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Author: Vladimir Arnold
Publisher: Springer Science & Business Media
ISBN: 9780792310389
Category : Mathematics
Languages : en
Pages : 284
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Book Description
One service mathematics has rendered the 'Et moi, ... ) si j'avait su comment en revenir, human race. It has put common sense back je n'y serais point aile.' Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non The series is divergent; therefore we may be sense'. ErieT. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
Author: Vladimir Arnold
Publisher: Springer Science & Business Media
ISBN: 9780792310389
Category : Mathematics
Languages : en
Pages : 284
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Book Description
One service mathematics has rendered the 'Et moi, ... ) si j'avait su comment en revenir, human race. It has put common sense back je n'y serais point aile.' Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non The series is divergent; therefore we may be sense'. ErieT. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
Author: Vladimir Igorevič Arnolʹd
Publisher:
ISBN: 9789075351019
Category : Caustics (Optics)
Languages : en
Pages : 0
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Book Description
Author: V.I. Arnold
Publisher: Springer Science & Business Media
ISBN: 1461251540
Category : Mathematics
Languages : en
Pages : 390
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Book Description
... there is nothing so enthralling, so grandiose, nothing that stuns or captivates the human soul quite so much as a first course in a science. After the first five or six lectures one already holds the brightest hopes, already sees oneself as a seeker after truth. I too have wholeheartedly pursued science passionately, as one would a beloved woman. I was a slave, and sought no other sun in my life. Day and night I crammed myself, bending my back, ruining myself over my books; I wept when I beheld others exploiting science fot personal gain. But I was not long enthralled. The truth is every science has a beginning, but never an end - they go on for ever like periodic fractions. Zoology, for example, has discovered thirty-five thousand forms of life ... A. P. Chekhov. "On the road" In this book a start is made to the "zoology" of the singularities of differentiable maps. This theory is a young branch of analysis which currently occupies a central place in mathematics; it is the crossroads of paths leading from very abstract corners of mathematics (such as algebraic and differential geometry and topology, Lie groups and algebras, complex manifolds, commutative algebra and the like) to the most applied areas (such as differential equations and dynamical systems, optimal control, the theory of bifurcations and catastrophes, short-wave and saddle-point asymptotics and geometrical and wave optics).
Author: Vladimir Igorevič Arnolʹd
Publisher:
ISBN: 9789075351019
Category : Caustics (Optics)
Languages : en
Pages : 259
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Book Description
Author: Vladimir I. Arnold
Publisher: Springer Science & Business Media
ISBN: 9783540206149
Category : Mathematics
Languages : en
Pages : 664
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Book Description
Vladimir Arnold is one of the most outstanding mathematicians of our time Many of these problems are at the front line of current research
Author: Denis Cheniot
Publisher: World Scientific
ISBN: 9812707492
Category : Mathematics
Languages : en
Pages : 1083
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Book Description
The Singularity School and Conference took place in Luminy, Marseille, from January 24th to February 25th 2005. More than 180 mathematicians from over 30 countries converged to discuss recent developments in singularity theory. The volume contains the elementary and advanced courses conducted by singularities specialists during the conference, general lectures on singularity theory, and lectures on applications of the theory to various domains. The subjects range from geometry and topology of singularities, through real and complex singularities, to applications of singularities.
Author: Andrej B¢na
Publisher: World Scientific
ISBN: 9814295515
Category : Science
Languages : en
Pages : 295
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Book Description
This textbook ? incorporated with many illuminating examples and exercises ? is aimed at graduate students of physical sciences and engineering. The purpose is to provide a background of physics and underlying mathematics for the concept of rays, filling the gap between mathematics and physics textbooks for a coherent treatment of all topics. The authors' emphasis and extremely good presentation of the theory of characteristics, which defines the rays, accentuate the beauty and versatility of this theory. To this end, the rigour of the formulation ? by a pure mathematician's standards ? is downplayed to highlight the physical meaning and to make the subject accessible to a wider audience. The authors describe in detail the theory of characteristics for different types of differential equations, the applications to wave propagation in different types of media, and the phenomena such as caustics.
Author: Andrej Bona
Publisher: World Scientific
ISBN: 9811226482
Category : Science
Languages : en
Pages : 357
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Book Description
Characteristics and asymptotics of partial differential equations play an important role in mathematical physics since they lead to insightful solutions of complex problems that might not be solvable otherwise. They constitute, however, a difficult subject, and the purpose of this book, with its additions and refinements that led to its third edition, is to present this subject in an accessible manner, without decreasing the rigor. As any method, characteristics and asymptotics have their limitations. This important issue is addressed in the last chapter, where we discuss caustics, which must be understood in applications of the method, and which constitute a fertile ground for further mathematical research.The book is both a research reference and a textbook. Its careful and explanatory style, which includes numerous exercises with detailed solutions, makes it an excellent textbook for senior undergraduate and graduate courses, as well as for independent studies. Six appendices are provided, which form a self-contained course on applied mathematics and can be used as a textbook on its own.
Author: J.F Nye
Publisher: CRC Press
ISBN: 9780750306102
Category : Technology & Engineering
Languages : en
Pages : 354
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Book Description
A new kind of optics has grown up during the last 25 years. Geometrical optics has been studied for centuries (the law of reflection was known to the ancient Greeks) and wave optics (heralded by Huygens' Treatise on Light) has been studied for more than 300 years. But in the mid 1970s it began to be understood that when natural processes focus light, as when sunlight is reflected from the sea at sunset, the light caustics that are produced have a systematic behavior previously unrecognized. Natural Focusing and Fine Structure of Light: Caustics and Wave Dislocations provides a definitive account of how classical optics has been reconstructed in a modern way by emphasizing the hierarchy of singularities that exists in light fields. The book discusses the singularities of geometrical optics and their systematization by catastrophe theory. It explores the diffraction patterns associated with caustics that are dominated by wave dislocations, line singularities of the phase, and analogous to crystal dislocations. The book is a perfect blend of mathematics and physics, combining theory, computer simulation, and beautiful experimental photographs of the phenomena studied.
Author:
Publisher: Academic Press
ISBN: 1483297454
Category : Computers
Languages : en
Pages : 532
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Book Description
The decades of the 1970s and 1980s were a very exciting period of discovery in the field of computer graphics. It was a time when new rendering algorithms, different modeling strategies, clever animation techniques,and significant advances in photorealism were being made. Complementing these software developments, hardware systems were dominated by raster technology and programmers had access to excellent workstations on which to develop their graphics systems.In the 1990s, incredible advances in computer graphics are far surpassing developments made during the last twenty years. Yesterdays computer graphics have given way to todays virtual reality. This volume brings together contributions from internationalexperts on the diverse, yet important, range of topics that impact the design and application of virtual environments. Topics covered include 3-D modeling; new approaches to rendering virtual environments; recent research into the problems of animating and visualizing virtual environments; applications for virtual reality systems; and simulation of complex behaviors.Computer Graphics: Developments in Virtual Environments provides a unique opportunity to examine current practice and expert thinking. It is essential reading for students, practitioners, researchers, or anyone else who wishes to find out more about this exciting area.Provides comprehensive coverage of the latest topics in computer graphics, virtual reality, and humancomputer interactionContributors are international experts in the fieldExamines many real-world applications in a wide variety of fields
