Real Quaternionic Calculus Handbook by João Pedro MoraisReal Quaternionic Calculus Handbook by João Pedro Morais

Real Quaternionic Calculus Handbook

byJoão Pedro Morais, Svetlin Georgiev, Wolfgang Spr

Paperback | January 21, 2014

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Real quaternion analysis is a multi-faceted subject. Created to describe phenomena in special relativity, electrodynamics, spin etc., it has developed into a body of material that interacts with many branches of mathematics, such as complex analysis, harmonic analysis, differential geometry, and differential equations. It is also a ubiquitous factor in the description and elucidation of problems in mathematical physics. In the meantime real quaternion analysis has become a well established branch in mathematics and has been greatly successful in many different directions. This book is based on concrete examples and exercises rather than general theorems, thus making it suitable for an introductory one- or two-semester undergraduate course on some of the major aspects of real quaternion analysis in exercises. Alternatively, it may be used for beginning graduate level courses and as a reference work. With exercises at the end of each chapter and its straightforward writing style the book addresses readers who have no prior knowledge on this subject but have a basic background in graduate mathematics courses, such as real and complex analysis, ordinary differential equations, partial differential equations, and theory of distributions.
João Pedro Morais (born 1982) is a Portuguese mathematician working in the areas of Clifford and quaternionic analysis. In 2009 he got his Ph.D. in mathematics from Bauhaus-University Weimar (Germany). At 2010 he joined the Institute of Applied Analysis at the Freiberg University of Mining and Technology (Germany) as a postdoctoral res...
Title:Real Quaternionic Calculus HandbookFormat:PaperbackDimensions:216 pagesPublished:January 21, 2014Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3034806213

ISBN - 13:9783034806213


Table of Contents

1 An introduction to quaternions.- 2 Quaternions and spatial rotation.- 3 Quaternion sequences.- 4 Quaternion series and infinite products.- 5 Exponents and logarithms.- 6 Trigonometric functions.- 7 Hyperbolic functions.- 8 Inverse hyperbolic and trigonometric functions.- 9 Quaternion matrices.- 10 Monomials, polynomials and binomials.- 11 Solutions.- Bibliography.- Index.

Editorial Reviews

From the book reviews:"Morais (Univ. of Aveiro, Portugal), Georgiev (Sofia Univ., Bulgaria), and Spröig (Freiberg Univ. of Mining and Technology, Germany) focus on properties and formulas concerning quaternionic variations on basic special functions (exponential, logarithmic, trigonometric, hyperbolic, polynomial, binomial). Additionally, a chapter on linear algebra shows something of the delicate issues arising from noncommutative scalars. . Summing Up: Recommended. Upper-division undergraduates, faculty, and professionals/practitioners." (D. V. Feldman, Choice, Vol. 52 (5), January, 2015)"Morais, Georgiev, and Sprößig's Real Quaternionic Calculus Handbook works through the fundamental properties and formulas necessary for working with quaternions. . there are lots of exercises throughout (with solutions), and it could be used as a text for an early graduate or advanced undergraduate course. I like it best as a self-study guide . . you are writing a test suite for quaternion computation in a computer algebra system, this is definitely the book for you." (Bill Wood, MAA Reviews, April, 2014)"The book is structured into ten chapters followed by another one containing the solutions of the problems proposed at the end of each chapter. . the book is quite informative and could be of great value for peoples who want to enter into and advance in the fascinating world of quaternions." (Ivailo Mladenov, zbMATH, Vol. 1297, 2014)