Holomorphic Functions in the Plane and n-dimensional Space
Gürlebeck, Klaus, Habetha, Klaus, Sprößig, Wolfgang
Original German edition published in the series: Grundstudium Mathematik
2008, XIV, 394 p.
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First textbook on elementary level introducing to classical complex analysis and its generalizations at the same time
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.