Quaternionic and Clifford Calculus for Physicists and Engineers

Klaus Gürlebeck (Author), Wolfgang Sprössig (Author)

9780471962007, Wiley

Hardback, published 28 August 1997

384 pages
23.4 x 15.8 x 2.7 cm, 0.709 kg

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.

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.

Subject Areas: Mathematics [PB]