Explorations In Complex Functions
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Explorations In Complex Functions
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Author : Richard Beals
language : en
Publisher: Springer Nature
Release Date : 2020-10-19
Explorations In Complex Functions written by Richard Beals and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-19 with Mathematics categories.
This textbook explores a selection of topics in complex analysis. From core material in the mainstream of complex analysis itself, to tools that are widely used in other areas of mathematics, this versatile compilation offers a selection of many different paths. Readers interested in complex analysis will appreciate the unique combination of topics and connections collected in this book. Beginning with a review of the main tools of complex analysis, harmonic analysis, and functional analysis, the authors go on to present multiple different, self-contained avenues to proceed. Chapters on linear fractional transformations, harmonic functions, and elliptic functions offer pathways to hyperbolic geometry, automorphic functions, and an intuitive introduction to the Schwarzian derivative. The gamma, beta, and zeta functions lead into L-functions, while a chapter on entire functions opens pathways to the Riemann hypothesis and Nevanlinna theory. Cauchy transforms give rise to Hilbert and Fourier transforms, with an emphasis on the connection to complex analysis. Valuable additional topics include Riemann surfaces, steepest descent, tauberian theorems, and the Wiener–Hopf method. Showcasing an array of accessible excursions, Explorations in Complex Functions is an ideal companion for graduate students and researchers in analysis and number theory. Instructors will appreciate the many options for constructing a second course in complex analysis that builds on a first course prerequisite; exercises complement the results throughout.
More Explorations In Complex Functions
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Author : Richard Beals
language : en
Publisher: Springer Nature
Release Date : 2023-07-01
More Explorations In Complex Functions written by Richard Beals and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-01 with Mathematics categories.
More Explorations in Complex Functions is something of a sequel to GTM 287, Explorations in Complex Functions. Both texts introduce a variety of topics, from core material in the mainstream of complex analysis to tools that are widely used in other areas of mathematics and applications, but there is minimal overlap between the two books. The intended readership is the same, namely graduate students and researchers in complex analysis, independent readers, seminar attendees, or instructors for a second course in complex analysis. Instructors will appreciate the many options for constructing a second course that builds on a standard first course in complex analysis. Exercises complement the results throughout. There is more material in this present text than one could expect to cover in a year’s course in complex analysis. A mapping of dependence relations among chapters enables instructors and independent readers a choice of pathway to reading the text. Chapters 2, 4, 5, 7, and 8 contain the function theory background for some stochastic equations of current interest, such as SLE. The text begins with two introductory chapters to be used as a resource. Chapters 3 and 4 are stand-alone introductions to complex dynamics and to univalent function theory, including deBrange’s theorem, respectively. Chapters 5—7 may be treated as a unit that leads from harmonic functions to covering surfaces to the uniformization theorem and Fuchsian groups. Chapter 8 is a stand-alone treatment of quasiconformal mapping that paves the way for Chapter 9, an introduction to Teichmüller theory. The final chapters, 10–14, are largely stand-alone introductions to topics of both theoretical and applied interest: the Bergman kernel, theta functions and Jacobi inversion, Padé approximants and continued fractions, the Riemann—Hilbert problem and integral equations, and Darboux’s method for computing asymptotics.
Geometric Function Theory
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Author : Steven G. Krantz
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-09-19
Geometric Function Theory written by Steven G. Krantz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-09-19 with Mathematics categories.
* Presented from a geometric analytical viewpoint, this work addresses advanced topics in complex analysis that verge on modern areas of research * Methodically designed with individual chapters containing a rich collection of exercises, examples, and illustrations
Explorations In Complex Analysis
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Author : Michael A. Brilleslyper
language : en
Publisher: American Mathematical Soc.
Release Date : 2012-12-31
Explorations In Complex Analysis written by Michael A. Brilleslyper and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-31 with Mathematics categories.
Research topics in the book include complex dynamics, minimal surfaces, fluid flows, harmonic, conformal, and polygonal mappings, and discrete complex analysis via circle packing. The nature of this book is different from many mathematics texts: the focus is on student-driven and technology-enhanced investigation. Interlaced in the reading for each chapter are examples, exercises, explorations, and projects, nearly all linked explicitly with computer applets for visualization and hands-on manipulation.
Geometric Function Theory
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Author : Steven G. Krantz
language : en
Publisher:
Release Date : 2005
Geometric Function Theory written by Steven G. Krantz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.
Explorations In Harmonic Analysis
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Author : Steven G. Krantz
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-05-24
Explorations In Harmonic Analysis written by Steven G. Krantz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-24 with Mathematics categories.
This self-contained text provides an introduction to modern harmonic analysis in the context in which it is actually applied, in particular, through complex function theory and partial differential equations. It takes the novice mathematical reader from the rudiments of harmonic analysis (Fourier series) to the Fourier transform, pseudodifferential operators, and finally to Heisenberg analysis.
Function Theory Of Several Complex Variables
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Author : Steven George Krantz
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Function Theory Of Several Complex Variables written by Steven George Krantz and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
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.
Explorations In Complex And Riemannian Geometry
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Author : John Bland
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Explorations In Complex And Riemannian Geometry written by John Bland and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
This book contains contributions by an impressive list of leading mathematicians. The articles include high-level survey and research papers exploring contemporary issues in geometric analysis, differential geometry, and several complex variables. Many of the articles will provide graduate students with a good entry point into important areas of modern research. The material is intended for researchers and graduate students interested in several complex variables and complex geometry.
Complex Functions
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Author : Gareth A. Jones
language : en
Publisher: Cambridge University Press
Release Date : 1987-03-19
Complex Functions written by Gareth A. Jones and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-03-19 with Mathematics categories.
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.
Complex Analysis
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Author : Theodore W. Gamelin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-01
Complex Analysis written by Theodore W. Gamelin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-01 with Mathematics categories.
An introduction to complex analysis for students with some knowledge of complex numbers from high school. It contains sixteen chapters, the first eleven of which are aimed at an upper division undergraduate audience. The remaining five chapters are designed to complete the coverage of all background necessary for passing PhD qualifying exams in complex analysis. Topics studied include Julia sets and the Mandelbrot set, Dirichlet series and the prime number theorem, and the uniformization theorem for Riemann surfaces, with emphasis placed on the three geometries: spherical, euclidean, and hyperbolic. Throughout, exercises range from the very simple to the challenging. The book is based on lectures given by the author at several universities, including UCLA, Brown University, La Plata, Buenos Aires, and the Universidad Autonomo de Valencia, Spain.