Numerical Approximation Methods

This book focuses on structure-preserving numerical methods for flexible multibody dynamics, including nonlinear elastodynamics and geometrically exact models for beams and shells. It also deals with

This book is a guide to modern production planning methods based on both new scientific achievements and various practical planning rules of thumb. Several numerical examples illustrate most of the ca

This book provides a comprehensive discussion of statistical methods that are useful to the business analyst. The book includes a substantial number of case studies and numerical illustrations using t

The subject of special functions is often presented as a collection of disparate results, rarely organized in a coherent way. This book emphasizes general principles that unify and demarcate the subjects of study. The authors' main goals are to provide clear motivation, efficient proofs, and original references for all of the principal results. The book covers standard material, but also much more. It shows how much of the subject can be traced back to two equations - the hypergeometric equation and confluent hypergeometric equation - and it details the ways in which these equations are canonical and special. There is extended coverage of orthogonal polynomials, including connections to approximation theory, continued fractions, and the moment problem, as well as an introduction to new asymptotic methods. There are also chapters on Meijer G-functions and elliptic functions. The final chapter introduces Painlevé transcendents, which have been termed the 'special functions of the twenty-

This volume sets out the basic applied mathematical and numerical methods of chaotic dynamics and illustrates the wide range of phenomena, inside and outside the laboratory, that can be treated as cha

In the summer of 2014 leading experts in the theory of water waves gathered at the Newton Institute for Mathematical Sciences in Cambridge for four weeks of research interaction. A cross-section of those experts was invited to give introductory-level talks on active topics. This book is a compilation of those talks and illustrates the diversity, intensity, and progress of current research in this area. The key themes that emerge are numerical methods for analysis, stability and simulation of water waves, transform methods, rigorous analysis of model equations, three-dimensionality of water waves, variational principles, shallow water hydrodynamics, the role of deterministic and random bottom topography, and modulation equations. This book is an ideal introduction for PhD students and researchers looking for a research project. It may also be used as a supplementary text for advanced courses in mathematics or fluid dynamics.

This new edition is a concise introduction to the basic methods of computational physics. Readers will discover the benefits of numerical methods for solving complex mathematical problems and for

Lyapunov exponents lie at the heart of chaos theory, and are widely used in studies of complex dynamics. Utilising a pragmatic, physical approach, this self-contained book provides a comprehensive description of the concept. Beginning with the basic properties and numerical methods, it then guides readers through to the most recent advances in applications to complex systems. Practical algorithms are thoroughly reviewed and their performance is discussed, while a broad set of examples illustrate the wide range of potential applications. The description of various numerical and analytical techniques for the computation of Lyapunov exponents offers an extensive array of tools for the characterization of phenomena such as synchronization, weak and global chaos in low and high-dimensional set-ups, and localization. This text equips readers with all the investigative expertise needed to fully explore the dynamical properties of complex systems, making it ideal for both graduate students and

Advances in Imaging and Electron Physics merges two long-running serials, Advances in Electronics and Electron Physics andAdvances in Optical and Electron Microscopy.The series features extended artic

This volume contains selected papers in three closely related areas: mathematical modeling in mechanics, numerical analysis, and optimization methods. The papers are based upon talks presented on the

This authoritative treatment covers theory, optimal estimation and a range of practical applications. The first book on the subject, and written by leading researchers, this clear and rigorous work presents a comprehensive theory for both the stability boundary and the stability regions of a range of nonlinear dynamical systems including continuous, discrete, complex, two-time-scale and non-hyperbolic systems, illustrated with numerical examples. The authors also propose new concepts of quasi-stability region and of relevant stability regions and their complete characterisations. Optimal schemes for estimating stability regions of general nonlinear dynamical systems are also covered, and finally the authors describe and explain how the theory is applied in applications including direct methods for power system transient stability analysis, nonlinear optimisation for finding a set of high-quality optimal solutions, stabilisation of nonlinear systems, ecosystem dynamics, and immunisation

In this book the authors describe the principles and methods behind probabilistic forecasting and Bayesian data assimilation. Instead of focusing on particular application areas, the authors adopt a general dynamical systems approach, with a profusion of low-dimensional, discrete-time numerical examples designed to build intuition about the subject. Part I explains the mathematical framework of ensemble-based probabilistic forecasting and uncertainty quantification. Part II is devoted to Bayesian filtering algorithms, from classical data assimilation algorithms such as the Kalman filter, variational techniques, and sequential Monte Carlo methods, through to more recent developments such as the ensemble Kalman filter and ensemble transform filters. The McKean approach to sequential filtering in combination with coupling of measures serves as a unifying mathematical framework throughout Part II. Assuming only some basic familiarity with probability, this book is an ideal introduction for

In this book the authors describe the principles and methods behind probabilistic forecasting and Bayesian data assimilation. Instead of focusing on particular application areas, the authors adopt a general dynamical systems approach, with a profusion of low-dimensional, discrete-time numerical examples designed to build intuition about the subject. Part I explains the mathematical framework of ensemble-based probabilistic forecasting and uncertainty quantification. Part II is devoted to Bayesian filtering algorithms, from classical data assimilation algorithms such as the Kalman filter, variational techniques, and sequential Monte Carlo methods, through to more recent developments such as the ensemble Kalman filter and ensemble transform filters. The McKean approach to sequential filtering in combination with coupling of measures serves as a unifying mathematical framework throughout Part II. Assuming only some basic familiarity with probability, this book is an ideal introduction for

Teach Your Students Both the Mathematics of Numerical Methods and the Art of Computer ProgrammingIntroduction to Computational Linear Algebra presents classroom-tested material on computational linear

Uniting classical and modern photonics approaches by presenting optical analyses as solutions of Maxwell's equations, this unique book enables students and practising engineers to fully understand the similarities and differences between the different methods. The book begins with a thorough discussion of plane wave analysis, which provides a clear understanding of optics without considering boundary condition or device configuration. It then goes on to cover diffraction analysis of many applications, including a rigorous analysis of TEM waves using Maxwell's equations with boundaries. Laser cavity modes and Gaussian beams are presented, modal analysis is covered, and approximation methods are discussed (including the perturbation technique, coupled mode analysis, and super mode analysis). With theory linked to practical examples throughout, it provides a clear understanding of the interplay between plane wave, diffraction and modal analysis, and how the different techniques can be app

Based on a starter course for beginning graduate students, Core Statistics provides concise coverage of the fundamentals of inference for parametric statistical models, including both theory and practical numerical computation. The book considers both frequentist maximum likelihood and Bayesian stochastic simulation while focusing on general methods applicable to a wide range of models and emphasizing the common questions addressed by the two approaches. This compact package serves as a lively introduction to the theory and tools that a beginning graduate student needs in order to make the transition to serious statistical analysis: inference; modeling; computation, including some numerics; and the R language. Aimed also at any quantitative scientist who uses statistical methods, this book will deepen readers' understanding of why and when methods work and explain how to develop suitable methods for non-standard situations, such as in ecology, big data and genomics.

Based on a starter course for beginning graduate students, Core Statistics provides concise coverage of the fundamentals of inference for parametric statistical models, including both theory and practical numerical computation. The book considers both frequentist maximum likelihood and Bayesian stochastic simulation while focusing on general methods applicable to a wide range of models and emphasizing the common questions addressed by the two approaches. This compact package serves as a lively introduction to the theory and tools that a beginning graduate student needs in order to make the transition to serious statistical analysis: inference; modeling; computation, including some numerics; and the R language. Aimed also at any quantitative scientist who uses statistical methods, this book will deepen readers' understanding of why and when methods work and explain how to develop suitable methods for non-standard situations, such as in ecology, big data and genomics.

Computational Fluid Dynamics: Principles and Applications, Third Edition presents students, engineers, and scientists with all they need to gain a solid understanding of the numerical methods and prin

This book gives a concise overview of the mathematical foundations of kinetics used in chemistry and systems biology. The analytical and numerical methods used to solve complex rate equations with the

??This volume arose from the Third Annual Workshop on Inverse Problems, held in Stockholm on May 2-6, 2012. The proceedings present new analytical developments and numerical methods for solutions of i

This comprehensive content and reference work on atmospheric models covers not only the methods for numerical modeling, but also the related fields of assimilation and predictability. It includes dist

This basic textbook presents the field of mechanical vibration and structural dynamics in an understandable and interdisciplinary way for students, engineers and researchers in mechanical engineering.

This book deals with the design, numerical simulation, state of the art fabrication processes and methods, qualitative and quantitative tests, and measurement techniques of wearable and flexible anten

This textbook introduces readers to the basic concepts of quasi-Monte Carlo methods for numerical integration and to the theory behind them. The comprehensive treatment of the subject with detailed ex

This volume sets out the basic applied mathematical and numerical methods of chaotic dynamics and illustrates the wide range of phenomena, inside and outside the laboratory, that can be treated as cha

The development of lasers capable of producing high-intensity pulses has opened a new area in the study of light-matter interactions. The corresponding laser fields are strong enough to compete with the Coulomb forces in controlling the dynamics of atomic systems and give rise to multiphoton processes. This book presents a unified account of this rapidly developing field of physics. The first part describes the fundamental phenomena occurring in intense laser-atom interactions and gives the basic theoretical framework to analyze them. The second part contains a detailed discussion of Floquet theory, the numerical integration of the wave equations and approximation methods for the low- and high-frequency regimes. In the third part, the main multiphoton processes are discussed: multiphoton ionization, high harmonic and attosecond pulse generation, and laser-assisted electron-atom collisions. Aimed at graduate students in atomic, molecular and optical physics, the book will also interest

Simulation of ODE/PDE Models with MATLABR, OCTAVE and SCILAB shows the reader how to exploit a fuller array of numerical methods for the analysis of complex scientific and engineering systems than is

Table of Contents: 1. Data and Distributions 2. Numerical Summary Measures 3. Bivariate and Multivariate Data 4. Obtaining Data 5. Probability and Sampling Distributions 6. Quality and Reliability 7. Estimation and Statistical Intervals 8. Testing Statistical Hypotheses 9. The Analysis of Variance 10. Experimental Design 11. Inferential Methods in Regression and Correlation

Over forty years of teaching experience are distilled into this text. The guiding principle is the wide use of the concept of intermediate asymptotics, which enables the natural introduction of the modeling of real bodies by continua. Beginning with a detailed explanation of the continuum approximation for the mathematical modeling of the motion and equilibrium of real bodies, the author continues with a general survey of the necessary methods and tools for analyzing models. Next, specific idealized approximations are presented, including ideal incompressible fluids, elastic bodies and Newtonian viscous fluids. The author not only presents general concepts but also devotes chapters to examining significant problems, including turbulence, wave-propagation, defects and cracks, fatigue and fracture. Each of these applications reveals essential information about the particular approximation. The author's tried and tested approach reveals insights that will be valued by every teacher and st

This textbook explores approximate solutions to general relativity and their consequences. It offers a unique presentation of Einstein's theory by developing powerful methods that can be applied to astrophysical systems. Beginning with a uniquely thorough treatment of Newtonian gravity, the book develops post-Newtonian and post-Minkowskian approximation methods to obtain weak-field solutions to the Einstein field equations. The book explores the motion of self-gravitating bodies, the physics of gravitational waves, and the impact of radiative losses on gravitating systems. It concludes with a brief overview of alternative theories of gravity. Ideal for graduate courses on general relativity and relativistic astrophysics, the book examines real-life applications, such as planetary motion around the Sun, the timing of binary pulsars, and gravitational waves emitted by binary black holes. Text boxes explore related topics and provide historical context, and over 100 exercises present chal

Boolean functions are perhaps the most basic objects of study in theoretical computer science. They also arise in other areas of mathematics, including combinatorics, statistical physics, and mathematical social choice. The field of analysis of Boolean functions seeks to understand them via their Fourier transform and other analytic methods. This text gives a thorough overview of the field, beginning with the most basic definitions and proceeding to advanced topics such as hypercontractivity and isoperimetry. Each chapter includes a 'highlight application' such as Arrow's theorem from economics, the Goldreich–Levin algorithm from cryptography/learning theory, Håstad's NP-hardness of approximation results, and 'sharp threshold' theorems for random graph properties. The book includes roughly 450 exercises and can be used as the basis of a one-semester graduate course. It should appeal to advanced undergraduates, graduate students and researchers in computer science theory and related mat

A solid introduction to mathematical modeling for a range of chemical engineering applications, covering model formulation, simplification and validation. It explains how to describe a physical/chemical reality in mathematical language and how to select the type and degree of sophistication for a model. Model reduction and approximation methods are presented, including dimensional analysis, time constant analysis and asymptotic methods. An overview of solution methods for typical classes of models is given. As final steps in model building, parameter estimation and model validation and assessment are discussed. The reader is given hands-on experience of formulating new models, reducing the models and validating the models. The authors assume the knowledge of basic chemical engineering, in particular transport phenomena, as well as basic mathematics, statistics and programming. The accompanying problems, tutorials, and projects include model formulation at different levels, analysis, pa

Among all the numerical methods in seismology, the finite-difference (FD) technique provides the best balance of accuracy and computational efficiency. This book offers a comprehensive introduction to FD and its applications to earthquake motion. Using a systematic tutorial approach, the book requires only undergraduate degree-level mathematics and provides a user-friendly explanation of the relevant theory. It explains FD schemes for solving wave equations and elastodynamic equations of motion in heterogeneous media, and provides an introduction to the rheology of viscoelastic and elastoplastic media. It also presents an advanced FD time-domain method for efficient numerical simulations of earthquake ground motion in realistic complex models of local surface sedimentary structures. Accompanied by a suite of online resources to help put the theory into practice, this is a vital resource for professionals and academic researchers using numerical seismological techniques, and graduate st

"This book gives a comprehensive introduction to numerical methods and analysis of stochastic processes, random fields and stochastic differential equations, and offers graduate students and researche

Plasmonic nanostructures provide new ways of manipulating the flow of light with nanostructures and nanoparticles exhibiting optical properties never before seen in the macro-world. Covering plasmonic technology from fundamental theory to real world applications, this work provides a comprehensive overview of the field. • Discusses the fundamental theory of plasmonics, enabling a deeper understanding of plasmonic technology • Details numerical methods for modeling, design and optimization of plasmonic nanostructures • Includes step-by-step design guidelines for active and passive plasmonic devices, demonstrating the implementation of real devices in the standard CMOS nanoscale electronic-photonic integrated circuit to help cut design, fabrication and characterisation time and cost • Includes real-world case studies of plasmonic devices and sensors, explaining the benefits and downsides of different nanophotonic integrated circuits and sensing platforms. Ideal for researchers, engineer

This book covers subjects in applied mathematics, numerical methods, solid mechanics, thermodynamics and fluid mechanics that mechanical engineers will meet in their careers, and covers the analysis o

Numerical and Analytical Methods with MATLAB for Electrical Engineers，by William Bober and Andrew Stevens 2013 by Taylor & Francis Group,LLC. Authorized translation from English language edition publ

Emphasizing fundamental concepts that allow a student, novice, or practicing engineer to carry out practical design decisions, Polymer Processing: Principles and Design provides the numerical methods

The book describes various unit operations in batch and bioprocessing and design methods for these units. Numerical methods are necessary to solve these design problems. The time-dependent nature of b

This book describes the theoretical and practical aspects of solving complicated and coupled models in engineering with analytical and numerical methods. It covers analytical and numerical methods in