Real Quaternionic Calculus Handbook, 2014

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.

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 researcher. His research interests include approximation theory, conformal and quasiconformal mappings, signal and image processing. João Pedro Morais is currently working as a postdoctoral researcher at the University of Aveiro (Portugal).

Svetlin Georgiev (born 1974) is a Bulgarian mathematician working in areas of ordinary differential equations, partial differential equations, stochastic differential equations, Clifford algebras and Clifford analysis. He is currently a Professor at Sorbonne University (Paris, France).

Wolfgang Sprößig is Professor of Mathematics at the Technische Universität Bergakademie Freiberg (retired in 2012). His main research interests are the applications of quaternionic and Clifford algebraic methods to solve boundary and initial boundary value problems; he has published and co-authored 5 books and edited 6 further books, and special issues in several mathematical journals. Wolfgang Sproessig is Editor-in-Chief of the journal Mathematical Methods in the Applied Sciences and serves on the advisory board of 5 further journals. He has comprehensive teaching experience in different levels for about 40 years. For some years he served as external examiner at the Darussalam University (Sultanate Brunei).

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