Nine Introductions in Complex Analysis, Revised Edition
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Author | : Sanford L. Segal |
Publisher | : Elsevier |
Total Pages | : 501 |
Release | : 2007-10-10 |
Genre | : Mathematics |
ISBN | : 0080550762 |
The book addresses many topics not usually in "second course in complex analysis" texts. It also contains multiple proofs of several central results, and it has a minor historical perspective. - Proof of Bieberbach conjecture (after DeBranges) - Material on asymptotic values - Material on Natural Boundaries - First four chapters are comprehensive introduction to entire and metomorphic functions - First chapter (Riemann Mapping Theorem) takes up where "first courses" usually leave off
Author | : Sanford L. Segal |
Publisher | : Elsevier |
Total Pages | : 733 |
Release | : 2011-08-18 |
Genre | : Mathematics |
ISBN | : 008087164X |
Nine Introductions in Complex Analysis
Author | : H. A. Priestley |
Publisher | : OUP Oxford |
Total Pages | : 343 |
Release | : 2003-08-28 |
Genre | : Mathematics |
ISBN | : 0191583332 |
Complex analysis is a classic and central area of mathematics, which is studied and exploited in a range of important fields, from number theory to engineering. Introduction to Complex Analysis was first published in 1985, and for this much awaited second edition the text has been considerably expanded, while retaining the style of the original. More detailed presentation is given of elementary topics, to reflect the knowledge base of current students. Exercise setshave been substantially revised and enlarged, with carefully graded exercises at the end of each chapter.This is the latest addition to the growing list of Oxford undergraduate textbooks in mathematics, which includes: Biggs: Discrete Mathematics 2nd Edition, Cameron: Introduction to Algebra, Needham: Visual Complex Analysis, Kaye and Wilson: Linear Algebra, Acheson: Elementary Fluid Dynamics, Jordan and Smith: Nonlinear Ordinary Differential Equations, Smith: Numerical Solution of Partial Differential Equations, Wilson: Graphs, Colourings and the Four-Colour Theorem, Bishop: Neural Networks forPattern Recognition, Gelman and Nolan: Teaching Statistics.
Author | : Barry Simon |
Publisher | : American Mathematical Soc. |
Total Pages | : 661 |
Release | : 2015-11-02 |
Genre | : Mathematics |
ISBN | : 1470411008 |
A Comprehensive Course in Analysis by Poincaré Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis. Part 2A is devoted to basic complex analysis. It interweaves three analytic threads associated with Cauchy, Riemann, and Weierstrass, respectively. Cauchy's view focuses on the differential and integral calculus of functions of a complex variable, with the key topics being the Cauchy integral formula and contour integration. For Riemann, the geometry of the complex plane is central, with key topics being fractional linear transformations and conformal mapping. For Weierstrass, the power series is king, with key topics being spaces of analytic functions, the product formulas of Weierstrass and Hadamard, and the Weierstrass theory of elliptic functions. Subjects in this volume that are often missing in other texts include the Cauchy integral theorem when the contour is the boundary of a Jordan region, continued fractions, two proofs of the big Picard theorem, the uniformization theorem, Ahlfors's function, the sheaf of analytic germs, and Jacobi, as well as Weierstrass, elliptic functions.
Author | : L. Hormander |
Publisher | : Elsevier |
Total Pages | : 227 |
Release | : 1973-02-12 |
Genre | : Mathematics |
ISBN | : 0444105239 |
An Introduction to Complex Analysis in Several Variables
Author | : Murali Rao |
Publisher | : World Scientific Publishing Company |
Total Pages | : 425 |
Release | : 2015-01-28 |
Genre | : Mathematics |
ISBN | : 9814579610 |
This volume is an enlarged edition of a classic textbook on complex analysis. In addition to the classical material of the first edition it provides a concise and accessible treatment of Loewner theory, both in the disc and in the half-plane. Some of the new material has been described in research papers only or appears here for the first time. Each chapter ends with exercises.
Author | : Pieter Moree |
Publisher | : American Mathematical Soc. |
Total Pages | : 347 |
Release | : 2020-02-12 |
Genre | : Education |
ISBN | : 147045100X |
This volume contains the proceedings of the conference Dynamics: Topology and Numbers, held from July 2–6, 2018, at the Max Planck Institute for Mathematics, Bonn, Germany. The papers cover diverse fields of mathematics with a unifying theme of relation to dynamical systems. These include arithmetic geometry, flat geometry, complex dynamics, graph theory, relations to number theory, and topological dynamics. The volume is dedicated to the memory of Sergiy Kolyada and also contains some personal accounts of his life and mathematics.
Author | : Sheng Gong |
Publisher | : World Scientific Publishing Company |
Total Pages | : 258 |
Release | : 2007-04-26 |
Genre | : Mathematics |
ISBN | : 9813106980 |
A concise textbook on complex analysis for undergraduate and graduate students, this book is written from the viewpoint of modern mathematics: the Bar {Partial}-equation, differential geometry, Lie groups, all the traditional material on complex analysis is included. Setting it apart from others, the book makes many statements and proofs of classical theorems in complex analysis simpler, shorter and more elegant: for example, the Mittag-Leffer theorem is proved using the Bar {Partial}-equation, and the Picard theorem is proved using the methods of differential geometry.
Author | : Eberhard Freitag |
Publisher | : Springer Science & Business Media |
Total Pages | : 553 |
Release | : 2006-01-17 |
Genre | : Mathematics |
ISBN | : 3540308237 |
All needed notions are developed within the book: with the exception of fundamentals which are presented in introductory lectures, no other knowledge is assumed Provides a more in-depth introduction to the subject than other existing books in this area Over 400 exercises including hints for solutions are included