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Euler As Physicist
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Book Synopsis Euler as Physicist by : Dieter Suisky
Download or read book Euler as Physicist written by Dieter Suisky and published by Springer Science & Business Media. This book was released on 2008-12-05 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of the book is the development of physics in the 18th century centered upon the fundamental contributions of Leonhard Euler to physics and mathematics. This is the first book devoted to Euler as a physicist. Classical mechanics are reconstructed in terms of the program initiated by Euler in 1736 and its completion over the following decades until 1760. The book examines how Euler coordinated his progress in mathematics with his progress in physics.
Book Synopsis Dr. Euler's Fabulous Formula by : Paul J. Nahin
Download or read book Dr. Euler's Fabulous Formula written by Paul J. Nahin and published by Princeton University Press. This book was released on 2017-04-04 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the mid-eighteenth century, Swiss-born mathematician Leonhard Euler developed a formula so innovative and complex that it continues to inspire research, discussion, and even the occasional limerick. Dr. Euler's Fabulous Formula shares the fascinating story of this groundbreaking formula—long regarded as the gold standard for mathematical beauty—and shows why it still lies at the heart of complex number theory. In some ways a sequel to Nahin's An Imaginary Tale, this book examines the many applications of complex numbers alongside intriguing stories from the history of mathematics. Dr. Euler's Fabulous Formula is accessible to any reader familiar with calculus and differential equations, and promises to inspire mathematicians for years to come.
Book Synopsis Euler's Pioneering Equation by : Robin Wilson
Download or read book Euler's Pioneering Equation written by Robin Wilson and published by Oxford University Press. This book was released on 2018-02-22 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1988 The Mathematical Intelligencer, a quarterly mathematics journal, carried out a poll to find the most beautiful theorem in mathematics. Twenty-four theorems were listed and readers were invited to award each a 'score for beauty'. While there were many worthy competitors, the winner was 'Euler's equation'. In 2004 Physics World carried out a similar poll of 'greatest equations', and found that among physicists Euler's mathematical result came second only to Maxwell's equations. The Stanford mathematician Keith Devlin reflected the feelings of many in describing it as "like a Shakespearian sonnet that captures the very essence of love, or a painting which brings out the beauty of the human form that is far more than just skin deep, Euler's equation reaches down into the very depths of existence". What is it that makes Euler's identity, eiπ + 1 = 0, so special? In Euler's Pioneering Equation Robin Wilson shows how this simple, elegant, and profound formula links together perhaps the five most important numbers in mathematics, each associated with a story in themselves: the number 1, the basis of our counting system; the concept of zero, which was a major development in mathematics, and opened up the idea of negative numbers; π an irrational number, the basis for the measurement of circles; the exponential e, associated with exponential growth and logarithms; and the imaginary number i, the square root of -1, the basis of complex numbers. Following a chapter on each of the elements, Robin Wilson discusses how the startling relationship between them was established, including the several near misses to the discovery of the formula.
Download or read book Euler written by William Dunham and published by American Mathematical Society. This book was released on 2022-01-13 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: Leonhard Euler was one of the most prolific mathematicians that have ever lived. This book examines the huge scope of mathematical areas explored and developed by Euler, which includes number theory, combinatorics, geometry, complex variables and many more. The information known to Euler over 300 years ago is discussed, and many of his advances are reconstructed. Readers will be left in no doubt about the brilliance and pervasive influence of Euler's work.
Book Synopsis Leonhard Euler by : Ronald S. Calinger
Download or read book Leonhard Euler written by Ronald S. Calinger and published by Princeton University Press. This book was released on 2019-12-03 with total page 689 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This is the first full-scale biography of Leonhard Euler (1707-83), one of the greatest mathematicians and theoretical physicists of all time. In this comprehensive and authoritative account, Ronald Calinger connects the story of Euler's eventful life to the astonishing achievements that place him in the company of Archimedes, Newton, and Gauss. Drawing chiefly on Euler's massive published works and correspondence, which fill more than eighty volumes so far, this biography sets Euler's work in its multilayered context--personal, intellectual, institutional, political, cultural, religious, and social. It is a story of nearly incessant accomplishment, from Euler's fundamental contributions to almost every area of pure and applied mathematics--especially calculus, number theory, notation, optics, and celestial, rational, and fluid mechanics--to his advancements in shipbuilding, telescopes, ballistics, cartography, chronology, and music theory. The narrative takes the reader from Euler's childhood and education in Basel through his first period in St. Petersburg, 1727-41, where he gained a European reputation by solving the Basel problem and systematically developing analytical mechanics. Invited to Berlin by Frederick II, Euler published his famous Introductio in analysin infinitorum, devised continuum mechanics, and proposed a pulse theory of light. Returning to St. Petersburg in 1766, he created the analytical calculus of variations, developed the most precise lunar theory of the time that supported Newton's dynamics, and published the best-selling Letters to a German Princess--all despite eye problems that ended in near-total blindness. In telling the remarkable story of Euler and how his achievements brought pan-European distinction to the Petersburg and Berlin academies of sciences, the book also demonstrates with new depth and detail the central role of mathematics in the Enlightenment."--Publisher's description.
Book Synopsis Leonhard Euler's Letters to a German Princess by : Ronald S Calinger
Download or read book Leonhard Euler's Letters to a German Princess written by Ronald S Calinger and published by Morgan & Claypool Publishers. This book was released on 2019-06-28 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: Leonhard Euler's Letters to a German Princess: A Milestone in the History of Physics Textbooks and More is a milestone in the history of physics textbooks and the instruction of women in the sciences. It also covers views of its author on epistemology, religion, and innovations in scientific equipment, including telescopes and microscopes. Today, 250 years later, we study this work of Euler's as a foundation for the history of physics teaching and analyze the letters from an historical and pedagogical point of view.
Book Synopsis Leonhard Euler by : Robert E. Bradley
Download or read book Leonhard Euler written by Robert E. Bradley and published by Elsevier. This book was released on 2007-03-20 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Letters of Euler on Different Subjects in Physics and Philosophy by : Leonhard Euler
Download or read book Letters of Euler on Different Subjects in Physics and Philosophy written by Leonhard Euler and published by . This book was released on 1802 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Leonhard Euler and the Foundations of Celestial Mechanics by : Dora Musielak
Download or read book Leonhard Euler and the Foundations of Celestial Mechanics written by Dora Musielak and published by Springer Nature. This book was released on 2022-11-01 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: The intention of this book is to shine a bright light on the intellectual context of Euler’s contributions to physics and mathematical astronomy. Leonhard Euler is one of the most important figures in the history of science, a blind genius who introduced mathematical concepts and many analytical tools to help us understand and describe the universe. Euler also made a monumental contribution to astronomy and orbital mechanics, developing what he called astronomia mechanica. Orbital mechanics of artificial satellites and spacecraft is based on Euler’s analysis of astromechanics. However, previous books have often neglected many of his discoveries in this field. For example, orbital mechanics texts refer to the five equilibrium points in the Sun-Earth-Moon system as Lagrange points, failing to credit Euler who first derived the differential equations for the general n-body problem and who discovered the three collinear points in the three-body problem of celestial mechanics. These equilibrium points are essential today in space exploration; the James Webb Space Telescope (successor to the Hubble), for example, now orbits the Sun near L2, one of the collinear points of the Sun-Earth-Moon system, while future missions to study the universe will place observatories in orbit around Sun-Earth and Earth-Moon equilibrium points that should be properly called Euler-Lagrange points. In this book, the author uses Euler’s memoirs, correspondence, and other scholarly sources to explore how he established the mathematical groundwork for the rigorous study of motion in our Solar System. The reader will learn how he studied comets and eclipses, derived planetary orbits, and pioneered the study of planetary perturbations, and how, old and blind, Euler put forward the most advanced lunar theory of his time.
Book Synopsis Newton-Euler Dynamics by : Mark D. Ardema
Download or read book Newton-Euler Dynamics written by Mark D. Ardema and published by Springer Science & Business Media. This book was released on 2006-10-28 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unlike other books on this subject, which tend to concentrate on 2-D dynamics, this text focuses on the application of Newton-Euler methods to complex, real-life 3-D dynamics problems. It is thus ideal for elective courses in intermediate dynamics.
Download or read book Euler's Gem written by David S. Richeson and published by Princeton University Press. This book was released on 2019-07-23 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: How a simple equation reshaped mathematics Leonhard Euler’s polyhedron formula describes the structure of many objects—from soccer balls and gemstones to Buckminster Fuller’s buildings and giant all-carbon molecules. Yet Euler’s theorem is so simple it can be explained to a child. From ancient Greek geometry to today’s cutting-edge research, Euler’s Gem celebrates the discovery of Euler’s beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. Using wonderful examples and numerous illustrations, David Richeson presents this mathematical idea’s many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map. Filled with a who’s who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem’s development, Euler’s Gem will fascinate every mathematics enthusiast. This paperback edition contains a new preface by the author.
Book Synopsis Letters of Euler on Different Subjects in Physics and Philosophy by : Leonhard Euler
Download or read book Letters of Euler on Different Subjects in Physics and Philosophy written by Leonhard Euler and published by . This book was released on 1802 with total page 558 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Legacy of Leonhard Euler by : Lokenath Debnath
Download or read book The Legacy of Leonhard Euler written by Lokenath Debnath and published by World Scientific. This book was released on 2010 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book primarily serves as a historical research monograph on the biographical sketch and career of Leonhard Euler and his major contributions to numerous areas in the mathematical and physical sciences. It contains fourteen chapters describing Euler''s works on number theory, algebra, geometry, trigonometry, differential and integral calculus, analysis, infinite series and infinite products, ordinary and elliptic integrals and special functions, ordinary and partial differential equations, calculus of variations, graph theory and topology, mechanics and ballistic research, elasticity and fluid mechanics, physics and astronomy, probability and statistics. The book is written to provide a definitive impression of Euler''s personal and professional life as well as of the range, power, and depth of his unique contributions. This tricentennial tribute commemorates Euler the great man and Euler the universal mathematician of all time. Based on the author''s historically motivated method of teaching, special attention is given to demonstrate that Euler''s work had served as the basis of research and developments of mathematical and physical sciences for the last 300 years. An attempt is also made to examine his research and its relation to current mathematics and science. Based on a series of Euler''s extraordinary contributions, the historical development of many different subjects of mathematical sciences is traced with a linking commentary so that it puts the reader at the forefront of current research. Erratum. Sample Chapter(s). Chapter 1: Mathematics Before Leonhard Euler (434 KB). Contents: Mathematics Before Leonhard Euler; Brief Biographical Sketch and Career of Leonhard Euler; Euler''s Contributions to Number Theory and Algebra; Euler''s Contributions to Geometry and Spherical Trigonometry; Euler''s Formula for Polyhedra, Topology and Graph Theory; Euler''s Contributions to Calculus and Analysis; Euler''s Contributions to the Infinite Series and the Zeta Function; Euler''s Beta and Gamma Functions and Infinite Products; Euler and Differential Equations; The Euler Equations of Motion in Fluid Mechanics; Euler''s Contributions to Mechanics and Elasticity; Euler''s Work on the Probability Theory; Euler''s Contributions to Ballistics; Euler and His Work on Astronomy and Physics. Readership: Undergraduate and graduate students of mathematics, mathematics education, physics, engineering and science. As well as professionals and prospective mathematical scientists.
Book Synopsis The Functions of Mathematical Physics by : Harry Hochstadt
Download or read book The Functions of Mathematical Physics written by Harry Hochstadt and published by Courier Corporation. This book was released on 2012-04-30 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: A modern classic, this clearly written, incisive textbook provides a comprehensive, detailed survey of the functions of mathematical physics, a field of study straddling the somewhat artificial boundary between pure and applied mathematics. In the 18th and 19th centuries, the theorists who devoted themselves to this field — pioneers such as Gauss, Euler, Fourier, Legendre, and Bessel — were searching for mathematical solutions to physical problems. Today, although most of the functions have practical applications, in areas ranging from the quantum-theoretical model of the atom to the vibrating membrane, some, such as those related to the theory of discontinuous groups, still remain of purely mathematical interest. Chapters One and Two examine orthogonal polynomials, with sections on such topics as the recurrence formula, the Christoffel-Darboux formula, the Weierstrass approximation theorem, and the application of Hermite polynomials to quantum mechanics. Chapter Three is devoted to the principal properties of the gamma function, including asymptotic expansions and Mellin-Barnes integrals. Chapter Four covers hypergeometric functions, including a review of linear differential equations with regular singular points, and a general method for finding integral representations. Chapters Five and Six are concerned with the Legendre functions and their use in the solutions of Laplace's equation in spherical coordinates, as well as problems in an n-dimension setting. Chapter Seven deals with confluent hypergeometric functions, and Chapter Eight examines, at length, the most important of these — the Bessel functions. Chapter Nine covers Hill's equations, including the expansion theorems.
Book Synopsis Euler Through Time by : V. S. Varadarajan
Download or read book Euler Through Time written by V. S. Varadarajan and published by American Mathematical Soc.. This book was released on 2006 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Euler is one of the greatest and most prolific mathematicians of all time. He wrote the first accessible books on calculus, created the theory of circular functions, and discovered new areas of research such as elliptic integrals, the calculus of variations, graph theory, divergent series, and so on. It took hundreds of years for his successors to develop in full the theories he began, and some of his themes are still at the center of today's mathematics. It is of great interesttherefore to examine his work and its relation to current mathematics. This book attempts to do that. In number theory the discoveries he made empirically would require for their eventual understanding such sophisticated developments as the reciprocity laws and class field theory. His pioneering work onelliptic integrals is the precursor of the modern theory of abelian functions and abelian integrals. His evaluation of zeta and multizeta values is not only a fantastic and exciting story but very relevant to us, because they are at the confluence of much research in algebraic geometry and number theory today (Chapters 2 and 3 of the book). Anticipating his successors by more than a century, Euler created a theory of summation of series that do not converge in the traditional manner. Chapter 5of the book treats the progression of ideas regarding divergent series from Euler to many parts of modern analysis and quantum physics. The last chapter contains a brief treatment of Euler products. Euler discovered the product formula over the primes for the zeta function as well as for a smallnumber of what are now called Dirichlet $L$-functions. Here the book goes into the development of the theory of such Euler products and the role they play in number theory, thus offering the reader a glimpse of current developments (the Langlands program).
Download or read book The God Equation written by Michio Kaku and published by Anchor. This book was released on 2021-04-06 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: #1 NEW YORK TIMES BESTSELLER • The epic story of the greatest quest in all of science—the holy grail of physics that would explain the creation of the universe—from renowned theoretical physicist and author of The Future of the Mind and The Future of Humanity. When Newton discovered the law of gravity, he unified the rules governing the heavens and the Earth. Since then, physicists have been placing new forces into ever-grander theories. But perhaps the ultimate challenge is achieving a monumental synthesis of the two remaining theories—relativity and the quantum theory. This would be the crowning achievement of science, a profound merging of all the forces of nature into one beautiful, magnificent equation to unlock the deepest mysteries in science: What happened before the Big Bang? What lies on the other side of a black hole? Are there other universes and dimensions? Is time travel possible? Why are we here? Kaku also explains the intense controversy swirling around this theory, with Nobel laureates taking opposite sides on this vital question. It is a captivating, gripping story; what’s at stake is nothing less than our conception of the universe. Written with Kaku’s trademark enthusiasm and clarity, this epic and engaging journey is the story of The God Equation.
Book Synopsis Letters of Euler to a German Princess, on Different Subjects in Physics and Philosophy by : Leonhard Euler
Download or read book Letters of Euler to a German Princess, on Different Subjects in Physics and Philosophy written by Leonhard Euler and published by . This book was released on 1802 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt:
