Titlebook: Complex Analysis; Taras Mel‘nyk Textbook 2023 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature

Longitude

Analytic Functions,s values on arbitrary sets that have a limit point inside. These functions are of great importance both in various branches of mathematics and in many applications. The study of their properties is the main goal of complex analysis. In this section, we prove a criterion for the differentiability of

tangle

Residue Calculus,at are responsible for its zeros. The theory also supplies a ready-made framework for counting zeros and poles of a given meromorphic function or zeros of an analytic function, in particular, we prove the argument principle and Rouché’s theorem.

atopic

Analytic Continuations,lued function, and under which conditions the newly extended function is single-valued. Along the way we will be introduced to various continuation techniques and other fundamental concepts of complex analysis such as monodromy, global analytic functions, their singularities and Riemann surfaces.

OCTO

squander

Günter Kirschlingve transformation” is compatible in most respects with a control approach, but (a) adds specificity regarding mechanisms underlying change, (b) explains some of control theory’s negative cases, and (c) seems to have a particularly good fit with the life course challenges facing contemporary serious

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