Foundations of Analysis has two main goals. The first is to develop in students the mathematical maturity and sophistication they will need as they move through the upper division curriculum. The second is to present a rigorous development of both single and several variable calculus, beginning with a study of the properties of the real number system. The presentation is both thorough and concise, with simple, straightforward explanations. The exercises differ widely in level of abstraction and level of difficulty. They vary from the simple to the quite difficult and from the computational to the theoretical. Each section contains a number of examples designed to illustrate the material in the section and to teach students how to approach the exercises for that section. --Book cover.
The text covers a broad spectrum between basic and advanced complex variables on the one hand and between theoretical and applied or computational material on the other hand. With careful selection of the emphasis put on the various sections, examples, and exercises, the book can be used in a one- or two-semester course for undergraduate mathematics majors, a one-semester course for engineering or physics majors, or a one-semester course for first-year mathematics graduate students. It has been tested in all three settings at the University of Utah. The exposition is clear, concise, and lively. There is a clean and modern approach to Cauchy's theorems and Taylor series expansions, with rigorous proofs but no long and tedious arguments. This is followed by the rich harvest of easy consequences of the existence of power series expansions. Through the central portion of the text, there is a careful and extensive treatment of residue theory and its application to computation of integrals, conformal mapping and its applications to applied problems, analytic continuation, and the proofs of the Picard theorems. Chapter 8 covers material on infinite products and zeroes of entire functions. This leads to the final chapter which is devoted to the Riemann zeta function, the Riemann Hypothesis, and a proof of the Prime Number Theorem." -- Publisher.
Foundations of Analysis has two main goals. The first is to develop in students the mathematical maturity and sophistication they will need as they move through the upper division curriculum. The second is to present a rigorous development of both single and several variable calculus, beginning with a study of the properties of the real number system. The presentation is both thorough and concise, with simple, straightforward explanations. The exercises differ widely in level of abstraction and level of difficulty. They vary from the simple to the quite difficult and from the computational to the theoretical. Each section contains a number of examples designed to illustrate the material in the section and to teach students how to approach the exercises for that section. --Book cover.
This book is the second edition of Environmental Monitoring using GNSS and highlights the latest developments in global navigation satellite systems (GNSS). It features a completely new title and additional chapters that present emerging challenges to environmental monitoring—“climate variability/change and food insecurity.” Since the publication of the first edition, much has changed in both the development and applications of GNSS, a satellite microwave remote sensing technique. It is the first tool to span all four dimensions of relevance to humans (position, navigation, timing and the environment), and it has widely been used for positioning (both by military and civilians), navigation and timing. Its increasing use is leading to a new era of remote sensing that is now revolutionizing the art of monitoring our environment in ways never imagined before. On the one hand, nearly all GNSS satellites (Global Positioning System (GPS), Global Navigation Satellite System (GLONASS), Galileo and Beidou) have become operational, thereby providing high-precision, continuous, all-weather and near real- time remote sensing multi-signals beneficial to environmental monitoring. On the other hand, the emerging challenges of precisely monitoring climate change and the demand for the production of sufficient food for ever-increasing populations are pushing traditional monitoring methods to their limits. In this regard, refracted GNSS signals (i.e., occulted GNSS signals or GNSS meteorology) are now emerging as sensors of climate variability, while the reflected signals (GNSS reflectometry or GNSS-R) are increasingly finding applications in determining, e.g., soil moisture content, ice and snow thickness, ocean heights, and wind speed and direction, among others. Furthermore, the increasing recognition and application of GNSS-supported unmanned aircraft vehicles (UAV)/drones in agriculture (e.g., through the determination of water holding capacity of soil) highlights the new challenges facing GNSS. As such, this new edition three new chapters address GNSS reflectometry and applications; GNSS sensing of climate variability; and the applications in UAV/drones. Moreover, it explores the application of GNSS to support integrated coastal zone management.
Practical, comprehensive, and updated throughout, the 4th edition of Dermatological Signs of Internal Diseases helps you identify a full range of common and rare systemic diseases early...so they can be managed as effectively as possible. Coverage of new disorders, including nephrogenic fibrosing dermopathy, new treatment options, expanded histopathology content, new color images, online image library and much more...to help you attain definitive diagnoses of internal diseases that manifest on the skin. Best of all, each chapter features an evidence-based approach to diagnosis and treatment so you know you can depend on the clinical recommendations presented. Expert Consult functionality allows you to access the entire contents of the book online at expertconsult.com from any Internet connection. Presents an evidence-based approach so you can depend on the clinical recommendations presented. Covers advice on patient evaluation and lab tests, as well as tables of differential diagnoses, to facilitate diagnosis for every condition. Uses a consistent, user-friendly format for easy reference. Discusses new diseases such as nephrogenic fibrosing dermopathy and new therapies, including biologics, to keep you on the cusp of this rapidly expanding field. Provides improved and expanded histopathology content for a better understanding in this difficult area of diagnosis. Features over 500 full-color illustrations—100 new to this edition—that provide the best possible representations of diseases as they appear in real life. Features a companion website at expertconsult.com with fully searchable text and an image library to enhanced visual guidance.
This book provides numerous examples of linear and nonlinear model applications. Here, we present a nearly complete treatment of the Grand Universe of linear and weakly nonlinear regression models within the first 8 chapters. Our point of view is both an algebraic view and a stochastic one. For example, there is an equivalent lemma between a best, linear uniformly unbiased estimation (BLUUE) in a Gauss–Markov model and a least squares solution (LESS) in a system of linear equations. While BLUUE is a stochastic regression model, LESS is an algebraic solution. In the first six chapters, we concentrate on underdetermined and overdetermined linear systems as well as systems with a datum defect. We review estimators/algebraic solutions of type MINOLESS, BLIMBE, BLUMBE, BLUUE, BIQUE, BLE, BIQUE, and total least squares. The highlight is the simultaneous determination of the first moment and the second central moment of a probability distribution in an inhomogeneous multilinear estimation by the so-called E-D correspondence as well as its Bayes design. In addition, we discuss continuous networks versus discrete networks, use of Grassmann–Plucker coordinates, criterion matrices of type Taylor–Karman as well as FUZZY sets. Chapter seven is a speciality in the treatment of an overjet. This second edition adds three new chapters: (1) Chapter on integer least squares that covers (i) model for positioning as a mixed integer linear model which includes integer parameters. (ii) The general integer least squares problem is formulated, and the optimality of the least squares solution is shown. (iii) The relation to the closest vector problem is considered, and the notion of reduced lattice basis is introduced. (iv) The famous LLL algorithm for generating a Lovasz reduced basis is explained. (2) Bayes methods that covers (i) general principle of Bayesian modeling. Explain the notion of prior distribution and posterior distribution. Choose the pragmatic approach for exploring the advantages of iterative Bayesian calculations and hierarchical modeling. (ii) Present the Bayes methods for linear models with normal distributed errors, including noninformative priors, conjugate priors, normal gamma distributions and (iii) short outview to modern application of Bayesian modeling. Useful in case of nonlinear models or linear models with no normal distribution: Monte Carlo (MC), Markov chain Monte Carlo (MCMC), approximative Bayesian computation (ABC) methods. (3) Error-in-variables models, which cover: (i) Introduce the error-in-variables (EIV) model, discuss the difference to least squares estimators (LSE), (ii) calculate the total least squares (TLS) estimator. Summarize the properties of TLS, (iii) explain the idea of simulation extrapolation (SIMEX) estimators, (iv) introduce the symmetrized SIMEX (SYMEX) estimator and its relation to TLS, and (v) short outview to nonlinear EIV models. The chapter on algebraic solution of nonlinear system of equations has also been updated in line with the new emerging field of hybrid numeric-symbolic solutions to systems of nonlinear equations, ermined system of nonlinear equations on curved manifolds. The von Mises–Fisher distribution is characteristic for circular or (hyper) spherical data. Our last chapter is devoted to probabilistic regression, the special Gauss–Markov model with random effects leading to estimators of type BLIP and VIP including Bayesian estimation. A great part of the work is presented in four appendices. Appendix A is a treatment, of tensor algebra, namely linear algebra, matrix algebra, and multilinear algebra. Appendix B is devoted to sampling distributions and their use in terms of confidence intervals and confidence regions. Appendix C reviews the elementary notions of statistics, namely random events and stochastic processes. Appendix D introduces the basics of Groebner basis algebra, its careful definition, the Buchberger algorithm, especially the C. F. Gauss combinatorial algorithm.
This text presents an integrated development of core material from several complex variables and complex algebraic geometry, leading to proofs of Serre's celebrated GAGA theorems relating the two subjects, and including applications to the representation theory of complex semisimple Lie groups. It includes a thorough treatment of the local theory using the tools of commutative algebra, an extensive development of sheaf theory and the theory of coherent analytic and algebraicsheaves, proofs of the main vanishing theorems for these categories of sheaves, and a complete proof of the finite dimensionality of the cohomology of coherent sheaves on compact varieties. The vanishing theorems have a wide variety of applications and these are covered in detail. Of particular interest arethe last three chapters, which are devoted to applications of the preceding material to the study of the structure theory and representation theory of complex semisimple Lie groups. Included are introductions to harmonic analysis, the Peter-Weyl theorem, Lie theory and the structure of Lie algebras, semisimple Lie algebras and their representations, algebraic groups and the structure of complex semisimple Lie groups. All of this culminates in Milicic's proof of the Borel-Weil-Bott theorem,which makes extensive use of the material developed earlier in the text. There are numerous examples and exercises in each chapter. This modern treatment of a classic point of view would be an excellent text for a graduate course on several complex variables, as well as a useful reference for theexpert.
The text covers a broad spectrum between basic and advanced complex variables on the one hand and between theoretical and applied or computational material on the other hand. With careful selection of the emphasis put on the various sections, examples, and exercises, the book can be used in a one- or two-semester course for undergraduate mathematics majors, a one-semester course for engineering or physics majors, or a one-semester course for first-year mathematics graduate students. It has been tested in all three settings at the University of Utah. The exposition is clear, concise, and lively. There is a clean and modern approach to Cauchy's theorems and Taylor series expansions, with rigorous proofs but no long and tedious arguments. This is followed by the rich harvest of easy consequences of the existence of power series expansions. Through the central portion of the text, there is a careful and extensive treatment of residue theory and its application to computation of integrals, conformal mapping and its applications to applied problems, analytic continuation, and the proofs of the Picard theorems. Chapter 8 covers material on infinite products and zeroes of entire functions. This leads to the final chapter which is devoted to the Riemann zeta function, the Riemann Hypothesis, and a proof of the Prime Number Theorem." -- Publisher.
The skyscraper is an American invention that has captured the public's imagination for over a century. The tall building is wholly manmade and borne in the minds of those with both slide rules and computers. This is the story of the skyscraper's rise and the recognition of those individuals who contributed to its development. This volume is unique; its approach, information, and images are fresh and telling. The text examines America's first tall buildings -- the result of twelve years of in-depth research by an accomplished and published architect and architectural historian. Over 300 compelling photographs, charts, and notes make this the ultimate tool of reference for this subject. Biographies woven throughout with period norms, politics and lifestyles help to place featured skyscrapers in context. Quite simply, there is no book like this. The text, carefully and insightfully written, is clear, concise, and easily digestible, the text being the product of well-documented original research written in an informative tone. The American Skyscraper 1850-1940: A Celebration of Height is a richly documented journey of a fascinating topic, and it promises to be a superb addition to libraries, schools of architecture, students of architecture, and lovers of art.
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