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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