Holomorphic Functions in the Plane and n-dimensional Space 2008th Edition by Klaus Gürlebeck (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is really a marvelous (largely geometric) introduction to the subject of extending some of the more familiar results in elementary complex analysis to quaternions and Clifford numbers. The approach is both historical and developmental. And the result is a well-organized, self-contained text that is fascinating, fun and extremely useful as a basic reference. It is aimed at the upper-division undergraduate mathematics and physics level, requiring nothing more than (1) a basic exposure to complex variables (e.g., Churchill & Brown); (2) very elementary linear algebra; and perhaps (3) a smidgeon of elementary topology (though this is not crucial). However, even a highly experienced math or physics person will find this a wonderful and masterfully organized text on a rarely examined subject. I believe I paid something like $1.14 (before shipping) for my copy, which is a jaw-dropping bargain for such a beautifully written text, which–although in paperback–is also well-bound (it won’t come apart) and of good print quality. I highly recommend this to all geometers and physicists–to those just beginning as well as to the seasoned veterans.

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