Quaternionic and Clifford Calculus for Physicists and Engineers

ISBN-13: 9780471962007 / Angielski / Twarda / 1997 / 384 str.

Klaus Gurlebeck;Gurlebeck;Sprossig

Opis

Quarternionic calculus covers a branch of mathematics which uses computational techniques to help solve problems from a wide variety of physical systems which are mathematically modelled in 3, 4 or more dimensions. Examples of the application areas include thermodynamics, hydrodynamics, geophysics and structural mechanics. Focusing on the Clifford algebra approach the authors have drawn together the research into quarternionic calculus to provide the non-expert or research student with an accessible introduction to the subject. This book fills the gap between the theoretical representations and the requirements of the user.

Spis treści

Quanternions and Multivectors.

Clifford Valued Functions and Forms.

Clifford Operator Calculus.

Boundary Value Problems.

Numerical Clifford Analysis.

Further Results and Research Problems.

Appendices.

Index.

Blurb

Quaternionic and Clifford analysis have in recent years become increasingly important tools in the analysis of partial differential equations and their application in mathematical physics and engineering. This book reflects the main ideas in the field and covers quaternions and multivectors, Clifford valued functions and forms, Clifford operator calculus, boundary value problems, numerical Clifford analysis. Further results and research problems are also included The authors′ intention is to equip the reader with the understanding necessary to adapt these methods to their own work. It is assumed that the reader is familiar with the basics of complex function theory in one variable, functional analysis and algebra. With an ever increasing literature on quaternionic and Clifford analysis the need for an accessible and applicable book on the subject has never been greater. This volume meets this need and will be invaluable for students and researchers in mathematics, physics and engineering who wish to apply quaternionic and Clifford analysis in their work.