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Functions, Quaternion --- Fonctions quaternioniennes --- Quaternions --- Functions of complex variables --- Fonctions d'une variable complexe --- Operator theory

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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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Hidden Harmony—Geometric Fantasies describes the history of complex function theory from its origins to 1914, when the essential features of the modern theory were in place. It is the first history of mathematics devoted to complex function theory, and it draws on a wide range of published and unpublished sources. In addition to an extensive and detailed coverage of the three founders of the subject—Cauchy, Riemann, and Weierstrass—it looks at the contributions of great mathematicians from d’Alembert to Poincaré, and Laplace to Weyl. Select chapters examine the rise and importance of elliptic function theory, differential equations in the complex domain, geometric function theory, and the early years of complex function theory in several variables. Unique emphasis has been placed on the creation of a textbook tradition in complex analysis by considering some seventy textbooks in nine different languages. This book is not a mere sequence of disembodied results and theories, but offers a comprehensive picture of the broad cultural and social context in which the main players lived and worked by paying attention to the rise of mathematical schools and of contrasting national traditions. This work is unrivaled for its breadth and depth, both in the core theory and its implications for other fields of mathematics. It is a major resource for professional mathematicians as well as advanced undergraduate and graduate students and anyone studying complex function theory.

Functional analysis. --- Functions of complex variables. --- Functions, Quaternion. --- Number theory. --- Functions of complex variables --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Mathematical analysis. --- 517.1 Mathematical analysis --- Mathematical analysis --- Complex variables --- Mathematics. --- History. --- Functional Analysis. --- History of Mathematical Sciences. --- Functions of a Complex Variable. --- Number Theory. --- Elliptic functions --- Functions of real variables --- Number study --- Numbers, Theory of --- Algebra --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Annals --- Auxiliary sciences of history --- Math --- Science --- Functional analysis --- Number Theory