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With this second volume, we enter the intriguing world of complex analysis. From the first theorems on, the elegance and sweep of the results is evident. The starting point is the simple idea of extending a function initially given for real values of the argument to one that is defined when the argument is complex. From there, one proceeds to the main properties of holomorphic functions, whose proofs are generally short and quite illuminating: the Cauchy theorems, residues, analytic continuation, the argument principle.
With this background, the reader is ready to learn a wealth of additional material connecting the subject with other areas of mathematics: the Fourier transform treated by contour integration, the zeta function and the prime number theorem, and an introduction to elliptic functions culminating in their application to combinatorics and number
With this second volume, we enter the intriguing world of complex analysis. From the first theorems on, the elegance and sweep of the results is evident. The starting point is the simple idea of extending a function initially given for real values of the argument to one that is defined when the
This first volume, a three-part introduction to the subject, is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis. It begins with the simple conviction that Fourier arrived at in the early nineteenth century
Complex Analysis: A First Course with Applications is a truly accessible introduction to the fundamental principles and applications of complex analysis. Designed for the undergraduate student with a calculus background but no prior experience with complex analysis, this text discusses the theory
This is the fourth edition of Serge Lang's Complex Analysis. The first part of the book covers the basic material of complex analysis, and the second covers many special topics, such as the Riemann Mapping Theorem, the gamma function, and analytic continuation. Power series methods are used more
This unusually lively textbook on complex variables introduces the theory of analytic functions, explores its diverse applications and shows the reader how to harness its powerful
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
As there is a need for careful analysis in a world where threats are growing more complex and serious, you need the tools to ensure that sensible methods are employed and correlated directly to risk. Counter threats such as terrorism, fraud, natural disasters, and information theft with the Fourth
Big data, genomics, and quantitative approaches to network-based analysis are combining to advance the frontiers of medicine as never before. Network Medicine introduces this rapidly evolving field of medical research, which promises to revolutionize the diagnosis and treatment of human diseases
The book provides an introduction to complex analysis for students with some familiarity with complex numbers from high school. Topics studied in the book include Julia sets and the Mandelbrot set, Dirichlet series and the prime number theorem, and the uniformization theorem for Riemann surfaces
This new edition of a classic textbook develops complex analysis from the established theory of real analysis by emphasising the differences that arise as a result of the richer geometry of the complex plane. Key features of the authors' approach are to use simple topological ideas to translate
Complex analysis is a classic and central area of mathematics, which is studies 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
A novel, integrative approach to cities as complex adaptive systems, applicable to issues ranging from innovation to economic prosperity to settlement patterns. Human beings around the world increasingly live in urban environments. In Introduction to Urban Science, Luis Bettencourt takes a novel,
Elias Martin lives a scowling, solitary life for a decade until a small, lost child wanders into his path. One in a series of illustrated short stories that explore the deeper, darker side of our connection with the natural world, this tale was inspired by ancient folklore. Read it and feel a
Principles of Analysis: Measure, Integration, Functional Analysis, and Applications prepares readers taking advanced courses in analysis, probability, harmonic analysis, and applied mathematics at the doctoral level. It is also designed so that the reader or instructor may select topics suitable to
Learn How to Design Effective Visualization SystemsVisualization Analysis and Design provides a systematic, comprehensive framework for thinking about visualization in terms of principles and design choices. The book features a unified approach encompassing information visualization techniques for
This case study-based textbook in multivariate analysis for advanced students in the humanities emphasizes descriptive, exploratory analyses of various types of datasets from a wide range of sub-disciplines, promoting the use of multivariate analysis and illustrating its wide applicability. Fields