Morais et al: Real Quaternionic Calculus Handbook

Real Quaternionic Calculus Handbook
by Morais, Joao Pedro, Georgiev, Svetlin, Sprößig, Wolfgang
2014, XII, 216 p. 1 illus. in color. Birkhäuser Basel.
Available Formats:

  • eBook 41,64 €, ISBN 978-3-0348-0622-0
  • Softcover 49,99 €, ISBN 978-3-0348-0621-3


  • Gives a brief introduction in the algebra, geometry and elementary analysis of quaternions and quaternion functions
  • Presents solutions or hints for the solution of 150 problems, and supplementary exercises for a course on quaternions
  • Provides basic knowledge for computing with matrices with quaternion entries
  • Includes important historical remarks
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.

Keywords » quaternion analysis – quaternion elementary functions – quaternion matrices – quaternion operations – quaternion sequences, series and products – rotations

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.

Source: Email from S. Georgiev, 28 Jan. 2014,,

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