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Real quaternion analysis is a multi-faceted subject. Created to describe phenomena in special relativity, electrodynamics, spin etc., it has developed into a body of material that interacts with many branches of mathematics, such as complex analysis, harmonic analysis, differential geometry, and differential equations. It is also a ubiquitous factor in the description and elucidation of problems in mathematical physics. In the meantime real quaternion analysis has become a well established branch in mathematics and has been greatly successful in many different directions. This book is based on concrete examples and exercises rather than general theorems, thus making it suitable for an introductory one- or two-semester undergraduate course on some of the major aspects of real quaternion analysis in exercises. Alternatively, it may be used for beginning graduate level courses and as a reference work. With exercises at the end of each chapter and its straightforward writing style the book addresses readers who have no prior knowledge on this subject but have a basic background in graduate mathematics courses, such as real and complex analysis, ordinary differential equations, partial differential equations, and theory of distributions.

Algebra. --- Combinatorics. --- Functions of complex variables. --- Geometry. --- Mathematics. --- Matrix theory. --- Quaternions --- Functions, Quaternion --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Quaternions. --- Analysis (Mathematics) --- Fluxions (Mathematics) --- Infinitesimal calculus --- Limits (Mathematics) --- Quaternion functions --- Nonassociative rings. --- Rings (Algebra). --- Non-associative Rings and Algebras. --- Functions of a Complex Variable. --- Linear and Multilinear Algebras, Matrix Theory. --- Combinatorics --- Mathematical analysis --- Euclid's Elements --- Complex variables --- Elliptic functions --- Functions of real variables --- Calculus. --- Functions, Quaternion. --- Algebraic rings --- Ring theory --- Algebraic fields --- Rings (Algebra)

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Complex analysis nowadays has higher-dimensional analoga: the algebra of complex numbers is replaced then by the non-commutative algebra of real quaternions or by Clifford algebras. During the last 30 years the so-called quaternionic and Clifford or hypercomplex analysis successfully developed to a powerful theory with many applications in analysis, engineering and mathematical physics. This textbook introduces both to classical and higher-dimensional results based on a uniform notion of holomorphy. Historical remarks, lots of examples, figures and exercises accompany each chapter.

Electronic books. -- local. --- Holomorphic functions -- Problems, exercises, etc. --- Holomorphic functions. --- Holomorphic functions --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- Functions, Holomorphic --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Functions of complex variables. --- Integral transforms. --- Operational calculus. --- Potential theory (Mathematics). --- Functions of a Complex Variable. --- Integral Transforms, Operational Calculus. --- Potential Theory. --- Analysis. --- Functions of several complex variables --- Integral Transforms. --- Global analysis (Mathematics). --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Mathematical analysis --- Mechanics --- Transform calculus --- Integral equations --- Transformations (Mathematics) --- Complex variables --- Elliptic functions --- Functions of real variables --- Global analysis (Mathematics) --- 517.1 Mathematical analysis --- Operational calculus --- Differential equations --- Electric circuits