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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 visual intuition to rigorous proof, and, in this edition, to address the conceptual conflicts between pure and applied approaches head-on. Beyond the material of the clarified and corrected original edition, there are three new chapters: Chapter 15, on infinitesimals in real and complex analysis; Chapter 16, on homology versions of Cauchy’s theorem and Cauchy’s residue theorem, linking back to geometric intuition; and Chapter 17, outlines some more advanced directions in which complex analysis has developed, and continues to evolve into the future. With numerous worked examples and exercises, clear and direct proofs, and a view to the future of the subject, this is an invaluable companion for any modern complex analysis course.
This handbook focuses on the enormous literature applying statistical methodology and modelling to environmental and ecological processes. The 21st century statistics community has become increasingly interdisciplinary, bringing a large collection of modern tools to all areas of application in environmental processes. In addition, the environmental community has substantially increased its scope of data collection including observational data, satellite-derived data, and computer model output. The resultant impact in this latter community has been substantial; no longer are simple regression and analysis of variance methods adequate. The contribution of this handbook is to assemble a state-of-the-art view of this interface. Features: An internationally regarded editorial team. A distinguished collection of contributors. A thoroughly contemporary treatment of a substantial interdisciplinary interface. Written to engage both statisticians as well as quantitative environmental researchers. 34 chapters covering methodology, ecological processes, environmental exposure, and statistical methods in climate science. About the Editors: Alan E. Gelfand is the James B. Duke Professor of Statistical Science at Duke University. He is a leader in Bayesian spatial modeling and analysis including a successful book in this area with Banerjee and Carlin. Montse Fuentes is the Dean of the Virginia Commonwealth University College of Humanities and Sciences and a Professor of Statistics. She leads a broad research program in statistical methods for spatial large scale environmental health studies. Jennifer A. Hoeting is Professor of Statistics at Colorado State University. Her research is focused on Bayesian, computational, and spatial statistics applied to address challenging problems in ecology. Richard L. Smith is the Mark L. Reed III Distinguished Professor of Statistics and Professor of Biostatistics at the University of North Carolina. His research covers theoretical and applied aspects of environmental statistics including extreme value theory, spatial statistics and applications to climate change, air pollution and health.
A Classic adapted to modern times Rewritten and updated, this new edition of Statistics for Experimenters adopts the same approaches as the landmark First Edition by teaching with examples, readily understood graphics, and the appropriate use of computers. Catalyzing innovation, problem solving, and discovery, the Second Edition provides experimenters with the scientific and statistical tools needed to maximize the knowledge gained from research data, illustrating how these tools may best be utilized during all stages of the investigative process. The authors’ practical approach starts with a problem that needs to be solved and then examines the appropriate statistical methods of design and analysis. Providing even greater accessibility for its users, the Second Edition is thoroughly revised and updated to reflect the changes in techniques and technologies since the publication of the classic First Edition. Among the new topics included are: Graphical Analysis of Variance Computer Analysis of Complex Designs Simplification by transformation Hands-on experimentation using Response Service Methods Further development of robust product and process design using split plot arrangements and minimization of error transmission Introduction to Process Control, Forecasting and Time Series Illustrations demonstrating how multi-response problems can be solved using the concepts of active and inert factor spaces and canonical spaces Bayesian approaches to model selection and sequential experimentation An appendix featuring Quaquaversal quotes from a variety of sources including noted statisticians and scientists to famous philosophers is provided to illustrate key concepts and enliven the learning process. All the computations in the Second Edition can be done utilizing the statistical language R. Functions for displaying ANOVA and lamba plots, Bayesian screening, and model building are all included and R packages are available online. All theses topics can also be applied utilizing easy-to-use commercial software packages. Complete with applications covering the physical, engineering, biological, and social sciences, Statistics for Experimenters is designed for individuals who must use statistical approaches to conduct an experiment, but do not necessarily have formal training in statistics. Experimenters need only a basic understanding of mathematics to master all the statistical methods presented. This text is an essential reference for all researchers and is a highly recommended course book for undergraduate and graduate students.
Students who have used Smith/Minton’s Calculus say it was easier to read than any other math book they’ve used. That testimony underscores the success of the authors’ approach, which combines the best elements of reform with the most reliable aspects of mainstream calculus teaching, resulting in a motivating, challenging book. Smith/Minton also provide exceptional, reality-based applications that appeal to students’ interests and demonstrate the elegance of math in the world around us. New features include: * A new organization placing all transcendental functions early in the book and consolidating the introduction to L’H�pital’s Rule in a single section. * More concisely written explanations in every chapter. * Many new exercises (for a total of 7,000 throughout the book) that require additional rigor not found in the 2nd Edition. * New exploratory exercises in every section that challenge students to synthesize key concepts to solve intriguing projects. * New commentaries (“Beyond Formulas”) that encourage students to think mathematically beyond the procedures they learn. * New counterpoints to the historical notes, “Today in Mathematics,” that stress the contemporary dynamism of mathematical research and applications, connecting past contributions to the present. * An enhanced discussion of differential equations and additional applications of vector calculus.
Financial Mathematics for Actuaries is a textbook for students in actuarial science, quantitative finance, financial engineering and quantitative risk management and is designed for a one-semester undergraduate course. Covering the theories of interest rates, with applications to the evaluation of cash flows, the pricing of fixed income securities and the management of bonds, this textbook also contains numerous examples and exercises and extensive coverage of various Excel functions for financial calculation. Discussions are linked to real financial market data, such as historical term structure, and traded financial securities. The topics discussed in this book are essential for actuarial science students. They are also useful for students in financial markets, investments and quantitative finance. Students preparing for examinations in financial mathematics with various professional actuarial bodies will also find this book useful for self-study. In this second edition, the recent additions in the learning objectives of the Society of Actuaries Exam FM have been covered.
Boyce′s ELEMENTARY DIFFERENTIAL EQUATIONS AND BOUNDARY VALUE PROBLEMS is primarily intended for undergraduate students of mathematics, science, or engineering, who typically take a course on differential equations during their first or second year of study. The main prerequisite for engaging with the program is a working knowledge of calculus, gained from a normal two or three semester course sequence or its equivalent. This book is authorized for sale in Europe, Asia, Africa and the Middle East only and may not be exported. The content is materially different than products for other markets including the authorized U.S. counterpart of this title. Exportation of this book to another region without the Publisher′s authorization may be illegal and a violation of the Publisher′s rights. The Publisher may take legal action to enforce its rights.
For courses in Introductory Business Statistics. Now in its 13th Edition, Statistics for Business and Economics introduces statistics in the context of contemporary business. Emphasizing statistical literacy in thinking, the text applies its concepts with real data and uses technology to develop a deeper conceptual understanding. Examples, activities, and case studies foster active learning in the classroom while emphasizing intuitive concepts of probability and teaching students to make informed business decisions. The 13th Edition continues to highlight the importance of ethical behaviour in collecting, interpreting, and reporting on data, while also providing a wealth of new and updated exercises and case studies.
Were you looking for the book with access to MyMathLab Global? This product is the book alone, and does NOT come with access to MyMathLab Global. Buy Foundation Maths, 6th edition with MyMathLab Global access card (ISBN 9781292095257) if you need access to MyMathLab Global as well, and save money on this resource. You will also need a course ID from your instructor to access MyLab. Foundation Maths has been written for students taking higher and further education courses who have not specialised in mathematics on post-16 qualifications and need to use mathematical tools in their courses. It is ideally suited to those studying marketing, business studies, management, science, engineering, social science, geography, combined studies and design. It will be useful for those who lack confidence and who need careful, steady guidance in mathematical methods. For those whose mathematical expertise is already established, the book will be a helpful revision and reference guide. The style of the book also makes it suitable for self-study and distance learning.
About the Author
Anthony Croft has taught mathematics in further and higher education institutions for over thirty years. He is currently Professor of Mathematics Education and Director of sigma – the Centre for Excellence in Teaching and Learning based in the Mathematics Education Centre at Loughborough University. He teaches mathematics and engineering undergraduates, and has championed mathematics support for students who find the transition from school to university difficult. He has authored many very successful mathematics textbooks, including several for engineering students. In 2008 he was awarded a National Teaching Fellowship in recognition of his work in these fields. Robert Davison has thirty years’ experience teaching mathematics in both further and higher education. He has authored many very successful mathematics textbooks, including several for engineering students.
This book requires knowledge of probability theory (combinatorics, probability distributions, functions and sequences of random variables) which is typically taught in the earlier semesters of scientific and mathematical study courses. After the basic ideas of mathematical statistics, Mathematical Statistics gives an introduction to point estimation, confidence intervals and statistical tests. Based on the general theory of linear models, the book provides an in-depth overview of the following: Analysis of variance for models with fixed, random and mixed effects Regression analysis is also first presented for linear models with fixed, random and mixed effects before being expanded to nonlinear models. Statistical multi-decision problems like statistical selection procedures (Bechhofer and Gupta) and sequential tests Design of experiments from a mathematical-statistical point of view. The chapters also contain exercises with hints for solutions.
This collection of expository articles by a range of established experts and newer researchers provides an overview of the recent developments in the theory of locally compact groups. It includes introductory articles on totally disconnected locally compact groups, profinite groups, p-adic Lie groups and the metric geometry of locally compact groups. Concrete examples, including groups acting on trees and Neretin groups, are discussed in detail. An outline of the emerging structure theory of locally compact groups beyond the connected case is presented through three complementary approaches: Willis’ theory of the scale function, global decompositions by means of subnormal series, and the local approach relying on the structure lattice. An introduction to lattices, invariant random subgroups and L2-invariants, and a brief account of the Burger-Mozes construction of simple lattices are also included. A final chapter collects various problems suggesting future research directions.