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This book enables the reader to discover elementary concepts of geometric algebra and its applications with lucid and direct explanations. Why would one want to explore geometric algebra? What if there existed a universal mathematical language that allowed one: to make rotations in any dimension with simple formulas, to see spinors or the Pauli matrices and their products, to solve problems of the special theory of relativity in three-dimensional Euclidean space, to formulate quantum mechanics without the imaginary unit, to easily solve difficult problems of electromagnetism, to treat the Kepler problem with the formulas for a harmonic oscillator, to eliminate unintuitive matrices and tensors, to unite many branches of mathematical physics? What if it were possible to use that same framework to generalize the complex numbers or fractals to any dimension, to play with geometry on a computer, as well as to make calculations in robotics, ray-tracing and brain science? In addition, what if such a language provided a clear, geometric interpretation of mathematical objects, even for the imaginary unit in quantum mechanics? Such a mathematical language exists and it is called geometric algebra. High school students have the potential to explore it, and undergraduate students can master it. The universality, the clear geometric interpretation, the power of generalizations to any dimension, the new insights into known theories, and the possibility of computer implementations make geometric algebra a thrilling field to unearth.

Clifford algebras. --- Mathematical physics. --- Physical mathematics --- Physics --- Geometric algebras --- Algebras, Linear --- Mathematics --- Matrix theory. --- Algebra. --- Quantum physics. --- Computer science—Mathematics. --- Linear and Multilinear Algebras, Matrix Theory. --- Quantum Physics. --- Math Applications in Computer Science. --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Mechanics --- Thermodynamics --- Mathematical analysis

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Quaternionic and Clifford analysis are an extension of complex analysis into higher dimensions. The unique starting point of Wolfgang Sprößig’s work was the application of quaternionic analysis to elliptic differential equations and boundary value problems. Over the years, Clifford analysis has become a broad-based theory with a variety of applications both inside and outside of mathematics, such as higher-dimensional function theory, algebraic structures, generalized polynomials, applications of elliptic boundary value problems, wavelets, image processing, numerical and discrete analysis. The aim of this volume is to provide an essential overview of modern topics in Clifford analysis, presented by specialists in the field, and to honor the valued contributions to Clifford analysis made by Wolfgang Sprößig throughout his career.

Clifford algebras. --- Geometric algebras --- Algebras, Linear --- Functions of complex variables. --- Algebra. --- Field theory (Physics). --- Potential theory (Mathematics). --- Difference equations. --- Functional equations. --- Algebraic geometry. --- Functions of a Complex Variable. --- Field Theory and Polynomials. --- Potential Theory. --- Several Complex Variables and Analytic Spaces. --- Difference and Functional Equations. --- Algebraic Geometry. --- Algebraic geometry --- Geometry --- Equations, Functional --- Functional analysis --- Calculus of differences --- Differences, Calculus of --- Equations, Difference --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Mathematical analysis --- Mechanics --- Classical field theory --- Continuum physics --- Physics --- Continuum mechanics --- Mathematics --- Complex variables --- Elliptic functions --- Functions of real variables