Numerical Approximation Methods

The stratified ocean mixes episodically in small patches where energy is dissipated and density smoothed over scales of centimeters. The net effect of these countless events effects the shape of the ocean's thermocline, how heat is transported from the sea surface to the interior, and how dense bottom water is lifted into the global overturning circulation. This book explores the primary factors affecting mixing, beginning with the thermodynamics of seawater, how they vary in the ocean and how they depend on the physical properties of seawater. Turbulence and double diffusion are then discussed, which determines how mixing evolves and the different impacts it has on velocity, temperature, and salinity. It reviews insights from both laboratory studies and numerical modelling, emphasising the assumptions and limitations of these methods. This is an excellent reference for researchers and graduate students working to advance our understanding of mixing, including oceanographers, atmospher

Insights from the history of numerical notation suggest that how humans write numbers is an active choice involving cognitive and social factors.Over the past 5,000 years, more than 100 methods of num

This combines theory and practice for the design of earth lateral support for deep excavations in soil, along with design methods, basic and computational numerical methods. It is heavily illustrated

This title begins with the basic principles of electromagnetics and builds up to intricate optical filter designs, numerical optimization techniques, and production methods. It includes worked and pra

This title begins with the basic principles of electromagnetics and builds up to intricate optical filter designs, numerical optimization techniques, and production methods. It includes worked and pra

This must-have manual provides detailed solutions to all of the 300 exercises in Dickson, Hardy and Waters' Actuarial Mathematics for Life Contingent Risks, 3 edition. This groundbreaking text on the modern mathematics of life insurance is required reading for the Society of Actuaries' (SOA) LTAM Exam. The new edition treats a wide range of newer insurance contracts such as critical illness and long-term care insurance; pension valuation material has been expanded; and two new chapters have been added on developing models from mortality data and on changing mortality. Beyond professional examinations, the textbook and solutions manual offer readers the opportunity to develop insight and understanding through guided hands-on work, and also offer practical advice for solving problems using straightforward, intuitive numerical methods. Companion Excel spreadsheets illustrating these techniques are available for free download.

Mathematical analysis is key to the modeling and management of natural resources. By presenting required mathematical methods, classic dynamic models for non-renewable and renewable resources, and by exploring several contemporary problems, this text provides a foundation for advanced research. Topics include seminal models in fishery, forestry and non-renewable resource management, as well as an extensive collection of contemporary applications that include the optimal transition from fossil fuels to clean energy, the optimal timing of interventions to save endangered species, pest control and the optimal management of antibiotic resistance. Deterministic and stochastic models in both discrete and continuous time are covered. The book encourages students to pursue a deeper understanding of the analytics of resource problems and to deploy numerical methods when analytical results prove intractable. The combination of analysis, theory and applications will launch the next generation of

Mathematical analysis is key to the modeling and management of natural resources. By presenting required mathematical methods, classic dynamic models for non-renewable and renewable resources, and by exploring several contemporary problems, this text provides a foundation for advanced research. Topics include seminal models in fishery, forestry and non-renewable resource management, as well as an extensive collection of contemporary applications that include the optimal transition from fossil fuels to clean energy, the optimal timing of interventions to save endangered species, pest control and the optimal management of antibiotic resistance. Deterministic and stochastic models in both discrete and continuous time are covered. The book encourages students to pursue a deeper understanding of the analytics of resource problems and to deploy numerical methods when analytical results prove intractable. The combination of analysis, theory and applications will launch the next generation of

The theory of Toeplitz matrices and operators is a vital part of modern analysis, with applications to moment problems, orthogonal polynomials, approximation theory, integral equations, bounded- and vanishing-mean oscillations, and asymptotic methods for large structured determinants, among others. This friendly introduction to Toeplitz theory covers the classical spectral theory of Toeplitz forms and Wiener–Hopf integral operators and their manifestations throughout modern functional analysis. Numerous solved exercises illustrate the results of the main text and introduce subsidiary topics, including recent developments. Each chapter ends with a survey of the present state of the theory, making this a valuable work for the beginning graduate student and established researcher alike. With biographies of the principal creators of the theory and historical context also woven into the text, this book is a complete source on Toeplitz theory.

This enduringly popular undergraduate textbook has been thoroughly reworked and updated, and now comprises twelve chapters covering the same breadth of topics as earlier editions, but in a substantially modernized fashion to facilitate classroom teaching. Covering both theoretical and applied aspects of geophysics, clear explanations of the physical principles are blended with step-by-step derivations of the key equations and over 400 explanatory figures to explain the internal structure and properties of the planet, including its petroleum and mineral resources. New topics include the latest data acquisition technologies, such as satellite geophysics, planetary landers, ocean bottom seismometers, and fibre optic methods, as well as recent research developments in ambient noise interferometry, seismic hazard analysis, rheology, and numerical modelling - all illustrated with examples from the scientific literature. Student-friendly features include separate text boxes with auxiliary exp

This enduringly popular undergraduate textbook has been thoroughly reworked and updated, and now comprises twelve chapters covering the same breadth of topics as earlier editions, but in a substantially modernized fashion to facilitate classroom teaching. Covering both theoretical and applied aspects of geophysics, clear explanations of the physical principles are blended with step-by-step derivations of the key equations and over 400 explanatory figures to explain the internal structure and properties of the planet, including its petroleum and mineral resources. New topics include the latest data acquisition technologies, such as satellite geophysics, planetary landers, ocean bottom seismometers, and fibre optic methods, as well as recent research developments in ambient noise interferometry, seismic hazard analysis, rheology, and numerical modelling - all illustrated with examples from the scientific literature. Student-friendly features include separate text boxes with auxiliary exp

This book provides a self-contained introduction to the simulation of flow and transport in porous media, written by a developer of numerical methods. The reader will learn how to implement reservoir simulation models and computational algorithms in a robust and efficient manner. The book contains a large number of numerical examples, all fully equipped with online code and data, allowing the reader to reproduce results, and use them as a starting point for their own work. All of the examples in the book are based on the MATLAB Reservoir Simulation Toolbox (MRST), an open-source toolbox popular popularity in both academic institutions and the petroleum industry. The book can also be seen as a user guide to the MRST software. It will prove invaluable for researchers, professionals and advanced students using reservoir simulation methods. This title is also available as Open Access on Cambridge Core.

Organizations and businesses strive toward excellence, and solutions to problems are based mostly on judgment and experience. However, increased competition and consumer demands require that the solutions be optimum and not just feasible. Theory leads to algorithms. Algorithms need to be translated into computer codes. Engineering problems need to be modeled. Optimum solutions are obtained using theory and computers, and then interpreted. Revised and expanded in its third edition, this textbook integrates theory, modeling, development of numerical methods, and problem solving, thus preparing students to apply optimization to real-world problems. This text covers a broad variety of optimization problems using: unconstrained, constrained, gradient, and non-gradient techniques; duality concepts; multi-objective optimization; linear, integer, geometric, and dynamic programming with applications; and finite element-based optimization. It is ideal for advanced undergraduate or graduate cours

The seismic ambient field allows us to study interactions between the atmosphere, the oceans and the solid Earth. The theoretical understanding of seismic ambient noise has improved substantially in the last decades, and the number of its applications has increased dramatically. With chapters written by eminent scientists from the field, this book covers a range of topics including ambient noise observations, generation models of their physical origins, numerical modelling and processing methods. The later chapters focus on applications in imaging and monitoring the internal structure of the Earth, including interferometry for time-dependant imaging and tomography. This volume thus provides a comprehensive overview of this cutting-edge discipline for graduate students studying geophysics and for scientists working in seismology and other imaging sciences.

This comprehensive and self-contained text presents the fundamentals of optical imaging from the viewpoint of both ray and wave optics, within a single volume. Comprising three distinct parts, it opens with an introduction to electromagnetic theory, including electromagnetic diffraction problems and how they can be solved with the aid of standard numerical methods such as RCWA or FDTD. The second part is devoted to the basic theory of geometrical optics and the study of optical aberrations inherent in imaging systems, including large-scale telescopes and high-resolution projection lenses. A detailed overview of state-of-the-art optical system design provides readers with the necessary tools to successfully use commercial optical design software. The final part explores diffraction theory and concludes with vectorial wave propagation, image formation and image detection in high-aperture imaging systems. The wide-ranging perspective of this important book provides researchers and profess

Instabilities are present in all natural fluids from rivers to atmospheres. This book considers the physical processes that generate instability. Part I describes the normal mode instabilities most important in geophysical applications, including convection, shear instability and baroclinic instability. Classical analytical approaches are covered, while also emphasising numerical methods, mechanisms such as internal wave resonance, and simple `rules of thumb' that permit assessment of instability quickly and intuitively. Part II introduces the cutting edge: nonmodal instabilities, the relationship between instability and turbulence, self-organised criticality, and advanced numerical techniques. Featuring numerous exercises and projects, the book is ideal for advanced students and researchers wishing to understand flow instability and apply it to their own research. It can be used to teach courses in oceanography, atmospheric science, coastal engineering, applied mathematics and environ

A modern pedagogical treatment of the latest industry trends in rocket propulsion, developed from the authors' extensive experience in both industry and academia. Students are guided along a step-by-step journey through modern rocket propulsion, beginning with the historical context and an introduction to top-level performance measures, and progressing on to in-depth discussions of the chemical aspects of fluid flow combustion thermochemistry and chemical equilibrium, solid, liquid, and hybrid rocket propellants, mission requirements, and an overview of electric propulsion. With a wealth of homework problems (and a solutions manual for instructors online), real-life case studies and examples throughout, and an appendix detailing key numerical methods and links to additional online resources, this is a must-have guide for senior and first year graduate students looking to gain a thorough understanding of the topic along with practical tools that can be applied in industry.

Covering basic physical concepts, experimental methods, and applications, this book is an indispensable text on the fascinating science of magnetism, and an invaluable source of practical reference data. Accessible, authoritative, and assuming undergraduate familiarity with vectors, electromagnetism and quantum mechanics, this textbook is well suited to graduate courses. Emphasis is placed on practical calculations and numerical magnitudes - from nanoscale to astronomical scale - focussing on modern applications, including permanent magnet structures and spin electronic devices. Each self-contained chapter begins with a summary, and ends with exercises and further reading. The book is thoroughly illustrated with over 600 figures to help convey concepts and explain ideas clearly. Easily digestible tables and data sheets provide a wealth of useful information on magnetic properties. The thirty-eight principal magnetic materials, and many more related compounds, are treated in detail.

Stochastic differential equations are differential equations whose solutions are stochastic processes. They exhibit appealing mathematical properties that are useful in modeling uncertainties and noisy phenomena in many disciplines. This book is motivated by applications of stochastic differential equations in target tracking and medical technology and, in particular, their use in methodologies such as filtering, smoothing, parameter estimation, and machine learning. It builds an intuitive hands-on understanding of what stochastic differential equations are all about, but also covers the essentials of Itô calculus, the central theorems in the field, and such approximation schemes as stochastic Runge–Kutta. Greater emphasis is given to solution methods than to analysis of theoretical properties of the equations. The book's practical approach assumes only prior understanding of ordinary differential equations. The numerous worked examples and end-of-chapter exercises include application-

Stochastic differential equations are differential equations whose solutions are stochastic processes. They exhibit appealing mathematical properties that are useful in modeling uncertainties and noisy phenomena in many disciplines. This book is motivated by applications of stochastic differential equations in target tracking and medical technology and, in particular, their use in methodologies such as filtering, smoothing, parameter estimation, and machine learning. It builds an intuitive hands-on understanding of what stochastic differential equations are all about, but also covers the essentials of Itô calculus, the central theorems in the field, and such approximation schemes as stochastic Runge–Kutta. Greater emphasis is given to solution methods than to analysis of theoretical properties of the equations. The book's practical approach assumes only prior understanding of ordinary differential equations. The numerous worked examples and end-of-chapter exercises include application-

This book aims at providing an overview of state-of-the-art in both the theory and methods of intuitionistic fuzzy logic, partial differential equations and numerical methods in informatics. It covers

This book explores the most significant computational methods and the history of their development. It begins with the earliest mathematical / numerical achievements made by the Babylonians and the Gr

This book presents a comprehensive introduction to design sensitivity analysis theory as applied to electromagnetic systems. It treats the subject in a unified manner, providing numerical methods and

This book focuses on finite element methods with emphasis on MATLAB for numerical modeling of electromagnetic problems. Providing readers with knowledge and skills thorough which they can develop thei

The book presents efficient numerical methods for simulation and analysis of physical processes exhibiting fractional order (FO) dynamics. The book introduces FO system identification method to estima

In this textbook a combination of standard mathematics and modern numerical methods is used to describe a wide range of natural wave phenomena, such as sound, light and water waves, particularly in sp

Discover a modern approach to the analysis, modeling and design of high sensitivity phased arrays. Network theory, numerical methods and computational electromagnetic simulation techniques are uniquely combined to enable full system analysis and design optimization. Beamforming and array signal processing theory are integrated into the treatment from the start. Digital signal processing methods such as polyphase filtering and RFI mitigation are described, along with technologies for real-time hardware implementation. Key concepts from interferometric imaging used in radio telescopes are also considered. A basic development of theory and modeling techniques is accompanied by problem sets that guide readers in developing modeling codes that retain the simplicity of the classical array factor method while incorporating mutual coupling effects and interactions between elements. Combining current research trends with pedagogical material suitable for a first-year graduate course, this is an

This easy-to-understand textbook presents a modern approach to learning numerical methods (or scientific computing), with a unique focus on the modeling and applications of the mathematical content. E

Wood Fracture Characterization provides a guide to the application of modern fracture mechanics concepts to wood materials. The authors cover tests, data reduction schemes and numerical methods for wo

This is a monograph on the emerging branch of mathematical biophysics combining asymptotic analysis with numerical and stochastic methods to analyze partial differential equations arising in biologica

The Hoovers provide an example-based treatment of numerical methods for atomistic and continuum simulations of systems at and away from equilibrium, but focus mostly on non-equilibrium systems, and

An Introduction to Generalized Linear Models, Fourth Edition provides a cohesive framework for statistical modelling, with an emphasis on numerical and graphical methods. This new edition of a bestsel

An Introduction to Generalized Linear Models, Fourth Edition provides a cohesive framework for statistical modelling, with an emphasis on numerical and graphical methods. This new edition of a bestsel

Written in a clear, logical and concise manner, this comprehensive resource provides discussion on essential mathematical tools, required for upgraded system performance. Understanding of basic principles and governing laws is essential to reduce complexity of the system, and this guide offers detailed discussion on analytical and numerical techniques to solve mathematical model equations. Important concepts including nonlinear algebraic equations, initial value ordinary differential equations (ODEs) and boundary value ODEs are discussed in detail. The concepts of optimization methods and sensitivity analysis, which are important from subject point of view, are explained with suitable examples. Numerous problems and MATLAB®/Scilab exercises are interspersed throughout the text. Several case studies involving full details of simulation are offered for better understanding. The accompanying website will host additional MATLAB®/Scilab problems, model question papers, simulation exercises,