The Solid Earth is a general introduction to the study of the physics of the solid Earth, including the workings of both the Earth's surface and its deep interior. The emphasis throughout is on basic physical principles rather than instrumentation or data handling. The second edition of this acclaimed textbook has been revised to bring the content fully up-to-date and to reflect the most recent advances in geophysical research. It is designed for undergraduates on introductory geophysics courses who have a general background in the physical sciences, including introductory calculus. It can also be used as a reference book for graduate students and other researchers in geology and geophysics. Each chapter ends with exercises of various degrees of complexity, for which solutions are available to instructors from www.cambridge.org/9780521893077. The book contains an extensive glossary of geological and physical terms, as well as appendices that develop more advanced mathematical topics.
In this short and very practical 2002 introduction to econometrics Philip Hans Franses guides the reader through the essential concepts of econometrics. Central to the book are practical questions in various economic disciplines, which can be answered using econometric methods and models. The book focuses on a limited number of the essential, most widely used methods, before going on to review the basics of econometrics. The book ends with a number of case studies drawn from recent empirical work to provide an intuitive illustration of what econometricians do when faced with practical questions. Throughout the book Franses emphasises the importance of specification, evaluation and implementation of models appropriate to the data. Assuming basic familiarity only with matrix algebra and calculus the book is designed to appeal as either a short stand-alone introduction for students embarking on an empirical research project or as a supplement to any standard introductory textbook.
International agreements, such as those governing arms control or the environment, virtually always require some degree of verification of information, in order that compliance can be established. To ensure that the verification process can be regarded as efficient, effective and impartial, it is important to have a mathematical model of it. One can be derived by applying methods from statistics and the theory of non-cooperative games, developed in part by John Nash, who received a Nobel prize in 1994 for his work. The methods permit the development of rational verification strategies, as well as such fundamental concepts as guaranteed probability of detection, timeliness of inspections and the deterrence of illegal activity. In this 1996 book, the required theory is introduced gradually in the context of specific real-world examples. The only prerequisites are simple calculus and statistics, so the book should be accessible to a broad range of scientists and non-scientists, in industr
Sub-Riemannian geometry is the geometry of a world with nonholonomic constraints. In such a world, one can move, send and receive information only in certain admissible directions but eventually can reach every position from any other. In the last two decades sub-Riemannian geometry has emerged as an independent research domain impacting on several areas of pure and applied mathematics, with applications to many areas such as quantum control, Hamiltonian dynamics, robotics and Lie theory. This comprehensive introduction proceeds from classical topics to cutting-edge theory and applications, assuming only standard knowledge of calculus, linear algebra and differential equations. The book may serve as a basis for an introductory course in Riemannian geometry or an advanced course in sub-Riemannian geometry, covering elements of Hamiltonian dynamics, integrable systems and Lie theory. It will also be a valuable reference source for researchers in various disciplines.
This text focuses on the parts of stochastic theory that are particularly relevant to applications. It begins with a description of Brownian motion and the associated stochastic calculus, including th
This book provides a rigorous course in the calculus of functions of a real variable. The companion onscreen version of this text contains hundreds of links to alternative approaches, more complete ex
An introductory text pinpointing the stochastic theories useful for application to mathematical finance, queuing, biology, and physics. Durrett (mathematics, Cornell U.) describes Brownian motion and
Combinatory logic and lambda-calculus, originally devised in the 1920s, have since developed into linguistic tools, especially useful in programming languages. The authors' previous book served as the main reference for introductory courses on lambda-calculus for over 20 years: this version is thoroughly revised and offers an account of the subject with the same authoritative exposition. The grammar and basic properties of both combinatory logic and lambda-calculus are discussed, followed by an introduction to type-theory. Typed and untyped versions of the systems, and their differences, are covered. Lambda-calculus models, which lie behind much of the semantics of programming languages, are also explained in depth. The treatment is as non-technical as possible, with the main ideas emphasized and illustrated by examples. Many exercises are included, from routine to advanced, with solutions to most at the end of the book.
Appropriate for a two-term course, this text is an introduction to calculus as applied to business, economics, the life- and physical sciences, the social sciences, and many general areas of interest
"Classroom-tested in a Princeton University honors course, this text offers a unified introduction to advanced calculus. Starting with an abstract treatment of vector spaces and linear transforms, the
Advanced Calculus: An Introduction to Modem Analysis, an advanced undergraduate textbook,provides mathematics majors, as well as students who need mathematics in their field of study,with an introduct
This book is designed to be an easily readable, intimidation-free guide to advanced calculus. Ideas and methods of proof build upon each other and are explained thoroughly. This is the first book to c
This important textbook is based on, though independent of, an educational TV series The Mechanical Universe broadcast on public television in the United States. Its aim is to guide students and general readers to an understanding of how the physical world works; physics is presented as a human endeavour, with historical development forming a thread throughout the text. The prerequisites are minimal, only basic algebra and trigonometry since the necessary calculus is developed in the text, with physics providing the motivation. New concepts are introduced at the natural, logical point with many historical references to place physics in a social perspective. Many topics from twentieth-century physics are included, for example energy, low temperature physics, relativity and black holes. The book is attractively and profusely illustrated and will be welcomed by students and also by general readers for whom this will be a stimulating alternative to other, less-thorough treatments.
Since the early eighteenth century, the theory of networks and graphs has matured into an indispensable tool for describing countless real-world phenomena. However, the study of large-scale features of a network often requires unrealistic limits, such as taking the network size to infinity or assuming a continuum. These asymptotic and analytic approaches can significantly diverge from real or simulated networks when applied at the finite scales of real-world applications. This book offers an approach to overcoming these limitations by introducing operator graph theory, an exact, non-asymptotic set of tools combining graph theory with operator calculus. The book is intended for mathematicians, physicists, and other scientists interested in discrete finite systems and their graph-theoretical description, and in delineating the abstract algebraic structures that characterise such systems. All the necessary background on graph theory and operator calculus is included for readers to underst
The differential geometry of curves and surfaces in Euclidean space has fascinated mathematicians since the time of Newton. Here the authors cast the theory into a new light, that of singularity theory. This second edition has been thoroughly revised throughout and includes a multitude of new exercises and examples. A new final chapter has been added which covers recently developed techniques in the classification of functions of several variables, a subject central to many applications of singularity theory. Also in this second edition are new sections on the Morse lemma and the classification of plane curve singularities. The only prerequisites for students to follow this textbook are a familiarity with linear algebra and advanced calculus. Thus it will be invaluable for anyone who would like an introduction to modern singularity theory.
The differential geometry of curves and surfaces in Euclidean space has fascinated mathematicians since the time of Newton. Here the authors cast the theory into a new light, that of singularity theory. This second edition has been thoroughly revised throughout and includes a multitude of new exercises and examples. A new final chapter has been added which covers recently developed techniques in the classification of functions of several variables, a subject central to many applications of singularity theory. Also in this second edition are new sections on the Morse lemma and the classification of plane curve singularities. The only prerequisites for students to follow this textbook are a familiarity with linear algebra and advanced calculus. Thus it will be invaluable for anyone who would like an introduction to modern singularity theory.
Calculus: A Complete Introduction is the most comprehensive yet easy-to-use introduction to using calculus. Written by a leading expert, this book will help you if you are studying for an important ex
This textbook gives a comprehensive introduction to stochastic processes and calculus in the fields of finance and economics, more specifically mathematical finance and time series econometrics. Over
Quantum gravity is among the most fascinating problems in physics. It modifies our understanding of time, space and matter. The recent development of the loop approach has allowed us to explore domains ranging from black hole thermodynamics to the early Universe. This book provides readers with a simple introduction to loop quantum gravity, centred on its covariant approach. It focuses on the physical and conceptual aspects of the problem and includes the background material needed to enter this lively domain of research, making it ideal for researchers and graduate students. Topics covered include quanta of space; classical and quantum physics without time; tetrad formalism; Holst action; lattice QCD; Regge calculus; ADM and Ashtekar variables; Ponzano-Regge and Turaev-Viro amplitudes; kinematics and dynamics of 4D Lorentzian quantum gravity; spectrum of area and volume; coherent states; classical limit; matter couplings; graviton propagator; spinfoam cosmology and black hole thermody
