Euler Through Time

Author : V. S. Varadarajan
Publisher : American Mathematical Soc.
Page : 312 pages
File Size : 47,8 Mb
Release : 2006
Category : Mathematics
ISBN : 9780821835807

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Euler Through Time by V. S. Varadarajan Pdf

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).

Author : William Dunham
Publisher : American Mathematical Society
Page : 185 pages
File Size : 41,9 Mb
Release : 2022-01-13
Category : Mathematics
ISBN : 9781470466183

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Euler by William Dunham Pdf

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.

Author : Ronald S. Calinger
Publisher : Princeton University Press
Page : 689 pages
File Size : 46,5 Mb
Release : 2019-12-03
Category : Biography & Autobiography
ISBN : 9780691196404

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Leonhard Euler by Ronald S. Calinger Pdf

"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.

Author : David S. Richeson
Publisher : Princeton University Press
Page : 336 pages
File Size : 41,6 Mb
Release : 2019-07-23
Category : Mathematics
ISBN : 9780691191997

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Euler's Gem by David S. Richeson Pdf

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.

Author : Euler
Publisher : Springer Science & Business Media
Page : 215 pages
File Size : 53,5 Mb
Release : 2000-05-23
Category : Mathematics
ISBN : 9780387985343

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Foundations of Differential Calculus by Euler Pdf

What differential calculus, and, in general, analysis ofthe infinite, might be can hardly be explainedto those innocent ofany knowledge ofit. Nor can we here offer a definition at the beginning of this dissertation as is sometimes done in other disciplines. It is not that there is no clear definition of this calculus; rather, the fact is that in order to understand the definition there are concepts that must first be understood. Besides those ideas in common usage, there are also others from finite analysis that are much less common and are usually explained in the courseofthe development ofthe differential calculus. For this reason, it is not possible to understand a definition before its principles are sufficiently clearly seen. In the first place, this calculus is concerned with variable quantities. Although every quantity can naturally be increased or decreased without limit, still, since calculus is directed to a certain purpose, we think of some quantities as being constantly the same magnitude, while others change through all the .stages of increasing and decreasing. We note this distinc tion and call the former constant quantities and the latter variables. This characteristic difference is not required by the nature of things, but rather because of the special question addressed by the calculus.

Author : Emil A. Fellmann
Publisher : Springer Science & Business Media
Page : 186 pages
File Size : 53,8 Mb
Release : 2007-04-05
Category : Mathematics
ISBN : 9783764375393

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Leonhard Euler by Emil A. Fellmann Pdf

Euler was not only by far the most productive mathematician in the history of mankind, but also one of the greatest scholars of all time. He attained, like only a few scholars, a degree of popularity and fame which may well be compared with that of Galilei, Newton, or Einstein. Moreover he was a cosmopolitan in the truest sense of the word; he lived during his first twenty years in Basel, was active altogether for more than thirty years in Petersburg and for a quarter of a century in Berlin. Leonhard Euler’s unusually rich life and broadly diversified activity in the immediate vicinity of important personalities which have made history, may well justify an exposition. This book is based in part on unpublished sources and comes right out of the current research on Euler. It is entirely free of formulae as it has been written for a broad audience with interests in the history of culture and science.

Author : Paul J. Nahin
Publisher : Princeton University Press
Page : 416 pages
File Size : 49,8 Mb
Release : 2017-04-04
Category : Mathematics
ISBN : 9780691175911

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Dr. Euler's Fabulous Formula by Paul J. Nahin Pdf

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.

Author : C. Edward Sandifer
Publisher : American Mathematical Soc.
Page : 391 pages
File Size : 48,9 Mb
Release : 2020-07-14
Category : Education
ISBN : 9781470451806

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The Early Mathematics of Leonhard Euler by C. Edward Sandifer Pdf

The Early Mathematics of Leonhard Euler gives an article-by-article description of Leonhard Euler's early mathematical works; the 50 or so mathematical articles he wrote before he left St. Petersburg in 1741 to join the Academy of Frederick the Great in Berlin. These early pieces contain some of Euler's greatest work, the Konigsberg bridge problem, his solution to the Basel problem, and his first proof of the Euler-Fermat theorem. It also presents important results that we seldom realize are due to Euler; that mixed partial derivatives are (usually) equal, our f(x) f(x) notation, and the integrating factor in differential equations. The books shows how contributions in diverse fields are related, how number theory relates to series, which, in turn, relate to elliptic integrals and then to differential equations. There are dozens of such strands in this beautiful web of mathematics. At the same time, we see Euler grow in power and sophistication, from a young student when at 18 he published his first work on differential equations (a paper with a serious flaw) to the most celebrated mathematician and scientist of his time. It is a portrait of the world's most exciting mathematics between 1725 and 1741, rich in technical detail, woven with connections within Euler's work and with the work of other mathematicians in other times and places, laced with historical context.

Author : Ronald Calinger,Thomas R. West
Publisher : Pearson
Page : 0 pages
File Size : 47,7 Mb
Release : 1999
Category : Mathematics
ISBN : 0023182857

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A Contextual History of Mathematics by Ronald Calinger,Thomas R. West Pdf

This history of mathematics stresses the historical imperative as to why maths happened from its beginnings to 1800 in Europe and beyond.

Author : Leonhard Euler
Publisher : Springer Science & Business Media
Page : 390 pages
File Size : 54,5 Mb
Release : 1957-01-01
Category : Mathematics
ISBN : 3764314346

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Commentationes mechanicae. Principia mechanica by Leonhard Euler Pdf

Author : David Stipp
Publisher : Basic Books
Page : 240 pages
File Size : 45,6 Mb
Release : 2017-11-07
Category : Mathematics
ISBN : 9780465093786

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A Most Elegant Equation by David Stipp Pdf

An award-winning science writer introduces us to mathematics using the extraordinary equation that unites five of mathematics' most important numbers Bertrand Russell wrote that mathematics can exalt "as surely as poetry." This is especially true of one equation: ei(pi) + 1 = 0, the brainchild of Leonhard Euler, the Mozart of mathematics. More than two centuries after Euler's death, it is still regarded as a conceptual diamond of unsurpassed beauty. Called Euler's identity or God's equation, it includes just five numbers but represents an astonishing revelation of hidden connections. It ties together everything from basic arithmetic to compound interest, the circumference of a circle, trigonometry, calculus, and even infinity. In David Stipp's hands, Euler's identity formula becomes a contemplative stroll through the glories of mathematics. The result is an ode to this magical field.

Author : Leonhard Euler
Publisher : Unknown
Page : 960 pages
File Size : 51,6 Mb
Release : 1810
Category : Algebra
ISBN : IOWA:31858049934619

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Elements of Algebra by Leonhard Euler Pdf

Author : Robin Wilson
Publisher : Oxford University Press
Page : 200 pages
File Size : 44,7 Mb
Release : 2018-02-22
Category : Mathematics
ISBN : 9780192514066

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Euler's Pioneering Equation by Robin Wilson Pdf

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.

Author : C. Edward Sandifer
Publisher : The Mathematical Association of America
Page : 254 pages
File Size : 42,8 Mb
Release : 2014-11-19
Category : Mathematics
ISBN : 9780883855843

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How Euler Did Even More by C. Edward Sandifer Pdf

Sandifer has been studying Euler for decades and is one of the world’s leading experts on his work. This volume is the second collection of Sandifer’s “How Euler Did It” columns. Each is a jewel of historical and mathematical exposition. The sum total of years of work and study of the most prolific mathematician of history, this volume will leave you marveling at Euler’s clever inventiveness and Sandifer’s wonderful ability to explicate and put it all in context.

Author : Emil A. Fellmann
Publisher : Birkhäuser
Page : 180 pages
File Size : 54,8 Mb
Release : 2009-09-03
Category : Mathematics
ISBN : 3764391138

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Leonhard Euler by Emil A. Fellmann Pdf

Euler was not only by far the most productive mathematician in the history of mankind, but also one of the greatest scholars of all time. He attained, like only a few scholars, a degree of popularity and fame which may well be compared with that of Galilei, Newton, or Einstein. Moreover he was a cosmopolitan in the truest sense of the word; he lived during his first twenty years in Basel, was active altogether for more than thirty years in Petersburg and for a quarter of a century in Berlin. Leonhard Euler’s unusually rich life and broadly diversified activity in the immediate vicinity of important personalities which have made history, may well justify an exposition. This book is based in part on unpublished sources and comes right out of the current research on Euler. It is entirely free of formulae as it has been written for a broad audience with interests in the history of culture and science.