Quaternionic and Clifford Calculus for Physicists and Engineers

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.Quaternionische Methoden finden Anwendung bei der Lösung einer breiten Vielfalt physikalischer Probleme, die in 3, 4 oder mehr Dimensionen modelliert werden. Die Autoren füllen mit diesem Buch eine Lücke zwischen rein theoretischer Darstellung und den Wünschen des Anwenders - sie konzentrieren sich auf die Clifford-Algebra und bieten fortgeschrittenen Interessenten eine gut nachvollziehbare Einführung in dieses Gebiet. Quanternions and Multivectors.

Clifford Valued Functions and Forms.

Clifford Operator Calculus.

Boundary Value Problems.

Numerical Clifford Analysis.

Further Results and Research Problems.

Appendices.

Index. Aus dem Inhalt:
Real and Complex Quaternions, Quaternions and Vector Algebra Relations, Rotations, General Clifford Algebras, Tensors and Clifford, Multivectors, Quaternionic Matrices, Classes of Regular Functions, Different Approaches of Regular Functions, Paravector Valued Elementary Functions, Functional Analytic Theorems, Special Systems Cl0,n -Regular Functions, Cl0,n -Regular Functions In Symmetric Domains, Approximation Theorems, Minimal Systems, Gram-Schmidt Procedure, Reprokernels, Fourier Transforms and Related Transforms, Teodorescu Transform, Hypercomplex Exterior Calculus, Mobius Transformations In Irn , Uniqueness of Clifford Regular Functions, Remarks On Residues In Clifford Analysis, Singular Integral Operators of Cauchy's Type, Formulae of Plemelj-Sokhotzki-Type, On a Decomposition of The Cl0,n -Valued Hilbert Space, On First Order Boundary Value Problems, Dirichlet Problems and Orthoprojections, Vekua Type Problems, On Weak Time-Dependent Maxwell Equations, a Coupled Problem of Thermoelasicity, Stokes Equation, Navier-Stokes Equations and Related Equations, Problems With Non-Linear Right Hand Side, Strong Non-Linear Boundary Value Problems, Multidimensional Reimann-Hilbert Problems, Domain Perturbation Problems, Hypercomplex Beltrami Equation, Integral Equations For Contact Problems, Estimation of Lower Bounds of Some Eigenvalue Problems, Discrete Fundamental Solutions, Discrete Reprokernels, Discrete Quaternionic Calculus, Convergence Results, Boundary Collation Methods, Parabolic Boundary Value Problems, On Field Equations, Recent Trends.

Klaus Gürlebeck is the author of Quaternionic and Clifford Calculus for Physicists and Engineers, published by Wiley.

Wolfgang Sprössig is the author of Quaternionic and Clifford Calculus for Physicists and Engineers, published by Wiley. 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.