Explorations in Complex Functions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Explorations in Complex Functions write by Richard Beals. This book was released on 2020-10-19. Explorations in Complex Functions available in PDF, EPUB and Kindle. 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.
Explorations in Complex Analysis
Explorations in Complex Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Explorations in Complex Analysis write by Michael A. Brilleslyper. This book was released on 2012-12-31. Explorations in Complex Analysis available in PDF, EPUB and Kindle. 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.
More Explorations in Complex Functions
More Explorations in Complex Functions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook More Explorations in Complex Functions write by Richard Beals. This book was released on 2023-07-01. More Explorations in Complex Functions available in PDF, EPUB and Kindle. 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
Geometric Function Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Function Theory write by Steven G. Krantz. This book was released on 2007-09-19. Geometric Function Theory available in PDF, EPUB and Kindle. * 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
Function Theory of Several Complex Variables
Function Theory of Several Complex Variables - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Function Theory of Several Complex Variables write by Steven George Krantz. This book was released on 2001. Function Theory of Several Complex Variables available in PDF, EPUB and Kindle. 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.
