Huygens and Barrow, Newton and Hooke

Pioneers in mathematical analysis and catastrophe theory from evolvents to quasicrystals
Author: Vladimir I. Arnold
Publisher: Birkhäuser
ISBN: 3034891296
Category: Mathematics
Page: 118
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Translated from the Russian by E.J.F. Primrose "Remarkable little book." -SIAM REVIEW V.I. Arnold, who is renowned for his lively style, retraces the beginnings of mathematical analysis and theoretical physics in the works (and the intrigues!) of the great scientists of the 17th century. Some of Huygens' and Newton's ideas. several centuries ahead of their time, were developed only recently. The author follows the link between their inception and the breakthroughs in contemporary mathematics and physics. The book provides present-day generalizations of Newton's theorems on the elliptical shape of orbits and on the transcendence of abelian integrals; it offers a brief review of the theory of regular and chaotic movement in celestial mechanics, including the problem of ports in the distribution of smaller planets and a discussion of the structure of planetary rings.

The Unreasonable Effectiveness of Number Theory


Author: Stefan Andrus Burr,George E. Andrews
Publisher: American Mathematical Soc.
ISBN: 9780821855010
Category: Mathematics
Page: 125
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This book is based on the AMS Short Course, The Unreasonable Effectiveness of Number Theory, held in Orono, Maine, in August 1991. This Short Course provided some views into the great breadth of applications of number theory outside cryptology and highlighted the power and applicability of number-theoretic ideas. Because number theory is one of the most accessible areas of mathematics, this book will appeal to a general mathematical audience as well as to researchers in other areas of science and engineering who wish to learn how number theory is being applied outside of mathematics. All of the chapters are written by leading specialists in number theory and provides excellent introduction to various applications.

Catastrophe Theory


Author: Vladimir I. Arnol'd
Publisher: Springer Science & Business Media
ISBN: 3642581242
Category: Mathematics
Page: 150
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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.

Optimization

Insights and Applications
Author: Jan Brinkhuis,Vladimir Tikhomirov
Publisher: Princeton University Press
ISBN: 9781400829361
Category: Mathematics
Page: 680
View: 6980

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This self-contained textbook is an informal introduction to optimization through the use of numerous illustrations and applications. The focus is on analytically solving optimization problems with a finite number of continuous variables. In addition, the authors provide introductions to classical and modern numerical methods of optimization and to dynamic optimization. The book's overarching point is that most problems may be solved by the direct application of the theorems of Fermat, Lagrange, and Weierstrass. The authors show how the intuition for each of the theoretical results can be supported by simple geometric figures. They include numerous applications through the use of varied classical and practical problems. Even experts may find some of these applications truly surprising. A basic mathematical knowledge is sufficient to understand the topics covered in this book. More advanced readers, even experts, will be surprised to see how all main results can be grounded on the Fermat-Lagrange theorem. The book can be used for courses on continuous optimization, from introductory to advanced, for any field for which optimization is relevant.

Pseudoperiodic topology


Author: Vladimir Igorevich Arnolʹd,Maxim Kontsevich,Anton Zorich
Publisher: N.A
ISBN: 9780821820940
Category:
Page: 178
View: 3995

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Chaos, Gaia, Eros

A Chaos Pioneer Uncovers the Three Great Streams of History
Author: Ralph Abraham
Publisher: Harper San Francisco
ISBN: N.A
Category: Philosophy
Page: 263
View: 7904

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A modern philosophy suggests that there are three main forces working to shape our lives

Choice


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Academic libraries
Page: N.A
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Spirals

from Theodorus to chaos
Author: Philip J. Davis,Walter Gautschi,A. Iserles
Publisher: A K Peters Ltd
ISBN: N.A
Category: Mathematics
Page: 237
View: 7647

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The Key to Newton's Dynamics

The Kepler Problem and the Principia
Author: J. Bruce Brackenridge
Publisher: Univ of California Press
ISBN: 9780520916852
Category: Science
Page: 330
View: 3804

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While much has been written on the ramifications of Newton's dynamics, until now the details of Newton's solution were available only to the physics expert. The Key to Newton's Dynamics clearly explains the surprisingly simple analytical structure that underlies the determination of the force necessary to maintain ideal planetary motion. J. Bruce Brackenridge sets the problem in historical and conceptual perspective, showing the physicist's debt to the works of both Descartes and Galileo. He tracks Newton's work on the Kepler problem from its early stages at Cambridge before 1669, through the revival of his interest ten years later, to its fruition in the first three sections of the first edition of the Principia.

Quicksilver

The Baroque Cycle #1
Author: Neal Stephenson
Publisher: Harper Collins
ISBN: 0060833165
Category: Fiction
Page: 480
View: 7037

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In which Daniel Waterhouse, fearless thinker and courageous Puritan, pursues knowledge in the company of the greatest minds of Baroque-era Europe -- in a chaotic world where reason wars with the bloody ambitions of the mighty, and where catastrophe, natural or otherwise, can alter the political landscape overnight.