03201nam 22005775 450 991099967210332120260126134632.03-031-64999-010.1007/978-3-031-64999-8(CKB)38586755700041(DE-He213)978-3-031-64999-8(MiAaPQ)EBC32027699(Au-PeEL)EBL32027699(EXLCZ)993858675570004120250424d2025 u| 0engur|||||||||||txtrdacontentcrdamediacrrdacarrierComplex Analysis and Dynamics in One Variable with Applications /by Luis T. Magalhães1st ed. 2025.Cham :Springer Nature Switzerland :Imprint: Springer,2025.1 online resource (XXXII, 714 p. 228 illus., 59 illus. in color.)3-031-64998-2 Complex plane -- Functions -- Derivative -- Integral -- Analyticity -- Uni cation of holomorphy cauchy theorem and analyticity -- Global cauchy theorem -- Meromorphic functions -- Harmonic functions -- Conformal regions -- Analytic continuation and riemann surfaces -- Uniformization of riemann surfaces -- Complex dynamics.This textbook has been designed to support the initial study of Complex Analysis, progressing to Complex Dynamics. It focuses on the fundamental aspects of one-variable complex functions, covering the geometric theory and dynamics of iterations of rational mappings. Following the standard material, the book delves into an extensive range of advanced topics, encompassing the requirements for a one-year graduate-level course or a preliminary exam. In this work, the reader will discover three distinctive characteristics: it simplifies and unifies ideas and concepts that might appear disparate or complicated in real analysis; it contributes to the development of other areas in mathematics; and it showcases relevance for applications in Science and Engineering, with many exercises. Historical notes throughout the text help to contextualize the theory. With its flexible structure, this textbook provides a solid foundation for a first course in Complex Analysis and for a second more advanced course, establishing a robust basis for subsequent studies.Functions of complex variablesDynamicsPotential theory (Mathematics)Functions of a Complex VariableDynamical SystemsPotential TheoryFuncionsthubLlibres electrònicsthubFunctions of complex variables.Dynamics.Potential theory (Mathematics)Functions of a Complex Variable.Dynamical Systems.Potential Theory.Funcions515.9Magalhães Luis T.authttp://id.loc.gov/vocabulary/relators/aut0MiAaPQMiAaPQMiAaPQBOOK9910999672103321Complex Analysis and Dynamics in One Variable with Applications4374689UNINA