Complex Analysis for Math

This user-friendly textbook introduces complex analysis at the beginning graduate or advanced undergraduate level. Unlike other textbooks, it follows Weierstrass' approach, stressing the importance of power series expansions instead of starting with the Cauchy integral formula, an approach that illuminates many important concepts. This view allows readers to quickly obtain and understand many fundamental results of complex analysis, such as the maximum principle, Liouville's theorem, and Schwarz's lemma. The book covers all the essential material on complex analysis, and includes several elegant proofs that were recently discovered. It includes the zipper algorithm for computing conformal maps, as well as a constructive proof of the Riemann mapping theorem, and culminates in a complete proof of the uniformization theorem. Aimed at students with some undergraduate background in real analysis, though not Lebesgue integration, this classroom-tested textbook will teach the skills and intui

Maximizing reader insights into the fundamentals of complex analysis, and providing complete instructions on how to construct and use mathematical tools to solve engineering problems in potential theo

This textbook is intended for a one semester course in complex analysis for upper level undergraduates in mathematics. Applications, primary motivations for this text, are presented hand-in-hand with

This book develops an understanding of sophisticated tools by using them. Complex variable theory is developed. The first three chapters and selected topics make a nice course. This course should appe

This work gathers international contributors in computer science, information systems, telecommunication engineering, and information technology to present the latest research in complex network analy

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 gr

Complex Analysis with Mathematica offers a way of learning and teaching a subject that lies at the heart of many areas of pure and applied mathematics, physics, engineering and even art. This book offers teachers and students an opportunity to learn about complex numbers in a state-of-the-art computational environment. The innovative approach also offers insights into many areas too often neglected in a student treatment, including complex chaos and mathematical art. Thus readers can also use the book for self-study and for enrichment. The use of Mathematica enables the author to cover several topics that are often absent from a traditional treatment. Students are also led, optionally, into cubic or quartic equations, investigations of symmetric chaos and advanced conformal mapping. A CD is included which contains a live version of the book: in particular all the Mathematica code enables the user to run computer experiments.

Complex Analysis and Applications, Second Edition explains complex analysis for students of applied mathematics and engineering. Restructured and completely revised, this textbook first develops the t

This book introduces recent results on output synchronization of complex dynamical networks with single and multiple weights. It discusses novel research ideas and a number of definitions in complex d

"This book explores node and edge centrality metrics and real-world network graphs, computationally-light vs. computationally-heavy centrality metrics, centrality-based connected dominating sets for c

In the past decade, post-structural policy analysis in education has evolved, primarily focusing on disrupting dominant narratives about education policy research, development and implementation, and

This book is a reference for anyone using SAS to analyse complex survey data. It covers all the nuances of the methodology, with detailed worked examples, and guidance on how to implement all the meth

The book constitutes a basic, concise, yet rigorous course in complex analysis, for students who have studied calculus in one and several variables, but have not previously been exposed to complex ana

Large surveys are becoming increasingly available for public use, and researchers are often faced with the need to analyse complex survey data to address key scientific issues. For proper analysis it

This book presents complex analysis in one variable in the context of modern mathematics, with clear connections to several complex variables, de Rham theory, real analysis, and other branches of math

This rigorous, self-contained book describes mathematical and, in particular, stochastic and graph theoretic methods to assess the performance of complex networks and systems. It comprises three parts: the first is a review of probability theory; Part II covers the classical theory of stochastic processes (Poisson, Markov and queueing theory), which are considered to be the basic building blocks for performance evaluation studies; Part III focuses on the rapidly expanding new field of network science. This part deals with the recently obtained insight that many very different large complex networks – such as the Internet, World Wide Web, metabolic and human brain networks, utility infrastructures, social networks – evolve and behave according to general common scaling laws. This understanding is useful when assessing the end-to-end quality of Internet services and when designing robust and secure networks. Containing problems and solved solutions, the book is ideal for graduate student

This new volume of Methods in Cell Biology looks at methods for analyzing of golgi complex function. Chapters cover such topics as in vitro reconstitution systems, fluorescence-based analysis of traff

This volume is based on lectures given during the program Complex Quantum Systems held at the National University of Singapore's Institute for Mathematical Sciences from 17 February to 27 March 2010.

This book is an outgrowth of the special summer session held at the Max Planck Institute for Mathematics and the Hausdorff Research Institute for Mathematics. The contributions in the volume provide a

For over a decade, complex networks have steadily grown as an important tool across a broad array of academic disciplines, with applications ranging from physics to social media. A tightly organized

This book develops a whole strategy for decision-making, with the full participation of the decision-maker and utilizing continuous feedback. It introduces the use of the very well-known and proven me

Analyzing the behavior of complex networks is an important element in the design of new man-made structures such as communication systems and biologically engineered molecules. Because any complex network can be represented by a graph, and therefore in turn by a matrix, graph theory has become a powerful tool in the investigation of network performance. This self-contained 2010 book provides a concise introduction to the theory of graph spectra and its applications to the study of complex networks. Covering a range of types of graphs and topics important to the analysis of complex systems, this guide provides the mathematical foundation needed to understand and apply spectral insight to real-world systems. In particular, the general properties of both the adjacency and Laplacian spectrum of graphs are derived and applied to complex networks. An ideal resource for researchers and students in communications networking as well as in physics and mathematics.

This is a reference book for academics working in the fields of several complex variables, PDE theory and geometry. The book collects articles on most recent developments in these fields with special

Mathematical problems such as graph theory problems are of increasing importance for the analysis of modelling data in biomedical research such as in systems biology, neuronal network modelling etc. T

The second edition of this standard text guides biomedical researchers in the selection and use of advanced statistical methods and the presentation of results to clinical colleagues. It assumes no knowledge of mathematics beyond high school level and is accessible to anyone with an introductory background in statistics. The Stata statistical software package is again used to perform the analyses, this time employing the much improved version 10 with its intuitive point and click as well as character-based commands. Topics covered include linear, logistic and Poisson regression, survival analysis, fixed-effects analysis of variance, and repeated-measure analysis of variance. Restricted cubic splines are used to model non-linear relationships. Each method is introduced in its simplest form and then extended to cover more complex situations. An appendix will help the reader select the most appropriate statistical methods for their data. The text makes extensive use of real data sets avai

This selection of 21 essays concentrates on using complexity theory, also known as complex adaptive system theory. Contributors describe moves toward a supportive nonlinear modeling structure, the rol

Power grids, flexible manufacturing, cellular communications: interconnectedness has consequences. This remarkable book gives the tools and philosophy you need to build network models detailed enough to capture essential dynamics but simple enough to expose the structure of effective control solutions. Core chapters assume only exposure to stochastic processes and linear algebra at undergraduate level; later chapters are for advanced graduate students and researchers/practitioners. This gradual development bridges classical theory with the state-of-the-art. The workload model at the heart of traditional analysis of the single queue becomes a foundation for workload relaxations used in the treatment of complex networks. Lyapunov functions and dynamic programming equations lead to the celebrated MaxWeight policy along with many generalizations. Other topics include methods for synthesizing hedging and safety stocks, stability theory for networks, and techniques for accelerated simulation

Pedagogical insights gained through 30 years of teaching applied mathematics led the author to write this set of student-oriented books. Topics such as complex analysis, matrix theory, vector and tens

This is a very successful textbook for undergraduate students of pure mathematics. Students often find the subject of complex analysis very difficult. Here the authors, who are experienced and well-known expositors, avoid many of such difficulties by using two principles: (1) generalising concepts familiar from real analysis; (2) adopting an approach which exhibits and makes use of the rich geometrical structure of the subject. An opening chapter provides a brief history of complex analysis which sets it in context and provides motivation.

Globalisation impacts every aspect of modern society and today's law graduates are expected to deal with complex legal problems that require knowledge and training that goes beyond domestic law. This textbook provides an overview of how law is becoming increasingly transnational, facilitating theoretical and practical engagement with transnational legal institutions and phenomena. It advances an analytic framework that will help students to understand what to look for when they encounter transnational legal institutions and practices, and what are the practical and normative implications of their findings. By considering both the theory and practice of transnational law and taking a discursive approach to the material, students are encouraged to arrive at their own conclusions. Adopting interdisciplinary techniques and using case studies from around the world, this book offers a holistic, balanced exploration of a new and emerging discipline.

This volume provides a practical introduction to the method of maximum likelihood as used in social science research. Ward and Ahlquist focus on applied computation in R and use real social science data from actual, published research. Unique among books at this level, it develops simulation-based tools for model evaluation and selection alongside statistical inference. The book covers standard models for categorical data as well as counts, duration data, and strategies for dealing with data missingness. By working through examples, math, and code, the authors build an understanding about the contexts in which maximum likelihood methods are useful and develop skills in translating mathematical statements into executable computer code. Readers will not only be taught to use likelihood-based tools and generate meaningful interpretations, but they will also acquire a solid foundation for continued study of more advanced statistical techniques.

Qualitative Comparative Analysis (QCA) is an emerging research method that is highly suitable for evaluation studies. Clear and concise, this book explains how researchers and evaluators can use QCA e

This book deals with fractals in understanding problems encountered in earth science, and their solutions. It starts with an analysis of two classes of methods (homogeneous fractals random models, and

This book presents a general method that lawyers, prosecutors and judges can follows to assess the quality and scientific content of technical work done for an accident and crime scene reconstruction.

This book reports on the latest advances in the study of Networked Control Systems (NCSs). It highlights novel research concepts on NCSs; the analysis and synthesis of NCSs with special attention to t