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Air-Ice-Ocean Interaction : Turbulent Ocean Boundary Layer Exchange Processes
At a time when the polar regions are undergoing rapid and unprecedented change, understanding exchanges of momentum, heat and salt at the ice-ocean interface is critical for realistically predicting the future state of sea ice. By offering a measurement platform largely unaffected by surface waves, drifting sea ice provides a unique laboratory for studying aspects of geophysical boundary layer flows that are extremely difficult to measure elsewhere. This book draws on both extensive observations and theoretical principles to develop a concise description of the impact of stress, rotation, and buoyancy on the turbulence scales that control exchanges between the atmosphere and underlying ocean when sea ice is present. Several interesting and unique observational data sets are used to illustrate different aspects of ice-ocean interaction ranging from the impact of salt on melting in the Greenland Sea marginal ice zone, to how nonlinearities in the equation of state for seawater affect mixing in the Weddell Sea.
Affect and Mathematics Education : Fresh Perspectives on Motivation, Engagement, and Identity
Presents the latest trends in research in the area. Following an introduction and a survey chapter providing a concise overview of the state-of-art in the field of mathematics-related affect, the book is divided into three main sections: motivation and values, engagement, and identity in mathematics education. Each section comprises several independent chapters based on original research, as well as a reflective commentary by an expert in the area. Collectively, the chapters present a rich methodological spectrum, from narrative analysis to structural equation modelling.
Advances in Mathematical and Statistical Modeling
Enrique Castillo is a leading figure in several mathematical, statistical, and engineering fields, having contributed seminal work in such areas as statistical modeling, extreme value analysis, multivariate distribution theory, Bayesian networks, neural networks, functional equations, artificial intelligence, linear algebra, optimization methods, numerical methods, reliability engineering, as well as sensitivity analysis and its applications. Organized to honor Castillo's significant contributions, this volume is an outgrowth of the International Conference on Mathematical and Statistical Modeling and covers recent advances in the field. Also presented are applications to safety, reliability and life-testing, financial modeling, quality control, general inference, as well as neural networks and computational techniques.
Advanced Visual Quantum Mechanics
Investigate and to teach quantum mechanics with the aid of computer-generated animations. It is a self-contained textbook that combines selected topics from atomic physics (spherical symmetry, the hydrogen atom, and particles with spin) with an introduction to quantum information theory (qubits, EPR paradox, teleportation, quantum computers). It explores relativistic quantum mechanics and the strange behavior of Dirac equation solutions. A series of appendices covers important topics from perturbation and scattering theory. The book places an emphasis on ideas and concepts, with a fair to moderate amount of mathematical rigor. Though this book stands alone, it can also be paired with Thaller Visual Quantum Mechanics to form a comprehensive course in quantum mechanics. The software for the first book earned the European Academic Software Award 2000 for outstanding innovation in its field.
Advanced Real Analysis
Basic Real Analysis and Advanced Real Analysis (available separately or together as a Set) systematically develop those concepts and tools in real analysis that are vital to every mathematician, whether pure or applied, aspiring or established. These works present a comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics.
Advanced Quantum Mechanics
Discusses nonrelativistic multi-particle systems, relativistic wave equations and relativistic quantum fields. Characteristic of the author´s work are the comprehensive mathematical discussions in which all intermediate steps are derived and where numerous examples of application and exercises help the reader gain a thorough working knowledge of the subject. The topics treated in the book lay the foundation for advanced studies in solid-state physics, nuclear and elementary particle physics. This text both extends and complements Schwabl´s introductory Quantum Mechanics, which covers nonrelativistic quantum mechanics and offers a short treatment of the quantization of the radiation field. The fourth edition has been thoroughly revised with new material having been added. Furthermore, the layout of the figures has been unified, which should facilitate comprehension.
Advanced Quantum Mechanics
Advanced Quantum Mechanics, the second volume on quantum mechanics by Franz Schwabl, discusses nonrelativistic multi-particle systems, relativistic wave equations and relativistic fields. Characteristic of Schwabl’s work, this volume features a compelling mathematical presentation in which all intermediate steps are derived and where numerous examples for application and exercises help the reader to gain a thorough working knowledge of the subject. The treatment of relativistic wave equations and their symmetries and the fundamentals of quantum field theory lay the foundations for advanced studies in solid-state physics, nuclear and elementary particle physics. This text extends and complements Schwabl’s introductory Quantum Mechanics, which covers nonrelativistic quantum mechanics and offers a short treatment of the quantization of the radiation field. New material has been added to this third edition of Advanced Quantum Mechanics on Bose gases, the Lorentz covariance of the Dirac equation, and the ‘hole theory’ in the chapter "Physical Interpretation of the Solutions to the Dirac Equation."
Adaptive Mesh Refinement - Theory and Applications; Proceedings of the Chicago Workshop on Adaptive Mesh Refinement Methods, Sept. 3-5, 2003
Advanced numerical simulations that use adaptive mesh refinement (AMR) methods have now become routine in engineering and science. Originally developed for computational fluid dynamics applications these methods have propagated to fields as diverse as astrophysics, climate modeling, combustion, biophysics and many others. The underlying physical models and equations used in these disciplines are rather different, yet algorithmic and implementation issues facing practitioners are often remarkably similar. Unfortunately, there has been little effort to review the advances and outstanding issues of adaptive mesh refinement methods across such a variety of fields. This book attempts to bridge this gap. The book presents a collection of papers by experts in the field of AMR who analyze past advances in the field and evaluate the current state of adaptive mesh refinement methods in scientific computing.
Acoustics for Engineers : Troy Lectures
This book provides the material for an introductory course in engineering acoustics for students with basic knowledge in mathematics. It is based on extensive teaching experience at the university level. Under the guidance of an academic teacher it is sufficient as the sole textbook for the subject.
Absolute Stability of Nonlinear Control Systems
Following the recent developments in the field of absolute stability, Professor Xiaoxin Liao, in conjunction with Professor Pei Yu, has created a second edition of his seminal work on the subject. Liao begins with an introduction to the Lurie problem and the Lurie control system, before moving on to the simple algebraic sufficient conditions for the absolute stability of autonomous and non-autonomous ODE systems, as well as several special classes of Lurie-type systems. The focus of the book then shifts toward the new results and research that have appeared in the decade since the first edition was published. This includes nonlinear control systems with multiple controls, interval control systems, time-delay and neutral Lurie control systems, systems described by functional differential equations, the absolute stability for neural networks, as well as applications to chaos control and chaos synchronization.
A Short Course on Operator Semigroups
Gives a streamlined and systematic introduction to strongly continuous semigroups of bounded linear operators on Banach spaces. It treats the fundamental Hille-Yosida generation theorem as well as perturbation and approximation theorems for generators and semigroups.
A Remarkable Collection of Babylonian Mathematical Texts : Manuscripts in the Schøyen Collection: Cuneiform Texts I
This new text from Jöran Friberg, the leading expert on Babylonian mathematics, presents 130 previously unpublished mathematical clay tablets from the Norwegian Schøyen collection, and provides a synthesis of the author's most important work. Through a close study of these tablets, Friberg has made numerous amazing discoveries, including the first known examples of pre-Classical labyrinths and mazes, a new understanding of the famous table text Plimpton 322, and new evidence of Babylonian familiarity with sophisticated mathematical ideas and objects, such as the three-dimensional Pythagorean equation and the icosahedron.
A Primer on Environmental Decision-Making: an integrative quantitative approach
Integrates decision-making and environmental science. For ecologists it will bridge the gap to economics. For practitioners in environmental economics and management it will be a major reference book. It probably contains the largest collection available of expressions and basic equations that are used in environmental sciences. Applying these expressions as "rules-of-thumb" will give participants in a decision-making process a common platform for discussion and arbitration.
A Geometric Approach to Differential Forms
The modern subject of differential forms subsumes classical vector calculus. This text presents differential forms from a geometric perspective accessible at the undergraduate level. The book begins with basic concepts such as partial differentiation and multiple integration and gently develops the entire machinery of differential forms. Each new concept is presented with a natural picture that students can easily grasp. Algebraic properties then follow. This facilitates the development of differential forms without assuming a background in linear algebra. Throughout the text, emphasis is placed on applications in 3 dimensions, but all definitions are given so as to be easily generalized to higher dimensions. A centerpiece of the text is the generalized Stokes' theorem. Although this theorem implies all of the classical integral theorems of vector calculus, it is far easier for students to both comprehend and remember.
A First Course in Differential Equations
This text is designed for the standard post-calculus course in elementary differential equations. It is a brief, one-semester treatment of the basic ideas, models, and solution methods. The book, which serves as an alternative to existing texts for instructors who want more concise coverage, emphasizes graphical, analytical, and numerical approaches, and is written with clear language in a user-friendly format. It provides students with the tools to continue on to the next level in applying differential equations to problems in engineering, science, and applied mathematics.
A Dressing Method in Mathematical Physics
The monograph is devoted to the systematic presentation of the so called "dressing method" for solving differential equations (both linear and nonlinear) of mathematical physics. The essence of the dressing method consists in a generation of new non-trivial solutions of a given equation from (maybe trivial) solution of the same or related equation.
A Course in Calculus and Real Analysis
This book provides a self-contained and rigorous introduction to calculus of functions of one variable. The presentation and sequencing of topics emphasizes the structural development of calculus. At the same time, due importance is given to computational techniques and applications. The authors have strived to make a distinction between the intrinsic definition of a geometric notion and its analytic characterization. It highlight the fact that calculus provides a firm foundation to several concepts and results that are generally encountered in high school and accepted on faith. For example, one can find here a proof of the classical result that the ratio of the circumference of a circle to its diameter is the same for all circles. Also, this book helps get a clear understanding of the concept of an angle and the definitions of the logarithmic, exponential and trigonometric functions together with a proof of the fact that these are not algebraic functions. A number of topics that may have been inadequately covered in calculus courses and glossed over in real analysis courses are treated here in considerable detail. As such, this book provides a unified exposition of calculus and real analysis.
A Concise Course on Stochastic Partial Differential Equations
Concentrate on (nonlinear) stochastic partial differential equations (SPDE) of evolutionary type. All kinds of dynamics with stochastic influence in nature or man-made complex systems can be modelled by such equations.
A Computational Differential Geometry Approach to Grid Generation
This monograph gives a detailed treatment of applications of geometric methods to advanced grid technology. It focuses on and describes a comprehensive approach based on the numerical solution of inverted Beltramian and diffusion equations with respect to monitor metrics for generating both structured and unstructured grids in domains and on surfaces.
A Benchmark Approach to Quantitative Finance
The general framework is used to provide an understanding of the nature of stochastic volatility. The book is intended for a wide audience that includes quantitative analysts, postgraduate students and practitioners in finance, economics and insurance. It aims to be a self-contained, accessible but mathematically rigorous introduction to quantitative finance for readers that have a reasonable mathematical or quantitative background. Finally, the book should stimulate interest in the benchmark approach by describing some of its power and wide applicability.
