Titlebook: Explorations in Complex Functions; Richard Beals,Roderick S. C. Wong Textbook 2020 Springer Nature Switzerland AG 2020 Complex analysis te

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https://doi.org/10.1007/978-3-658-30637-3ach harmonic. Conversely, at least locally, a real-valued harmonic function is the real part of a holomorphic function. A mean value property of these functions leads to analogues of the maximum modulus principle and its strong version.

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Medical Manpower Planning in Swedenithmic derivative . of .. Here we show that the Schwarzian derivative is a natural object: a measure of the “curvature” of ., the pointwise deviation from a best approximation of . by a linear fractional transformation.

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https://doi.org/10.1057/9780230228375tions is .: periodic with respect to two sets of translations. This chapter presents the general theory of such functions, and Jacobi’s construction via theta functions. The following two chapters, which are independent of each other, present constructions due to Jacobi and to Weierstrass, respectiv

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Derek M. Griffith,Emily C. Jaegerpoles in a period parallelogram that are odd around each pole. These functions come up naturally in certain problems of mechanics, such as the motion of an ideal pendulum. In pure mathematics they arise, for example, in connection with maps from the upper half plane to a parallelogram. In this chapt

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Cognitive Aspects of Illness and Health,basic conclusion is that a function holomorphic on an unbounded domain ., and continuous on the closure, either grows very fast at infinity or is bounded by its values on the boundary of .. This has a number of interesting applications. Among them are a theorem of Hardy that characterizes the Gaussi

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Basics,ingularities, residues, and the complex logarithm. Also included are three topics that are not as standard for an elementary course, but are used in many of the following chapters: reflection properties, infinite products, and analytic continuation. For all this material we give brief discussions an

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Linear Fractional Transformations,s in complex analysis, and in its applications to geometry and algebra. Of particular importance are the transformations that map the upper half-plane to itself, and the transformations that map the unit disk to itself.