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| Author | : Paul J. Nahin |
| Publisher | : Princeton University Press |
| Total Pages | : 416 |
| Release | : 2017-04-04 |
| Genre | : Mathematics |
| ISBN | : 0691175918 |
Download Dr. Euler's Fabulous Formula Book in PDF, ePub and Kindle
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 | : Paul Nahin |
| Publisher | : Princeton University Press |
| Total Pages | : 297 |
| Release | : 2010-02-22 |
| Genre | : Mathematics |
| ISBN | : 1400833892 |
Download An Imaginary Tale Book in PDF, ePub and Kindle
Today complex numbers have such widespread practical use--from electrical engineering to aeronautics--that few people would expect the story behind their derivation to be filled with adventure and enigma. In An Imaginary Tale, Paul Nahin tells the 2000-year-old history of one of mathematics' most elusive numbers, the square root of minus one, also known as i. He recreates the baffling mathematical problems that conjured it up, and the colorful characters who tried to solve them. In 1878, when two brothers stole a mathematical papyrus from the ancient Egyptian burial site in the Valley of Kings, they led scholars to the earliest known occurrence of the square root of a negative number. The papyrus offered a specific numerical example of how to calculate the volume of a truncated square pyramid, which implied the need for i. In the first century, the mathematician-engineer Heron of Alexandria encountered I in a separate project, but fudged the arithmetic; medieval mathematicians stumbled upon the concept while grappling with the meaning of negative numbers, but dismissed their square roots as nonsense. By the time of Descartes, a theoretical use for these elusive square roots--now called "imaginary numbers"--was suspected, but efforts to solve them led to intense, bitter debates. The notorious i finally won acceptance and was put to use in complex analysis and theoretical physics in Napoleonic times. Addressing readers with both a general and scholarly interest in mathematics, Nahin weaves into this narrative entertaining historical facts and mathematical discussions, including the application of complex numbers and functions to important problems, such as Kepler's laws of planetary motion and ac electrical circuits. This book can be read as an engaging history, almost a biography, of one of the most evasive and pervasive "numbers" in all of mathematics. Some images inside the book are unavailable due to digital copyright restrictions.
| Author | : Seanan McGuire |
| Publisher | : National Geographic Books |
| Total Pages | : 0 |
| Release | : 2020-02-25 |
| Genre | : Fiction |
| ISBN | : 0756413788 |
Download Imaginary Numbers Book in PDF, ePub and Kindle
The ninth book in the fast-paced InCryptid urban fantasy series returns to the mishaps of the Price family, eccentric cryptozoologists who safeguard the world of magical creatures living in secret among humans. Sarah Zellaby has always been in an interesting position. Adopted into the Price family at a young age, she's never been able to escape the biological reality of her origins: she's a cuckoo, a telepathic ambush predator closer akin to a parasitic wasp than a human being. Friend, cousin, mathematician; it's never been enough to dispel the fear that one day, nature will win out over nurture, and everything will change. Maybe that time has finally come. After spending the last several years recuperating in Ohio with her adoptive parents, Sarah is ready to return to the world--and most importantly, to her cousin Artie, with whom she has been head-over-heels in love since childhood. But there are cuckoos everywhere, and when the question of her own survival is weighed against the survival of her family, Sarah's choices all add up to one inescapable conclusion. This is war. Cuckoo vs. Price, human vs. cryptid...and not all of them are going to walk away.
| Author | : William Frucht |
| Publisher | : |
| Total Pages | : 360 |
| Release | : 1999-09-28 |
| Genre | : Fiction |
| ISBN | : |
Download Imaginary Numbers Book in PDF, ePub and Kindle
"Enter the wildly inventive world of Imaginary Numbers, in which a marvelous roster of acclaimed writers conjure up magical happenings, fantastic visions, and brainteasing puzzles, all based in some way on mathematical ideas. This anthology offers a connoisseur's selection of a special brand of creative writing in which the authors play with a vast array of mathematical notions - from the marvels of infinity to the peculiarities of space-time to quantum weirdness, the relativity of time, and the curious attraction of black holes." --Book Jacket.
| Author | : Irena Swanson |
| Publisher | : World Scientific |
| Total Pages | : 455 |
| Release | : 2021-02-18 |
| Genre | : Mathematics |
| ISBN | : 9811225877 |
Download Introduction To Analysis With Complex Numbers Book in PDF, ePub and Kindle
This is a self-contained book that covers the standard topics in introductory analysis and that in addition constructs the natural, rational, real and complex numbers, and also handles complex-valued functions, sequences, and series.The book teaches how to write proofs. Fundamental proof-writing logic is covered in Chapter 1 and is repeated and enhanced in two appendices. Many examples of proofs appear with words in a different font for what should be going on in the proof writer's head.The book contains many examples and exercises to solidify the understanding. The material is presented rigorously with proofs and with many worked-out examples. Exercises are varied, many involve proofs, and some provide additional learning materials.
| Author | : D. Hestenes |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 716 |
| Release | : 2005-12-17 |
| Genre | : Science |
| ISBN | : 0306471221 |
Download New Foundations for Classical Mechanics Book in PDF, ePub and Kindle
(revised) This is a textbook on classical mechanics at the intermediate level, but its main purpose is to serve as an introduction to a new mathematical language for physics called geometric algebra. Mechanics is most commonly formulated today in terms of the vector algebra developed by the American physicist J. Willard Gibbs, but for some applications of mechanics the algebra of complex numbers is more efficient than vector algebra, while in other applications matrix algebra works better. Geometric algebra integrates all these algebraic systems into a coherent mathematical language which not only retains the advantages of each special algebra but possesses powerful new capabilities. This book covers the fairly standard material for a course on the mechanics of particles and rigid bodies. However, it will be seen that geometric algebra brings new insights into the treatment of nearly every topic and produces simplifications that move the subject quickly to advanced levels. That has made it possible in this book to carry the treatment of two major topics in mechanics well beyond the level of other textbooks. A few words are in order about the unique treatment of these two topics, namely, rotational dynamics and celestial mechanics.
| Author | : Hans Schwerdtfeger |
| Publisher | : Courier Corporation |
| Total Pages | : 228 |
| Release | : 2012-05-23 |
| Genre | : Mathematics |
| ISBN | : 0486135861 |
Download Geometry of Complex Numbers Book in PDF, ePub and Kindle
Illuminating, widely praised book on analytic geometry of circles, the Moebius transformation, and 2-dimensional non-Euclidean geometries.
| Author | : Tristan Needham |
| Publisher | : Oxford University Press |
| Total Pages | : 620 |
| Release | : 1997 |
| Genre | : Mathematics |
| ISBN | : 9780198534464 |
Download Visual Complex Analysis Book in PDF, ePub and Kindle
This radical first course on complex analysis brings a beautiful and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack of advanced prerequisites, and consciously user-friendly prose style will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones. These geometric arguments are communicated with the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields.
| Author | : Elias Wegert |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 374 |
| Release | : 2012-08-30 |
| Genre | : Mathematics |
| ISBN | : 3034801807 |
Download Visual Complex Functions Book in PDF, ePub and Kindle
This book provides a systematic introduction to functions of one complex variable. Its novel feature is the consistent use of special color representations – so-called phase portraits – which visualize functions as images on their domains. Reading Visual Complex Functions requires no prerequisites except some basic knowledge of real calculus and plane geometry. The text is self-contained and covers all the main topics usually treated in a first course on complex analysis. With separate chapters on various construction principles, conformal mappings and Riemann surfaces it goes somewhat beyond a standard programme and leads the reader to more advanced themes. In a second storyline, running parallel to the course outlined above, one learns how properties of complex functions are reflected in and can be read off from phase portraits. The book contains more than 200 of these pictorial representations which endow individual faces to analytic functions. Phase portraits enhance the intuitive understanding of concepts in complex analysis and are expected to be useful tools for anybody working with special functions – even experienced researchers may be inspired by the pictures to new and challenging questions. Visual Complex Functions may also serve as a companion to other texts or as a reference work for advanced readers who wish to know more about phase portraits.
| Author | : Donu Arapura |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 326 |
| Release | : 2012-02-15 |
| Genre | : Mathematics |
| ISBN | : 1461418097 |
Download Algebraic Geometry over the Complex Numbers Book in PDF, ePub and Kindle
This is a relatively fast paced graduate level introduction to complex algebraic geometry, from the basics to the frontier of the subject. It covers sheaf theory, cohomology, some Hodge theory, as well as some of the more algebraic aspects of algebraic geometry. The author frequently refers the reader if the treatment of a certain topic is readily available elsewhere but goes into considerable detail on topics for which his treatment puts a twist or a more transparent viewpoint. His cases of exploration and are chosen very carefully and deliberately. The textbook achieves its purpose of taking new students of complex algebraic geometry through this a deep yet broad introduction to a vast subject, eventually bringing them to the forefront of the topic via a non-intimidating style.
