Singularities Of Caustics And Wave Fronts
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Singularities Of Caustics And Wave Fronts
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Author : Vladimir Arnold
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Singularities Of Caustics And Wave Fronts written by Vladimir Arnold and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
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.
Singularities Of Caustics And Wave Fronts
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Author : Vladimir Arnold
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-11-30
Singularities Of Caustics And Wave Fronts written by Vladimir Arnold and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-11-30 with Mathematics categories.
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.
Singularities Of Caustics And Wave Fronts
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Author : Vladimir Igorevič Arnolʹd
language : en
Publisher:
Release Date : 1990
Singularities Of Caustics And Wave Fronts written by Vladimir Igorevič Arnolʹd and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Caustics (Optics) categories.
Singularities Of Caustics And Wave Fronts
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Author : Vladimir Igorevič Arnolʹd
language : en
Publisher:
Release Date : 1990
Singularities Of Caustics And Wave Fronts written by Vladimir Igorevič Arnolʹd and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Caustics (Optics) categories.
Singularities Of Differentiable Maps
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Author : V.I. Arnold
language : en
Publisher: Springer Science & Business Media
Release Date : 1985-01-01
Singularities Of Differentiable Maps written by V.I. Arnold and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-01-01 with Mathematics categories.
... 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).
Singularities Formation Structure And Propagation
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Author : J. Eggers
language : en
Publisher: Cambridge University Press
Release Date : 2015-09-10
Singularities Formation Structure And Propagation written by J. Eggers and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-10 with Mathematics categories.
This book explores a wide range of singular phenomena, providing mathematical tools for understanding them and highlighting their common features.
Progress In Optics
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Author :
language : en
Publisher: Elsevier
Release Date : 1980-01-01
Progress In Optics written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980-01-01 with Science categories.
Progress in Optics
Dynamical Systems V
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Author : V.I. Arnold
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Dynamical Systems V written by V.I. Arnold and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
Bifurcation theory and catastrophe theory are two well-known areas within the field of dynamical systems. Both are studies of smooth systems, focusing on properties that seem to be manifestly non-smooth. Bifurcation theory is concerned with the sudden changes that occur in a system when one or more parameters are varied. Examples of such are familiar to students of differential equations, from phase portraits. Understanding the bifurcations of the differential equations that describe real physical systems provides important information about the behavior of the systems. Catastrophe theory became quite famous during the 1970's, mostly because of the sensation caused by the usually less than rigorous applications of its principal ideas to "hot topics", such as the characterization of personalities and the difference between a "genius" and a "maniac". Catastrophe theory is accurately described as singularity theory and its (genuine) applications. The authors of this book, previously published as Volume 5 of the Encyclopaedia, have given a masterly exposition of these two theories, with penetrating insight.
Wavefronts And Rays As Characteristics And Asymptotics
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Author : Andrej Bóna
language : en
Publisher: World Scientific Publishing Company
Release Date : 2011-05-09
Wavefronts And Rays As Characteristics And Asymptotics written by Andrej Bóna and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-05-09 with Science categories.
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.
Topics In Singularity Theory
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Author : Alekseĭ Nikolaevich Khovanskiĭ
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Topics In Singularity Theory written by Alekseĭ Nikolaevich Khovanskiĭ and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Geometry, Projective categories.