Variations On A Theme Of Euler

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Variations On A Theme Of Euler

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Author : Takashi Ono
language : en
Publisher:
Release Date : 2014-01-15

Variations On A Theme Of Euler written by Takashi Ono and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.

Variations On A Theme Of Euler

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Author : Takashi Ono
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Variations On A Theme Of Euler written by Takashi Ono 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 2013-03-09 with Mathematics categories.

The first six chapters and Appendix 1 of this book appeared in Japanese in a book of the same title 15years aga (Jikkyo, Tokyo, 1980).At the request of some people who do not wish to learn Japanese, I decided to rewrite my old work in English. This time, I added a chapter on the arithmetic of quadratic maps (Chapter 7) and Appendix 2, A Short Survey of Subsequent Research on Congruent Numbers, by M. Kida. Some 20 years ago, while rifling through the pages of Selecta Heinz Hopj (Springer, 1964), I noticed a system of three quadratic forms in four variables with coefficientsin Z that yields the map of the 3-sphere to the 2-sphere with the Hopf invariant r =1 (cf. Selecta, p. 52). Immediately I feit that one aspect of classical and modern number theory, including quadratic forms (Pythagoras, Fermat, Euler, and Gauss) and space elliptic curves as intersection of quadratic surfaces (Fibonacci, Fermat, and Euler), could be considered as the number theory of quadratic maps-especially of those maps sending the n-sphere to the m-sphere, i.e., the generalized Hopf maps. Having these in mind, I deliveredseverallectures at The Johns Hopkins University (Topics in Number Theory, 1973-1974, 1975-1976, 1978-1979, and 1979-1980). These lectures necessarily contained the following three basic areas of mathematics: v vi Preface Theta Simple Functions Aigebras Elliptic Curves Number Theory Figure P.l.

Six Themes On Variation

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Author : Steven James Cox
language : en
Publisher: American Mathematical Soc.
Release Date : 2004

Six Themes On Variation written by Steven James Cox 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 2004 with Computers categories.

The calculus of variations is a beautiful subject with a rich history and with origins in the minimization problems of calculus. Although it is now at the core of many modern mathematical fields, it does not have a well-defined place in most undergraduate mathematics curricula. This volume should nevertheless give the undergraduate reader a sense of its great character and importance. Interesting functionals, such as area or energy, often give rise to problems whose most natural solution occurs by differentiating a one-parameter family of variations of some function. The critical points of the functional are related to the solutions of the associated Euler-Lagrange equation. These differential equations are at the heart of the calculus of variations and its applications to wave mechanics, minimal surfaces, soap bubbles, and modeling traffic flow. All are readily accessible to advanced undergraduates. This book is derived from a workshop sponsored by Rice University. It is suitable for advanced undergraduates, graduate students and research mathematicians interested in the calculus of variations and its applications to other subjects.

Leonhard Euler S Contributions To The Method Of The Variation Of The Orbital Elements

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Author : Louise Ahrndt Golland
language : en
Publisher:
Release Date : 1991

Leonhard Euler S Contributions To The Method Of The Variation Of The Orbital Elements written by Louise Ahrndt Golland and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Celestial mechanics categories.

Leonhard Euler S Elastic Curves

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Author : Leonhard Euler
language : en
Publisher:
Release Date : 1933

Leonhard Euler S Elastic Curves written by Leonhard Euler and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1933 with Calculus of variations categories.

Euler Und Die Variationsrechnung

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Author : J C C. Adolf Kneser
language : en
Publisher:
Release Date : 1907

Euler Und Die Variationsrechnung written by J C C. Adolf Kneser and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1907 with categories.

Variational Methods In Optimization

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Author : Donald R. Smith
language : en
Publisher: Courier Corporation
Release Date : 1998-01-01

Variational Methods In Optimization written by Donald R. Smith and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-01 with Mathematics categories.

Highly readable text elucidates applications of the chain rule of differentiation, integration by parts, parametric curves, line integrals, double integrals, and elementary differential equations. 1974 edition.

Symmetry A Very Short Introduction

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Author : Ian Stewart
language : en
Publisher: OUP Oxford
Release Date : 2013-05-30

Symmetry A Very Short Introduction written by Ian Stewart and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-30 with Mathematics categories.

In the 1800s mathematicians introduced a formal theory of symmetry: group theory. Now a branch of abstract algebra, this subject first arose in the theory of equations. Symmetry is an immensely important concept in mathematics and throughout the sciences, and its applications range across the entire subject. Symmetry governs the structure of crystals, innumerable types of pattern formation, how systems change their state as parameters vary; and fundamental physics is governed by symmetries in the laws of nature. It is highly visual, with applications that include animal markings, locomotion, evolutionary biology, elastic buckling, waves, the shape of the Earth, and the form of galaxies. In this Very Short Introduction, Ian Stewart demonstrates its deep implications, and shows how it plays a major role in the current search to unify relativity and quantum theory. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

Significant Figures

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Author : Ian Stewart
language : en
Publisher: Profile Books
Release Date : 2017-08-10

Significant Figures written by Ian Stewart and has been published by Profile Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-10 with Science categories.

Which mathematician elaborated a crucial concept the night before he died in a duel? Who funded his maths and medical career through gambling and chess? Who learned maths from her wallpaper? Ian Stewart presents the extraordinary lives and amazing discoveries of twenty-five of history's greatest mathematicians from Archimedes and Liu Hui to Benoit Mandelbrot and William Thurston. His subjects are the inspiring individuals from all over the world who have made crucial contributions to mathematics. They include the rediscovered geniuses Srinivasa Ramanujan and Emmy Noether, alongside the towering figures of Muhammad al-Khwarizmi (inventor of the algorithm), Pierre de Fermat, Isaac Newton, Carl Friedrich Gauss, Nikolai Ivanovich Lobachevsky, Bernhard Reimann (precursor to Einstein), Henri Poincar, Ada Lovelace (arguably the first computer programmer), Kurt Gdel and Alan Turing. Ian Stewart's vivid accounts are fascinating in themselves and, taken together, cohere into a riveting history of key steps in the development of mathematics.

Statistics On The Table

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Author : Stephen M. Stigler
language : en
Publisher: Harvard University Press
Release Date : 2002-09-30

Statistics On The Table written by Stephen M. Stigler and has been published by Harvard University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-09-30 with Mathematics categories.

This lively collection of essays examines in witty detail the history of some of the concepts involved in bringing statistical argument "to the table," and some of the pitfalls that have been encountered. The topics range from seventeenth-century medicine and the circulation of blood, to the cause of the Great Depression and the effect of the California gold discoveries of 1848 upon price levels, to the determinations of the shape of the Earth and the speed of light, to the meter of Virgil's poetry and the prediction of the Second Coming of Christ. The title essay tells how the statistician Karl Pearson came to issue the challenge to put "statistics on the table" to the economists Marshall, Keynes, and Pigou in 1911. The 1911 dispute involved the effect of parental alcoholism upon children, but the challenge is general and timeless: important arguments require evidence, and quantitative evidence requires statistical evaluation. Some essays examine deep and subtle statistical ideas such as the aggregation and regression paradoxes; others tell of the origin of the Average Man and the evaluation of fingerprints as a forerunner of the use of DNA in forensic science. Several of the essays are entirely nontechnical; all examine statistical ideas with an ironic eye for their essence and what their history can tell us about current disputes.