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Author: Puma Tse Publisher: CreateSpace ISBN: 9781500237899 Category : Mathematics Languages : en Pages : 134
Book Description
A comprehensive rewriting of the metaphorical book on imaginary numbers that defines them in logical and rational terms with examples anyone can understand, even computers. Then expands their applications in algebra, quadratic equations, defining radians, circular and hyperbolic functions. Identifies and defines their roles in entropy exploring topics in topology, differential equations, and partial differential equations. Applies the concepts to elementary entanglements like gluons, magnetic field induction through the dynamo-effect, and time. Re-evaluates Euler's Complex Variables and Helix differentiating mechanical rules for which heuristics are devised from applied understanding of imaginary numbers upon which exact solutions can be obtained. A concise treatment useful to students, teachers, and experts in mathematics and physics. Includes the text of Phase Theory of Everything, the cosmology (including Unified Field Theory) and related mathematical systems resulting from and coinciding with applications of imaginary numbers. This text in large print and full color also appears in Phase Theory of Everything. Metastar and white hole data appearing in a paragraph of the "Lemaitre Epoch" section of "Bang Starts Here" chapter is incorrect and was overlooked in editing. The correct estimates appear in the comparative table in the next ("Pre-Quasar Epoch") section. Further corrections, should they be necessary, will appear at akademe.org.
Author: Puma Tse Publisher: CreateSpace ISBN: 9781500237899 Category : Mathematics Languages : en Pages : 134
Book Description
A comprehensive rewriting of the metaphorical book on imaginary numbers that defines them in logical and rational terms with examples anyone can understand, even computers. Then expands their applications in algebra, quadratic equations, defining radians, circular and hyperbolic functions. Identifies and defines their roles in entropy exploring topics in topology, differential equations, and partial differential equations. Applies the concepts to elementary entanglements like gluons, magnetic field induction through the dynamo-effect, and time. Re-evaluates Euler's Complex Variables and Helix differentiating mechanical rules for which heuristics are devised from applied understanding of imaginary numbers upon which exact solutions can be obtained. A concise treatment useful to students, teachers, and experts in mathematics and physics. Includes the text of Phase Theory of Everything, the cosmology (including Unified Field Theory) and related mathematical systems resulting from and coinciding with applications of imaginary numbers. This text in large print and full color also appears in Phase Theory of Everything. Metastar and white hole data appearing in a paragraph of the "Lemaitre Epoch" section of "Bang Starts Here" chapter is incorrect and was overlooked in editing. The correct estimates appear in the comparative table in the next ("Pre-Quasar Epoch") section. Further corrections, should they be necessary, will appear at akademe.org.
Author: Verity Carr Publisher: Newnes ISBN: 0750625597 Category : Business & Economics Languages : en Pages : 149
Book Description
This text provides clear information about complex numbers. The text is supported by worked examples and it includes past examination questions and solutions. This is a title in the Maths Made Simple series.
Author: Puma Tse Publisher: CreateSpace ISBN: 9781500238261 Category : Mathematics Languages : en Pages : 134
Book Description
A comprehensive rewriting of the metaphorical book on imaginary numbers that defines them in logical and rational terms with examples anyone can understand, even computers. Then expands their applications in algebra, quadratic equations, defining radians, circular and hyperbolic functions. Identifies and defines their roles in entropy exploring topics in topology, differential equations, and partial differential equations. Applies the concepts to elementary entanglements like gluons, magnetic field induction through the dynamo-effect, and time. Re-evaluates Euler's Complex Variables and Helix differentiating mechanical rules for which heuristics are devised from applied understanding of imaginary numbers upon which exact solutions can be obtained. A concise treatment useful to students, teachers, and experts in mathematics and physics. Includes the text of Phase Theory of Everything, the cosmology (including Unified Field Theory) and related mathematical systems resulting from and coinciding with applications of imaginary numbers. This text in full color also appears under this title and in large print in Phase Theory of Everything. Metastar and white hole data appearing in a paragraph of the "Lemaitre Epoch" section of "Bang Starts Here" chapter is incorrect and was overlooked in editing. The correct estimates appear in the comparative table in the next ("Pre-Quasar Epoch") section. Further corrections, should they be necessary, will appear at akademe.org.
Author: David C. Ullrich Publisher: American Mathematical Soc. ISBN: 0821844792 Category : Mathematics Languages : en Pages : 506
Book Description
Presents the Dirichlet problem for harmonic functions twice: once using the Poisson integral for the unit disk and again in an informal section on Brownian motion, where the reader can understand intuitively how the Dirichlet problem works for general domains. This book is suitable for a first-year course in complex analysis
Author: Verity Carr Publisher: Newnes ISBN: 0080938442 Category : Business & Economics Languages : en Pages : 149
Book Description
Complex Numbers lie at the heart of most technical and scientific subjects. This book can be used to teach complex numbers as a course text,a revision or remedial guide, or as a self-teaching work. The author has designed the book to be a flexiblelearning tool, suitable for A-Level students as well as other students in higher and further education whose courses include a substantial maths component (e.g. BTEC or GNVQ science and engineering courses). Verity Carr has accumulated nearly thirty years of experience teaching mathematics at all levels and has a rare gift for making mathematics simple and enjoyable. At Brooklands College, she has taken a leading role in the development of a highly successful Mathematics Workshop. This series of Made Simple Maths books widens her audience but continues to provide the kind of straightforward and logical approach she has developed over her years of teaching.
Author: Paul Nahin Publisher: Princeton University Press ISBN: 1400833892 Category : Mathematics Languages : en Pages : 297
Book Description
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: D. Hestenes Publisher: Springer Science & Business Media ISBN: 0306471221 Category : Science Languages : en Pages : 716
Book Description
(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: Tristan Needham Publisher: Oxford University Press ISBN: 9780198534464 Category : Mathematics Languages : en Pages : 620
Book Description
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: Paul J. Nahin Publisher: Princeton University Press ISBN: 0691175918 Category : Mathematics Languages : en Pages : 416
Book Description
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: Puma Tse
Author: Puma Tse
Author: Kalid Azad
Author: Verity Carr
Author: Puma Tse
Author: David C. Ullrich
Author: Verity Carr
Author: Paul Nahin
Author: D. Hestenes
Author: Tristan Needham
Author: Paul J. Nahin