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Complex Analysis and Dynamics in One Variable with Applications / by Luis T. Magalhães.
Springer Nature - Springer Mathematics and Statistics (R0) eBooks 2025 English International Available online
View online- Format:
- Book
- Author/Creator:
- Magalhães, Luis T., Author.
- Series:
- Mathematics and Statistics Series
- Language:
- English
- Subjects (All):
- Functions of complex variables.
- Dynamics.
- Potential theory (Mathematics).
- Functions of a Complex Variable.
- Dynamical Systems.
- Potential Theory.
- Local Subjects:
- Functions of a Complex Variable.
- Dynamical Systems.
- Potential Theory.
- Physical Description:
- 1 online resource (XXXII, 714 p. 228 illus., 59 illus. in color.)
- Edition:
- 1st ed. 2025.
- Place of Publication:
- Cham : Springer Nature Switzerland : Imprint: Springer, 2025.
- Summary:
- 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.
- Contents:
- 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.
- Notes:
- Description based on publisher supplied metadata and other sources.
- ISBN:
- 3-031-64999-0
- OCLC:
- 1519126224
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