969372
Category : Mathematics
Languages : en
Pages : 120
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Book Description
Author: James Montaldi
Publisher: Cambridge University Press
ISBN: 1009064398
Category : Mathematics
Languages : en
Pages : 450
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Book Description
Suitable for advanced undergraduates, postgraduates and researchers, this self-contained textbook provides an introduction to the mathematics lying at the foundations of bifurcation theory. The theory is built up gradually, beginning with the well-developed approach to singularity theory through right-equivalence. The text proceeds with contact equivalence of map-germs and finally presents the path formulation of bifurcation theory. This formulation, developed partly by the author, is more general and more flexible than the original one dating from the 1980s. A series of appendices discuss standard background material, such as calculus of several variables, existence and uniqueness theorems for ODEs, and some basic material on rings and modules. Based on the author's own teaching experience, the book contains numerous examples and illustrations. The wealth of end-of-chapter problems develop and reinforce understanding of the key ideas and techniques: solutions to a selection are provided.
Author: Vladimir I. Arnol'd
Publisher: Springer Science & Business Media
ISBN: 3642581242
Category : Mathematics
Languages : en
Pages : 161
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Book Description
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: Vladimir Igorevich Arnold
Publisher: Springer Science & Business Media
ISBN: 9783540505839
Category : Celestial mechanics
Languages : en
Pages : 264
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Book Description
'EMS 6' is the latest volume in the sub series 'Dynamical Systems of the Encyclopaedia'. It is the first of two volumes covering Singularity Theory, which, besides its fundamental use in Dynamical Systems and Bifurcation Theory, is an important part of other fields such as algebraic geometry, differential geometry and geometric optics.
Author: Arlie O. Petters
Publisher: Springer Science & Business Media
ISBN: 1461201454
Category : Science
Languages : en
Pages : 616
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Book Description
This monograph is the first to develop a mathematical theory of gravitational lensing. The theory applies to any finite number of deflector planes and highlights the distinctions between single and multiple plane lensing. Introductory material in Parts I and II present historical highlights and the astrophysical aspects of the subject. Part III employs the ideas and results of singularity theory to put gravitational lensing on a rigorous mathematical foundation.
Author: James William Bruce
Publisher: Cambridge University Press
ISBN: 9780521429993
Category : Mathematics
Languages : en
Pages : 344
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Book Description
This second edition is an invaluable textbook for anyone who would like an introduction to the modern theories of catastrophies and singularities.
Author: J. Barkley Rosser
Publisher: Springer Science & Business Media
ISBN: 9780792377702
Category : Business & Economics
Languages : en
Pages : 330
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Book Description
From Catastrophe to Chaos: A General Theory of Economic Discontinuities presents and unusual perspective on economics and economic analysis. Current economic theory largely depends upon assuming that the world is fundamentally continuous. However, an increasing amount of economic research has been done using approaches that allow for discontinuities such as catastrophe theory, chaos theory, synergetics, and fractal geometry. The spread of such approaches across a variety of disciplines of thought has constituted a virtual intellectual revolution in recent years. This book reviews the applications of these approaches in various subdisciplines of economics and draws upon past economic thinkers to develop an integrated view of economics as a whole from the perspective of inherent discontinuity.
