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 : 1994-11-30

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 1994-11-30 with Mathematics categories.

The text, a translation of Dr. Ono's earlier work, provides a solution to this problem by employing three areas of mathematics: linear algebra, algebraic geometry, and simple algebras. This English-language edition presents a new chapter on arithmetic of quadratic maps, along with an appendix featuring a short survey of subsequent research on congruent numbers by Masanari Kida. The original appendix containing historical and scientific comments on Euler's Elements of Algebra is also included.

Lie Groups And Algebras With Applications To Physics Geometry And Mechanics

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Author : D.H. Sattinger
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11

Lie Groups And Algebras With Applications To Physics Geometry And Mechanics written by D.H. Sattinger 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 2013-11-11 with Mathematics categories.

This book is intended as an introductory text on the subject of Lie groups and algebras and their role in various fields of mathematics and physics. It is written by and for researchers who are primarily analysts or physicists, not algebraists or geometers. Not that we have eschewed the algebraic and geo metric developments. But we wanted to present them in a concrete way and to show how the subject interacted with physics, geometry, and mechanics. These interactions are, of course, manifold; we have discussed many of them here-in particular, Riemannian geometry, elementary particle physics, sym metries of differential equations, completely integrable Hamiltonian systems, and spontaneous symmetry breaking. Much ofthe material we have treated is standard and widely available; but we have tried to steer a course between the descriptive approach such as found in Gilmore and Wybourne, and the abstract mathematical approach of Helgason or Jacobson. Gilmore and Wybourne address themselvesto the physics community whereas Helgason and Jacobson address themselves to the mathematical community. This book is an attempt to synthesize the two points of view and address both audiences simultaneously. We wanted to present the subject in a way which is at once intuitive, geometric, applications oriented, mathematically rigorous, and accessible to students and researchers without an extensive background in physics, algebra, or geometry.

Variational Calculus

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Author : Jean-Pierre Bourguignon
language : en
Publisher: Springer Nature
Release Date : 2022-11-12

Variational Calculus written by Jean-Pierre Bourguignon and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-12 with Mathematics categories.

This book provides a comprehensive introduction to the Calculus of Variations and its use in modelling mechanics and physics problems. Presenting a geometric approach to the subject, it progressively guides the reader through this very active branch of mathematics, accompanying key statements with a huge variety of exercises, some of them solved. Stressing the need to overcome limitations of the initial point of view, and emphasising the interconnectivity of various branches of mathematics (algebra, analysis and geometry), the book includes some advanced material to challenge the most motivated students. Systematic, short historical notes provide details on the subject’s odyssey, and how new tools have been developed over the last two centuries. This English translation updates a set of notes for a course first given at the École polytechnique in 1987. It will be accessible to graduate students and advanced undergraduates.

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.

Steps Into Analytic Number Theory

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Author : Paul Pollack
language : en
Publisher: Springer Nature
Release Date : 2021-02-08

Steps Into Analytic Number Theory written by Paul Pollack and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-08 with Mathematics categories.

This problem book gathers together 15 problem sets on analytic number theory that can be profitably approached by anyone from advanced high school students to those pursuing graduate studies. It emerged from a 5-week course taught by the first author as part of the 2019 Ross/Asia Mathematics Program held from July 7 to August 9 in Zhenjiang, China. While it is recommended that the reader has a solid background in mathematical problem solving (as from training for mathematical contests), no possession of advanced subject-matter knowledge is assumed. Most of the solutions require nothing more than elementary number theory and a good grasp of calculus. Problems touch at key topics like the value-distribution of arithmetic functions, the distribution of prime numbers, the distribution of squares and nonsquares modulo a prime number, Dirichlet's theorem on primes in arithmetic progressions, and more. This book is suitable for any student with a special interest in developing problem-solving skills in analytic number theory. It will be an invaluable aid to lecturers and students as a supplementary text for introductory Analytic Number Theory courses at both the undergraduate and graduate level.

Leonhard Euler

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Author : Robert E. Bradley
language : en
Publisher: Elsevier
Release Date : 2007-03-20

Leonhard Euler written by Robert E. Bradley and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-03-20 with Mathematics categories.

The year 2007 marks the 300th anniversary of the birth of one of the Enlightenment's most important mathematicians and scientists, Leonhard Euler. This volume is a collection of 24 essays by some of the world's best Eulerian scholars from seven different countries about Euler, his life and his work. Some of the essays are historical, including much previously unknown information about Euler's life, his activities in the St. Petersburg Academy, the influence of the Russian Princess Dashkova, and Euler's philosophy. Others describe his influence on the subsequent growth of European mathematics and physics in the 19th century. Still others give technical details of Euler's innovations in probability, number theory, geometry, analysis, astronomy, mechanics and other fields of mathematics and science.- Over 20 essays by some of the best historians of mathematics and science, including Ronald Calinger, Peter Hoffmann, Curtis Wilson, Kim Plofker, Victor Katz, Ruediger Thiele, David Richeson, Robin Wilson, Ivor Grattan-Guinness and Karin Reich- New details of Euler's life in two essays, one by Ronald Calinger and one he co-authored with Elena Polyakhova- New information on Euler's work in differential geometry, series, mechanics, and other important topics including his influence in the early 19th century

Excursions In Multiplicative Number Theory

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Author : Olivier Ramaré
language : en
Publisher: Springer Nature
Release Date : 2022-03-03

Excursions In Multiplicative Number Theory written by Olivier Ramaré and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-03 with Mathematics categories.

This textbook offers a unique exploration of analytic number theory that is focused on explicit and realistic numerical bounds. By giving precise proofs in simplified settings, the author strategically builds practical tools and insights for exploring the behavior of arithmetical functions. An active learning style is encouraged across nearly three hundred exercises, making this an indispensable resource for both students and instructors. Designed to allow readers several different pathways to progress from basic notions to active areas of research, the book begins with a study of arithmetic functions and notions of arithmetical interest. From here, several guided “walks” invite readers to continue, offering explorations along three broad themes: the convolution method, the Levin–Faĭnleĭb theorem, and the Mellin transform. Having followed any one of the walks, readers will arrive at “higher ground”, where they will find opportunities for extensions and applications, such as the Selberg formula, Brun’s sieve, and the Large Sieve Inequality. Methodology is emphasized throughout, with frequent opportunities to explore numerically using computer algebra packages Pari/GP and Sage. Excursions in Multiplicative Number Theory is ideal for graduate students and upper-level undergraduate students who are familiar with the fundamentals of analytic number theory. It will also appeal to researchers in mathematics and engineering interested in experimental techniques in this active area.

Leonhard Euler

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Author : Andreas K. Heyne
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-01-22

Leonhard Euler written by Andreas K. Heyne 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 2007-01-22 with Biography & Autobiography categories.

This illustrated account of Euler's life and livings is embedded in the great political developments of his time, particularly in Austria, Prussia and Russia. The comic follows the life of the genius from Basel, who, born 300 years ago, set out to change the scientific world.

Calculus In A Real And Complex World

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Author : Frank Wattenberg
language : en
Publisher: Brooks/Cole
Release Date : 1995

Calculus In A Real And Complex World written by Frank Wattenberg and has been published by Brooks/Cole this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.