Complex Analysis
| Author | : Steven G. Krantz |
| Publisher | : Cambridge University Press |
| Total Pages | : 252 |
| Release | : 2004 |
| Genre | : Mathematics |
| ISBN | : 9780883850350 |
Advanced textbook on central topic of pure mathematics.
Geometric Complex Analysis
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An Introduction to Complex Analysis and Geometry
| Author | : John P. D'Angelo |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 177 |
| Release | : 2010 |
| Genre | : Functions of complex variables |
| ISBN | : 0821852744 |
Provides the reader with a deep appreciation of complex analysis and how this subject fits into mathematics. The first four chapters provide an introduction to complex analysis with many elementary and unusual applications. Chapters 5 to 7 develop the Cauchy theory and include some striking applications to calculus. Chapter 8 glimpses several appealing topics, simultaneously unifying the book and opening the door to further study.
Function Theory of Several Complex Variables
| Author | : Steven George Krantz |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 586 |
| Release | : 2001 |
| Genre | : Mathematics |
| ISBN | : 0821827243 |
Emphasizing integral formulas, the geometric theory of pseudoconvexity, estimates, partial differential equations, approximation theory, inner functions, invariant metrics, and mapping theory, this title is intended for the student with a background in real and complex variable theory, harmonic analysis, and differential equations.
Classical Complex Analysis
| Author | : I-Hsiung Lin |
| Publisher | : World Scientific |
| Total Pages | : 713 |
| Release | : 2011 |
| Genre | : Mathematics |
| ISBN | : 9814271284 |
Classical Complex Analysis provides an introduction to one of the remarkable branches of exact science, with an emphasis on the geometric aspects of analytic functions. This volume begins with a geometric description of what a complex number is, followed by a detailed account of algebraic, analytic and geometric properties of standard complex-valued functions. Geometric properties of analytic functions are then developed and described In detail, and various applications of residues are Included; analytic continuation is also introduced. --Book Jacket.
Visual Complex Analysis
| Author | : Tristan Needham |
| Publisher | : Oxford University Press |
| Total Pages | : 620 |
| Release | : 1997 |
| Genre | : Mathematics |
| ISBN | : 9780198534464 |
This radical first course on complex analysis brings a beautiful and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack of advanced prerequisites, and consciously user-friendly prose style will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones. These geometric arguments are communicated with the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields.
Complex Analysis and CR Geometry
| Author | : Giuseppe Zampieri |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 210 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : 0821844423 |
Cauchy-Riemann (CR) geometry is the study of manifolds equipped with a system of CR-type equations. Compared to the early days when the purpose of CR geometry was to supply tools for the analysis of the existence and regularity of solutions to the $\bar\partial$-Neumann problem, it has rapidly acquired a life of its own and has became an important topic in differential geometry and the study of non-linear partial differential equations. A full understanding of modern CR geometryrequires knowledge of various topics such as real/complex differential and symplectic geometry, foliation theory, the geometric theory of PDE's, and microlocal analysis. Nowadays, the subject of CR geometry is very rich in results, and the amount of material required to reach competence is daunting tograduate students who wish to learn it.
Algebraic Curves and Riemann Surfaces
| Author | : Rick Miranda |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 414 |
| Release | : 1995 |
| Genre | : Mathematics |
| ISBN | : 0821802682 |
In this book, Miranda takes the approach that algebraic curves are best encountered for the first time over the complex numbers, where the reader's classical intuition about surfaces, integration, and other concepts can be brought into play. Therefore, many examples of algebraic curves are presented in the first chapters. In this way, the book begins as a primer on Riemann surfaces, with complex charts and meromorphic functions taking centre stage. But the main examples come fromprojective curves, and slowly but surely the text moves toward the algebraic category. Proofs of the Riemann-Roch and Serre Dualtiy Theorems are presented in an algebraic manner, via an adaptation of the adelic proof, expressed completely in terms of solving a Mittag-Leffler problem. Sheaves andcohomology are introduced as a unifying device in the later chapters, so that their utility and naturalness are immediately obvious. Requiring a background of one term of complex variable theory and a year of abstract algebra, this is an excellent graduate textbook for a second-term course in complex variables or a year-long course in algebraic geometry.
Geometry and Complex Variables
| Author | : S. Coen |
| Publisher | : CRC Press |
| Total Pages | : 522 |
| Release | : 1991-06-03 |
| Genre | : Mathematics |
| ISBN | : 9780824784454 |
This reference presents the proceedings of an international meeting on the occasion of theUniversity of Bologna's ninth centennial-highlighting the latest developments in the field ofgeometry and complex variables and new results in the areas of algebraic geometry, differential geometry, and analytic functions of one or several complex variables.Building upon the rich tradition of the University of Bologna's great mathematics teachers, thisvolume contains new studies on the history of mathematics, including the algebraic geometrywork of F. Enriques, B. Levi, and B. Segre ... complex function theory ideas of L. Fantappie, B. Levi, S. Pincherle, and G. Vitali ... series theory and logarithm theory contributions of P.Mengoli and S. Pincherle ... and much more. Additionally, the book lists all the University ofBologna's mathematics professors-from 1860 to 1940-with precise indications of eachcourse year by year.Including survey papers on combinatorics, complex analysis, and complex algebraic geometryinspired by Bologna's mathematicians and current advances, Geometry and ComplexVariables illustrates the classic works and ideas in the field and their influence on today'sresearc
Complex Functions
| Author | : Gareth A. Jones |
| Publisher | : Cambridge University Press |
| Total Pages | : 362 |
| Release | : 1987-03-19 |
| Genre | : Mathematics |
| ISBN | : 9780521313667 |
An elementary account of many aspects of classical complex function theory, including Mobius transformations, elliptic functions, Riemann surfaces, Fuchsian groups and modular functions. The book is based on lectures given to advanced undergraduate students and is well suited as a textbook for a second course in complex function theory.
From Holomorphic Functions to Complex Manifolds
| Author | : Klaus Fritzsche |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 406 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 146849273X |
This introduction to the theory of complex manifolds covers the most important branches and methods in complex analysis of several variables while completely avoiding abstract concepts involving sheaves, coherence, and higher-dimensional cohomology. Only elementary methods such as power series, holomorphic vector bundles, and one-dimensional cocycles are used. Each chapter contains a variety of examples and exercises.
