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1 Software Dvelopment 2 Solution of Transcendental Equation 3 Numerical Integration 4 Solutions of ordinary Differential Equations 5 Interpolation 6 Curve Fitting 7 Solution of Linear Algebraic Equation & Iterative method 8 Finite Element Analysis 9 Finite Difference Methods
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Reviews the fundamental concepts behind the theory and computation of electromagnetic fields The book is divided in two parts. The first part covers both fundamental theories (such as vector analysis, Maxwell’s equations, boundary condition, and transmission line theory) and advanced topics (such as wave transformation, addition theorems, and fields in layered media) in order to benefit students at all levels. The second part of the book covers the major computational methods for numerical analysis of electromagnetic fields for engineering applications. These methods include the three fundamental approaches for numerical analysis of electromagnetic fields: the finite difference method (the finite difference time-domain method in particular), the finite element method, and the integral equation-based moment method. The second part also examines fast algorithms for solving integral equations and hybrid techniques that combine different numerical methods to seek more efficient solutions of complicated electromagnetic problems. Theory and Computation of Electromagnetic Fields, Second Edition: Provides the foundation necessary for graduate students to learn and understand more advanced topics Discusses electromagnetic analysis in rectangular, cylindrical and spherical coordinates Covers computational electromagnetics in both frequency and time domains Includes new and updated homework problems and examples Theory and Computation of Electromagnetic Fields, Second Edition is written for advanced undergraduate and graduate level electrical engineering students. This book can also be used as a reference for professional engineers interested in learning about analysis and computation skills.
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A much-needed guide on how to use numerical methods to solve practical engineering problems Bridging the gap between mathematics and engineering, Numerical Analysis with Applications in Mechanics and Engineering arms readers with powerful tools for solving real-world problems in mechanics, physics, and civil and mechanical engineering. Unlike most books on numerical analysis, this outstanding work links theory and application, explains the mathematics in simple engineering terms, and clearly demonstrates how to use numerical methods to obtain solutions and interpret results. Each chapter is devoted to a unique analytical methodology, including a detailed theoretical presentation and emphasis on practical computation. Ample numerical examples and applications round out the discussion, illustrating how to work out specific problems of mechanics, physics, or engineering. Readers will learn the core purpose of each technique, develop hands-on problem-solving skills, and get a complete picture of the studied phenomenon. Coverage includes: How to deal with errors in numerical analysis Approaches for solving problems in linear and nonlinear systems Methods of interpolation and approximation of functions Formulas and calculations for numerical differentiation and integration Integration of ordinary and partial differential equations Optimization methods and solutions for programming problems Numerical Analysis with Applications in Mechanics and Engineering is a one-of-a-kind guide for engineers using mathematical models and methods, as well as for physicists and mathematicians interested in engineering problems.
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Magnets are widely used in industry, medical, scientific instruments, and electrical equipment. They are the basic tools for scientific research and electromagnetic devices. Numerical methods for the magnetic field analysis combined with mathematical optimization from practical applications of the magnets have been widely studied in recent years. It is necessary for professional researchers, engineers, and students to study these numerical methods for the complex magnet structure design instead of using traditional «trial-and-error» methods. Those working in this field will find this book useful as a reference to help reduce costs and obtain good magnetic field quality. Presents a clear introduction to magnet technology, followed by basic theories, numerical analysis, and practical applications Emphasizes the latest developments in magnet design, including MRI systems Provides comprehensive numerical techniques that provide solutions to practical problems Introduces the latest computation techniques for optimizing and characterizing the magnetostatic structure design Well organized and adaptable by researchers, engineers, lecturers, and students Appendix available on the Wiley Companion Website As a comprehensive treatment of the topic, Practical Design of Magnetostatic Structure Using Numerical Simulation is ideal for researchers in the field of magnets and their applications, materials scientists, structural engineers, and graduate students in electrical engineering. The book will also better equip mechanical engineers and aerospace engineers.
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This book concentrates on modeling and numerical simulations of combustion in liquid rocket engines, covering liquid propellant atomization, evaporation of liquid droplets, turbulent flows, turbulent combustion, heat transfer, and combustion instability. It presents some state of the art models and numerical methodologies in this area. The book can be categorized into two parts. Part 1 describes the modeling for each subtopic of the combustion process in the liquid rocket engines. Part 2 presents detailed numerical methodology and several representative applications in simulations of rocket engine combustion.
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Analysis of Structures offers an original way of introducing engineering students to the subject of stress and deformation analysis of solid objects, and helps them become more familiar with how numerical methods such as the finite element method are used in industry. Eisley and Waas secure for the reader a thorough understanding of the basic numerical skills and insight into interpreting the results these methods can generate. Throughout the text, they include analytical development alongside the computational equivalent, providing the student with the understanding that is necessary to interpret and use the solutions that are obtained using software based on the finite element method. They then extend these methods to the analysis of solid and structural components that are used in modern aerospace, mechanical and civil engineering applications. Analysis of Structures is accompanied by a book companion website www.wiley.com/go/waas housing exercises and examples that use modern software which generates color contour plots of deformation and internal stress.It offers invaluable guidance and understanding to senior level and graduate students studying courses in stress and deformation analysis as part of aerospace, mechanical and civil engineering degrees as well as to practicing engineers who want to re-train or re-engineer their set of analysis tools for contemporary stress and deformation analysis of solids and structures. Provides a fresh, practical perspective to the teaching of structural analysis using numerical methods for obtaining answers to real engineering applications Proposes a new way of introducing students to the subject of stress and deformation analysis of solid objects that are used in a wide variety of contemporary engineering applications Casts axial, torsional and bending deformations of thin walled objects in a framework that is closely amenable to the methods by which modern stress analysis software operates.
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Features a simplified presentation of numerical methods by introducing and implementing SAGE programs An Introduction to SAGE Programming: With Applications to SAGE Interacts for Numerical Methods emphasizes how to implement numerical methods using SAGE Math and SAGE Interacts and also addresses the fundamentals of computer programming, including if statements, loops, functions, and interacts. The book also provides a unique introduction to SAGE and its computer algebra system capabilities; discusses second and higher order equations and estimate limits; and determines derivatives, integrals, and summations. Providing critical resources for developing successful interactive SAGE numerical computations, the book is accessible without delving into the mathematical rigor of numerical methods. The author illustrates the benefits of utilizing the SAGE language for calculus and the numerical analysis of various methods such as bisection methods, numerical integration, Taylor’s expansions, and Newton’s iterations. Providing an introduction to the terminology and concepts involved, An Introduction to SAGE Programming: With Applications to SAGE Interacts for Numerical Methods also features: An introduction to computer programming using SAGE Many practical examples throughout to illustrate the application of SAGE Interacts for various numerical methods Discussions on how to use SAGE Interacts and SAGE Cloud in order to create mathematical demonstrations Numerous homework problems and exercises that allow readers to practice their programming skillset A companion website that includes related SAGE programming code and select solutions to the homework problems and exercises An Introduction to SAGE Programming: With Applications to SAGE Interacts for Numerical Methods is an ideal reference for applied mathematicians who need to employ SAGE for the study of numerical methods and analysis. The book is also an appropriate supplemental textbook for upper-undergraduate and graduate-level courses in numerical methods.
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A balanced guide to the essential techniques for solving elliptic partial differential equations Numerical Analysis of Partial Differential Equations provides a comprehensive, self-contained treatment of the quantitative methods used to solve elliptic partial differential equations (PDEs), with a focus on the efficiency as well as the error of the presented methods. The author utilizes coverage of theoretical PDEs, along with the nu merical solution of linear systems and various examples and exercises, to supply readers with an introduction to the essential concepts in the numerical analysis of PDEs. The book presents the three main discretization methods of elliptic PDEs: finite difference, finite elements, and spectral methods. Each topic has its own devoted chapters and is discussed alongside additional key topics, including: The mathematical theory of elliptic PDEs Numerical linear algebra Time-dependent PDEs Multigrid and domain decomposition PDEs posed on infinite domains The book concludes with a discussion of the methods for nonlinear problems, such as Newton's method, and addresses the importance of hands-on work to facilitate learning. Each chapter concludes with a set of exercises, including theoretical and programming problems, that allows readers to test their understanding of the presented theories and techniques. In addition, the book discusses important nonlinear problems in many fields of science and engineering, providing information as to how they can serve as computing projects across various disciplines. Requiring only a preliminary understanding of analysis, Numerical Analysis of Partial Differential Equations is suitable for courses on numerical PDEs at the upper-undergraduate and graduate levels. The book is also appropriate for students majoring in the mathematical sciences and engineering.
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A comprehensive approach to numerical partial differential equations Spline Collocation Methods for Partial Differential Equations combines the collocation analysis of partial differential equations (PDEs) with the method of lines (MOL) in order to simplify the solution process. Using a series of example applications, the author delineates the main features of the approach in detail, including an established mathematical framework. The book also clearly demonstrates that spline collocation can offer a comprehensive method for numerical integration of PDEs when it is used with the MOL in which spatial (boundary value) derivatives are approximated with splines, including the boundary conditions. R, an open-source scientific programming system, is used throughout for programming the PDEs and numerical algorithms, and each section of code is clearly explained. As a result, readers gain a complete picture of the model and its computer implementation without having to fill in the details of the numerical analysis, algorithms, or programming. The presentation is not heavily mathematical, and in place of theorems and proofs, detailed example applications are provided. Appropriate for scientists, engineers, and applied mathematicians, Spline Collocation Methods for Partial Differential Equations: Introduces numerical methods by first presenting basic examples followed by more complicated applications Employs R to illustrate accurate and efficient solutions of the PDE models Presents spline collocation as a comprehensive approach to the numerical integration of PDEs and an effective alternative to other, well established methods Discusses how to reproduce and extend the presented numerical solutions Identifies the use of selected algorithms, such as the solution of nonlinear equations and banded or sparse matrix processing Features a companion website that provides the related R routines Spline Collocation Methods for Partial Differential Equations is a valuable reference and/or self-study guide for academics, researchers, and practitioners in applied mathematics and engineering, as well as for advanced undergraduates and graduate-level students.
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Praise for the First Edition «. . . outstandingly appealing with regard to its style, contents, considerations of requirements of practice, choice of examples, and exercises.»—Zentralblatt MATH «. . . carefully structured with many detailed worked examples.»—The Mathematical Gazette The Second Edition of the highly regarded An Introduction to Numerical Methods and Analysis provides a fully revised guide to numerical approximation. The book continues to be accessible and expertly guides readers through the many available techniques of numerical methods and analysis. An Introduction to Numerical Methods and Analysis, Second Edition reflects the latest trends in the field, includes new material and revised exercises, and offers a unique emphasis on applications. The author clearly explains how to both construct and evaluate approximations for accuracy and performance, which are key skills in a variety of fields. A wide range of higher-level methods and solutions, including new topics such as the roots of polynomials, spectral collocation, finite element ideas, and Clenshaw-Curtis quadrature, are presented from an introductory perspective, and the Second Edition also features: Chapters and sections that begin with basic, elementary material followed by gradual coverage of more advanced material Exercises ranging from simple hand computations to challenging derivations and minor proofs to programming exercises Widespread exposure and utilization of MATLAB An appendix that contains proofs of various theorems and other material The book is an ideal textbook for students in advanced undergraduate mathematics and engineering courses who are interested in gaining an understanding of numerical methods and numerical analysis.
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Focusing on basic lubrication problems this book offers specific engineering applications. The book introduces methods and programs for the most important lubrication problems and their solutions. It is divided into four parts. The first part is about the general solving methods of the Reynolds equation, including solutions of Reynolds equations with different conditions and their discrete forms, such as a steady-state incompressible slider, journal bearing, dynamic bearing, gas bearing and grease lubrication. The second part gives the ‘energy equation solution’. The third part introduces methods and programs for elasto-hydrodynamic lurbication, which links the Reynolds equation with the elastic deformation equation. The final part presents application lubrication programs used in engineering. Provides numerical solution methodologies including appropriate software for the hydrodynamic and elasto-hydrodynamic lubrication of bearings Offers a clear introduction and orientation to all major engineering lubrication problems and their solutions Presents numerical programs for specific applications in engineering, with special topics including grease-lubricated bearings and gas bearings Equips those working in tribology and those new to the topic with the fundamental tools of calculation Downloadable programs are available at the companion website With an emphasis on clear explanations, the text offers a thorough understanding of the numerical calculation of lubrication for graduate students on tribology and engineering mechanics courses, with more detailed materials suitable for engineers. This is an accessible reference for senior undergraduate students of tribology and researchers in thin-film fluid mechanics.
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Praise for the First Edition «. . . fills a considerable gap in the numerical analysis literature by providing a self-contained treatment . . . this is an important work written in a clear style . . . warmly recommended to any graduate student or researcher in the field of the numerical solution of partial differential equations.» —SIAM Review Time-Dependent Problems and Difference Methods, Second Edition continues to provide guidance for the analysis of difference methods for computing approximate solutions to partial differential equations for time-dependent problems. The book treats differential equations and difference methods with a parallel development, thus achieving a more useful analysis of numerical methods. The Second Edition presents hyperbolic equations in great detail as well as new coverage on second-order systems of wave equations including acoustic waves, elastic waves, and Einstein equations. Compared to first-order hyperbolic systems, initial-boundary value problems for such systems contain new properties that must be taken into account when analyzing stability. Featuring the latest material in partial differential equations with new theorems, examples, and illustrations,Time-Dependent Problems and Difference Methods, Second Edition also includes: High order methods on staggered grids Extended treatment of Summation By Parts operators and their application to second-order derivatives Simplified presentation of certain parts and proofs Time-Dependent Problems and Difference Methods, Second Edition is an ideal reference for physical scientists, engineers, numerical analysts, and mathematical modelers who use numerical experiments to test designs and to predict and investigate physical phenomena. The book is also excellent for graduate-level courses in applied mathematics and scientific computations.
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Published by the American Geophysical Union as part of the Geophysical Monograph Series, Volume 201. Modeling the Ionosphere-Thermosphere System brings together for the first time a detailed description of the physics of the IT system in conjunction with numerical techniques to solve the complex system of equations that describe the system, as well as issues of current interest. Volume highlights include discussions of: Physics of the ionosphere and thermosphere IT system, and the numerical methods to solve the basic equations of the IT system The physics and numerical methods to determine the global electrodynamics of the IT system The response of the IT system to forcings from below (i.e., the lower atmosphere) and from above (i.e., the magnetosphere) The physics and numerical methods to model ionospheric irregularities Data assimilation techniques, comparison of model results to data, climate variability studies, and applications to space weather Providing a clear description of the physics of this system in several tutorial-like articles, Modeling the Ionosphere-Thermosphere System is of value to the upper atmosphere science community in general. Chapters describing details of the numerical methods used to solve the equations that describe the IT system make the volume useful to both active researchers in the field and students.
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Scientific computing has become an indispensable tool in numerous fields, such as physics, mechanics, biology, finance and industry. For example, it enables us, thanks to efficient algorithms adapted to current computers, to simulate, without the help of models or experimentations, the deflection of beams in bending, the sound level in a theater room or a fluid flowing around an aircraft wing. This book presents the scientific computing techniques applied to parallel computing for the numerical simulation of large-scale problems; these problems result from systems modeled by partial differential equations. Computing concepts will be tackled via examples. Implementation and programming techniques resulting from the finite element method will be presented for direct solvers, iterative solvers and domain decomposition methods, along with an introduction to MPI and OpenMP.
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Numerical Methods for Partial Differential Equations: An Introduction Vitoriano Ruas, Sorbonne Universités, UPMC – Université Paris 6, France A comprehensive overview of techniques for the computational solution of PDE's Numerical Methods for Partial Differential Equations: An Introduction covers the three most popular methods for solving partial differential equations: the finite difference method, the finite element method and the finite volume method. The book combines clear descriptions of the three methods, their reliability, and practical implementation aspects. Justifications for why numerical methods for the main classes of PDE's work or not, or how well they work, are supplied and exemplified. Aimed primarily at students of Engineering, Mathematics, Computer Science, Physics and Chemistry among others this book offers a substantial insight into the principles numerical methods in this class of problems are based upon. The book can also be used as a reference for research work on numerical methods for PDE’s. Key features: A balanced emphasis is given to both practical considerations and a rigorous mathematical treatment The reliability analyses for the three methods are carried out in a unified framework and in a structured and visible manner, for the basic types of PDE's Special attention is given to low order methods, as practitioner's overwhelming default options for everyday use New techniques are employed to derive known results, thereby simplifying their proof Supplementary material is available from a companion website.
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Introduces readers to core algorithmic techniques for next-generation sequencing (NGS) data analysis and discusses a wide range of computational techniques and applications This book provides an in-depth survey of some of the recent developments in NGS and discusses mathematical and computational challenges in various application areas of NGS technologies. The 18 chapters featured in this book have been authored by bioinformatics experts and represent the latest work in leading labs actively contributing to the fast-growing field of NGS. The book is divided into four parts: Part I focuses on computing and experimental infrastructure for NGS analysis, including chapters on cloud computing, modular pipelines for metabolic pathway reconstruction, pooling strategies for massive viral sequencing, and high-fidelity sequencing protocols. Part II concentrates on analysis of DNA sequencing data, covering the classic scaffolding problem, detection of genomic variants, including insertions and deletions, and analysis of DNA methylation sequencing data. Part III is devoted to analysis of RNA-seq data. This part discusses algorithms and compares software tools for transcriptome assembly along with methods for detection of alternative splicing and tools for transcriptome quantification and differential expression analysis. Part IV explores computational tools for NGS applications in microbiomics, including a discussion on error correction of NGS reads from viral populations, methods for viral quasispecies reconstruction, and a survey of state-of-the-art methods and future trends in microbiome analysis. Computational Methods for Next Generation Sequencing Data Analysis: Reviews computational techniques such as new combinatorial optimization methods, data structures, high performance computing, machine learning, and inference algorithms Discusses the mathematical and computational challenges in NGS technologies Covers NGS error correction, de novo genome transcriptome assembly, variant detection from NGS reads, and more This text is a reference for biomedical professionals interested in expanding their knowledge of computational techniques for NGS data analysis. The book is also useful for graduate and post-graduate students in bioinformatics.
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This book serves as a complete and self-contained introduction to the principles of Computational Fluid Dynamic (CFD) analysis. It is deliberately short (at approximately 300 pages) and can be used as a text for the first part of the course of applied CFD followed by a software tutorial. The main objectives of this non-traditional format are: 1) To introduce and explain, using simple examples where possible, the principles and methods of CFD analysis and to demystify the `black box’ of a CFD software tool, and 2) To provide a basic understanding of how CFD problems are set and which factors affect the success and failure of the analysis. Included in the text are the mathematical and physical foundations of CFD, formulation of CFD problems, basic principles of numerical approximation (grids, consistency, convergence, stability, and order of approximation, etc), methods of discretization with focus on finite difference and finite volume techniques, methods of solution of transient and steady state problems, commonly used numerical methods for heat transfer and fluid flows, plus a brief introduction into turbulence modeling.
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Scientists and engineers often use algorithms without fully knowing what's happening inside them. This blind faith can lead to inefficient solutions and sometimes flat-out wrong ones. This book breaks open the algorithmic black boxes to help you understand how they work and why they can break down. Ideal for first-year graduate students, this book works to build both the intuitive understanding of underlying mathematical theory and useful skills for research. Examples worked out in detail provide a practical guide for using numerical methods in linear algebra, numerical analysis, and partial differential equations.
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Are you someone that involves in computation? Numerical methods cover some approaches and popular methods that you use daily. One of the best ways to apply numerical methods in any of your computations is by using Matlab. Yes, Matlab! This might seems like a big deal to you, but we believe it shouldn’t. So we came up with an incredibly short book titled “Top Numerical Methods with Matlab for Beginners.” If you already have the basic math knowledge, fundamental knowledge of computing and some familiarity with Matlab, applying the top numerical methods with Matlab as a beginner is not going to be a problem. With our powerful short product, you will not have any difficulty obtaining numerical solutions to problems. Of course, it is just one of the many benefits our top-notch book has to offer you if you purchase it. Some of the other advantages you can derive from our product are:•Top numerical methods with Matlab and how to apply them•It offers navigation index you can use as reference guide•It shows how computations involving vectors and matrices are naturally expressed in Matlab•Also, you will know how numerical methods work and why they fail•Examples are provided for you to have a better understandingThe advantages above are just little out of the huge benefits our top winning short book is ready to offer you.We know our book does not provide ultimate information about Matlab. But we have a primary goal, and it is to provide a solid foundation in top numerical methods using ...
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A comprehensive guide to numerical methods for simulating physical-chemical systems This book offers a systematic, highly accessible presentation of numerical methods used to simulate the behavior of physical-chemical systems. Unlike most books on the subject, it focuses on methodology rather than specific applications. Written for students and professionals across an array of scientific and engineering disciplines and with varying levels of experience with applied mathematics, it provides comprehensive descriptions of numerical methods without requiring an advanced mathematical background. Based on its author’s more than forty years of experience teaching numerical methods to engineering students, Numerical Methods for Solving Partial Differential Equations presents the fundamentals of all of the commonly used numerical methods for solving differential equations at a level appropriate for advanced undergraduates and first-year graduate students in science and engineering. Throughout, elementary examples show how numerical methods are used to solve generic versions of equations that arise in many scientific and engineering disciplines. In writing it, the author took pains to ensure that no assumptions were made about the background discipline of the reader. Covers the spectrum of numerical methods that are used to simulate the behavior of physical-chemical systems that occur in science and engineering Written by a professor of engineering with more than forty years of experience teaching numerical methods to engineers Requires only elementary knowledge of differential equations and matrix algebra to master the material Designed to teach students to understand, appreciate and apply the basic mathematics and equations on which Mathcad and similar commercial software packages are based Comprehensive yet accessible to readers with limited mathematical knowledge, Numerical Methods for Solving Partial Differential Equations is an excellent text for advanced undergraduates and first-year graduate students in the sciences and engineering. It is also a valuable working reference for professionals in engineering, physics, chemistry, computer science, and applied mathematics.
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Use chemometric techniques to develop optimum separation conditions for capillary electrophoreses For all its advantages, capillary electrophoresis (CE) also carries significant disadvantages for the researcher. Offering a unique blend of information from authors active in a variety of developments of chemometrics in CE, Chemometric Methods in Capillary Electrophoresis presents modern chemometric methods as an alternative to help alleviate the problems commonly encountered during routine analysis and method development. Focusing on current chemometric methods utilized in CE endeavours by research-active experts in the field, the book begins with a thorough introduction to CE and chemometric-related concepts and the need for modern chemometric methods in CE. Part 1 discusses differing types of screening designs and response surface methodology¿in an¿application based format Part 2 includes vital discussion on various exploratory data analysis, prediction, and classification techniques utilized in CE-related studies Part 3 provides practical information on modelling quantitative structure relationships Part 4 explores transformation techniques, in particular fundamental studies and applications of cross-correlation and Hadamard Transform Electrophoresis Showing how chemometric methods are applied in a wide array of applications including biological, medical, pharmaceutical, food, forensic, and environmental science, Chemometric Methods in Capillary Electrophoresis is not only highly significant to capillary electrophoresis-based endeavours, but instructive for investigators active in other areas of separation science who could benefit from its informative content.
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Uses mathematical, numerical, and programming tools to solve differential equations for physical phenomena and engineering problems Introduction to Computation and Modeling for Differential Equations, Second Edition features the essential principles and applications of problem solving across disciplines such as engineering, physics, and chemistry. The Second Edition integrates the science of solving differential equations with mathematical, numerical, and programming tools, specifically with methods involving ordinary differential equations; numerical methods for initial value problems (IVPs); numerical methods for boundary value problems (BVPs); partial differential equations (PDEs); numerical methods for parabolic, elliptic, and hyperbolic PDEs; mathematical modeling with differential equations; numerical solutions; and finite difference and finite element methods. The author features a unique “Five-M” approach: Modeling, Mathematics, Methods, MATLAB®, and Multiphysics, which facilitates a thorough understanding of how models are created and preprocessed mathematically with scaling, classification, and approximation and also demonstrates how a problem is solved numerically using the appropriate mathematical methods. With numerous real-world examples to aid in the visualization of the solutions, Introduction to Computation and Modeling for Differential Equations, Second Edition includes: New sections on topics including variational formulation, the finite element method, examples of discretization, ansatz methods such as Galerkin’s method for BVPs, parabolic and elliptic PDEs, and finite volume methods Numerous practical examples with applications in mechanics, fluid dynamics, solid mechanics, chemical engineering, heat conduction, electromagnetic field theory, and control theory, some of which are solved with computer programs MATLAB and COMSOL Multiphysics® Additional exercises that introduce new methods, projects, and problems to further illustrate possible applications A related website with select solutions to the exercises, as well as the MATLAB data sets for ordinary differential equations (ODEs) and PDEs Introduction to Computation and Modeling for Differential Equations, Second Edition is a useful textbook for upper-undergraduate and graduate-level courses in scientific computing, differential equations, ordinary differential equations, partial differential equations, and numerical methods. The book is also an excellent self-study guide for mathematics, science, computer science, physics, and engineering students, as well as an excellent reference for practitioners and consultants who use differential equations and numerical methods in everyday situations.
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Analysis and Modelling of Non-Steady Flow in Pipe and Channel Networks deals with flows in pipes and channel networks from the standpoints of hydraulics and modelling techniques and methods. These engineering problems occur in the course of the design and construction of hydroenergy plants, water-supply and other systems. In this book, the author presents his experience in solving these problems from the early 1970s to the present day. During this period new methods of solving hydraulic problems have evolved, due to the development of computers and numerical methods. This book is accompanied by a website which hosts the author's software package, Simpip (an abbreviation of simulation of pipe flow) for solving non-steady pipe flow using the finite element method. The program also covers flows in channels. The book presents the numerical core of the SimpipCore program (written in Fortran). Key features: Presents the theory and practice of modelling different flows in hydraulic networks Takes a systematic approach and addresses the topic from the fundamentals Presents numerical solutions based on finite element analysis Accompanied by a website hosting supporting material including the SimpipCore project as a standalone program Analysis and Modelling of Non-Steady Flow in Pipe and Channel Networks is an ideal reference book for engineers, practitioners and graduate students across engineering disciplines.
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Demonstrates the application of DSM to solve a broad range of operator equations The dynamical systems method (DSM) is a powerful computational method for solving operator equations. With this book as their guide, readers will master the application of DSM to solve a variety of linear and nonlinear problems as well as ill-posed and well-posed problems. The authors offer a clear, step-by-step, systematic development of DSM that enables readers to grasp the method's underlying logic and its numerous applications. Dynamical Systems Method and Applications begins with a general introduction and then sets forth the scope of DSM in Part One. Part Two introduces the discrepancy principle, and Part Three offers examples of numerical applications of DSM to solve a broad range of problems in science and engineering. Additional featured topics include: General nonlinear operator equations Operators satisfying a spectral assumption Newton-type methods without inversion of the derivative Numerical problems arising in applications Stable numerical differentiation Stable solution to ill-conditioned linear algebraic systems Throughout the chapters, the authors employ the use of figures and tables to help readers grasp and apply new concepts. Numerical examples offer original theoretical results based on the solution of practical problems involving ill-conditioned linear algebraic systems, and stable differentiation of noisy data. Written by internationally recognized authorities on the topic, Dynamical Systems Method and Applications is an excellent book for courses on numerical analysis, dynamical systems, operator theory, and applied mathematics at the graduate level. The book also serves as a valuable resource for professionals in the fields of mathematics, physics, and engineering.
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This book studies methods to concretely address inverse problems. An inverse problem arises when the causes that produced a given effect must be determined or when one seeks to indirectly estimate the parameters of a physical system. The author uses practical examples to illustrate inverse problems in physical sciences. He presents the techniques and specific methods chosen to solve inverse problems in a general domain of application, choosing to focus on a small number of methods that can be used in most applications. This book is aimed at readers with a mathematical and scientific computing background. Despite this, it is a book with a practical perspective. The methods described are applicable, have been applied, and are often illustrated by numerical examples.
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Stochastic Numerical Methods introduces at Master level the numerical methods that use probability or stochastic concepts to analyze random processes. The book aims at being rather general and is addressed at students of natural sciences (Physics, Chemistry, Mathematics, Biology, etc.) and Engineering, but also social sciences (Economy, Sociology, etc.) where some of the techniques have been used recently to numerically simulate different agent-based models. Examples included in the book range from phase-transitions and critical phenomena, including details of data analysis (extraction of critical exponents, finite-size effects, etc.), to population dynamics, interfacial growth, chemical reactions, etc. Program listings are integrated in the discussion of numerical algorithms to facilitate their understanding. From the contents: Review of Probability Concepts Monte Carlo Integration Generation of Uniform and Non-uniform Random Numbers: Non-correlated Values Dynamical Methods Applications to Statistical Mechanics Introduction to Stochastic Processes Numerical Simulation of Ordinary and Partial Stochastic Differential Equations Introduction to Master Equations Numerical Simulations of Master Equations Hybrid Monte Carlo Generation of n-Dimensional Correlated Gaussian Variables Collective Algorithms for Spin Systems Histogram Extrapolation Multicanonical Simulations
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Triangulations, and more precisely meshes, are at the heart of many problems relating to a wide variety of scientific disciplines, and in particular numerical simulations of all kinds of physical phenomena. In numerical simulations, the functional spaces of approximation used to search for solutions are defined from meshes, and in this sense these meshes play a fundamental role. This strong link between the meshes and functional spaces leads us to consider advanced simulation methods in which the meshes are adapted to the behaviors of the underlying physical phenomena. This book presents the basic elements of this meshing vision.
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A new edition of this classic work, comprehensively revised to present exciting new developments in this important subject The study of numerical methods for solving ordinary differential equations is constantly developing and regenerating, and this third edition of a popular classic volume, written by one of the world’s leading experts in the field, presents an account of the subject which reflects both its historical and well-established place in computational science and its vital role as a cornerstone of modern applied mathematics. In addition to serving as a broad and comprehensive study of numerical methods for initial value problems, this book contains a special emphasis on Runge-Kutta methods by the mathematician who transformed the subject into its modern form dating from his classic 1963 and 1972 papers. A second feature is general linear methods which have now matured and grown from being a framework for a unified theory of a wide range of diverse numerical schemes to a source of new and practical algorithms in their own right. As the founder of general linear method research, John Butcher has been a leading contributor to its development; his special role is reflected in the text. The book is written in the lucid style characteristic of the author, and combines enlightening explanations with rigorous and precise analysis. In addition to these anticipated features, the book breaks new ground by including the latest results on the highly efficient G-symplectic methods which compete strongly with the well-known symplectic Runge-Kutta methods for long-term integration of conservative mechanical systems. This third edition of Numerical Methods for Ordinary Differential Equations will serve as a key text for senior undergraduate and graduate courses in numerical analysis, and is an essential resource for research workers in applied mathematics, physics and engineering.
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Mark H.A. Davis introduced the Piecewise-Deterministic Markov Process (PDMP) class of stochastic hybrid models in an article in 1984. Today it is used to model a variety of complex systems in the fields of engineering, economics, management sciences, biology, Internet traffic, networks and many more. Yet, despite this, there is very little in the way of literature devoted to the development of numerical methods for PDMDs to solve problems of practical importance, or the computational control of PDMPs. This book therefore presents a collection of mathematical tools that have been recently developed to tackle such problems. It begins by doing so through examples in several application domains such as reliability. The second part is devoted to the study and simulation of expectations of functionals of PDMPs. Finally, the third part introduces the development of numerical techniques for optimal control problems such as stopping and impulse control problems.
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This book explores the state-of-the art in computational modelling techniques for photonic devices In this book, the author provides a comprehensive coverage of modern numerical modelling techniques for designing photonic devices for use in modern optical telecommunications systems. In addition the book presents the state-of-the-art in computational photonics techniques, covering methods such as full-vectorial finite-element beam propagation, bidirectional beam propagation, complex-envelope alternative direction implicit finite difference time domain, multiresolution time domain, and finite volume time domain. The book guides the reader through the concepts of modelling, analysing, designing and optimising the performance of a wide range of photonic devices by building their own numerical code using these methods. Key Features: Provides a thorough presentation of the state-of-the art in computational modelling techniques for photonics Contains broad coverage of both frequency- and time-domain techniques to suit a wide range of photonic devices Reviews existing commercial software packages for photonics Presents the advantages and disadvantages of the different modelling techniques as well as their suitability for various photonic devices Shows the reader how to model, analyse, design and optimise the performance of a wide range of photonic devices by building their own numerical code using these methods Accompanying website contains the numerical examples representing the numerical techniques in this book, as well as several design examples (http://www.wiley.com/go/obayya_computational) This book will serve as an invaluable reference for researchers, optical telecommunications engineers, engineers in the photonics industry. PhD and MSc students undertaking courses in the areas of photonics and optical telecommunications will also find this book of interest.
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This series of five volumes proposes an integrated description of physical processes modeling used by scientific disciplines from meteorology to coastal morphodynamics. Volume 1 describes the physical processes and identifies the main measurement devices used to measure the main parameters that are indispensable to implement all these simulation tools. Volume 2 presents the different theories in an integrated approach: mathematical models as well as conceptual models, used by all disciplines to represent these processes. Volume 3 identifies the main numerical methods used in all these scientific fields to translate mathematical models into numerical tools. Volume 4 is composed of a series of case studies, dedicated to practical applications of these tools in engineering problems. To complete this presentation, volume 5 identifies and describes the modeling software in each discipline.
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This book explores the state-of-the art in computational modelling techniques for photonic devices In this book, the author provides a comprehensive coverage of modern numerical modelling techniques for designing photonic devices for use in modern optical telecommunications systems. In addition the book presents the state-of-the-art in computational photonics techniques, covering methods such as full-vectorial finite-element beam propagation, bidirectional beam propagation, complex-envelope alternative direction implicit finite difference time domain, multiresolution time domain, and finite volume time domain. The book guides the reader through the concepts of modelling, analysing, designing and optimising the performance of a wide range of photonic devices by building their own numerical code using these methods. Key Features: Provides a thorough presentation of the state-of-the art in computational modelling techniques for photonics Contains broad coverage of both frequency- and time-domain techniques to suit a wide range of photonic devices Reviews existing commercial software packages for photonics Presents the advantages and disadvantages of the different modelling techniques as well as their suitability for various photonic devices Shows the reader how to model, analyse, design and optimise the performance of a wide range of photonic devices by building their own numerical code using these methods Accompanying website contains the numerical examples representing the numerical techniques in this book, as well as several design examples (http://www.wiley.com/go/obayya_computational) This book will serve as an invaluable reference for researchers, optical telecommunications engineers, engineers in the photonics industry. PhD and MSc students undertaking courses in the areas of photonics and optical telecommunications will also find this book of interest.
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This series of five volumes proposes an integrated description of physical processes modeling used by scientific disciplines from meteorology to coastal morphodynamics. Volume 1 describes the physical processes and identifies the main measurement devices used to measure the main parameters that are indispensable to implement all these simulation tools. Volume 2 presents the different theories in an integrated approach: mathematical models as well as conceptual models, used by all disciplines to represent these processes. Volume 3 identifies the main numerical methods used in all these scientific fields to translate mathematical models into numerical tools. Volume 4 is composed of a series of case studies, dedicated to practical applications of these tools in engineering problems. To complete this presentation, volume 5 identifies and describes the modeling software in each discipline.
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A Definitive text on developing circuit simulators Circuit Simulation gives a clear description of the numerical techniques and algorithms that are part of modern circuit simulators, with a focus on the most commonly used simulation modes: DC analysis and transient analysis. Tested in a graduate course on circuit simulation at the University of Toronto, this unique text provides the reader with sufficient detail and mathematical rigor to write his/her own basic circuit simulator. There is detailed coverage throughout of the mathematical and numerical techniques that are the basis for the various simulation topics, which facilitates a complete understanding of practical simulation techniques. In addition, Circuit Simulation: Explores a number of modern techniques from numerical analysis that are not synthesized anywhere else Covers network equation formulation in detail, with an emphasis on modified nodal analysis Gives a comprehensive treatment of the most relevant aspects of linear and nonlinear system solution techniques States all theorems without proof in order to maintain the focus on the end-goal of providing coverage of practical simulation methods Provides ample references for further study Enables newcomers to circuit simulation to understand the material in a concrete and holistic manner With problem sets and computer projects at the end of every chapter, Circuit Simulation is ideally suited for a graduate course on this topic. It is also a practical reference for design engineers and computer-aided design practitioners, as well as researchers and developers in both industry and academia.
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A solutions manual to accompany An Introduction to Numerical Methods and Analysis, Second Edition An Introduction to Numerical Methods and Analysis, Second Edition reflects the latest trends in the field, includes new material and revised exercises, and offers a unique emphasis on applications. The author clearly explains how to both construct and evaluate approximations for accuracy and performance, which are key skills in a variety of fields. A wide range of higher-level methods and solutions, including new topics such as the roots of polynomials, spectral collocation, finite element ideas, and Clenshaw-Curtis quadrature, are presented from an introductory perspective, and theSecond Edition also features: Chapters and sections that begin with basic, elementary material followed by gradual coverage of more advanced material Exercises ranging from simple hand computations to challenging derivations and minor proofs to programming exercises Widespread exposure and utilization of MATLAB® An appendix that contains proofs of various theorems and other material
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Modeling Atmospheric and Oceanic Flows: Insights from Laboratory Experiments and Numerical Simulations provides a broad overview of recent progress in using laboratory experiments and numerical simulations to model atmospheric and oceanic fluid motions. This volume not only surveys novel research topics in laboratory experimentation, but also highlights recent developments in the corresponding computational simulations. As computing power grows exponentially and better numerical codes are developed, the interplay between numerical simulations and laboratory experiments is gaining paramount importance within the scientific community. The lessons learnt from the laboratory–model comparisons in this volume will act as a source of inspiration for the next generation of experiments and simulations. Volume highlights include: Topics pertaining to atmospheric science, climate physics, physical oceanography, marine geology and geophysics Overview of the most advanced experimental and computational research in geophysics Recent developments in numerical simulations of atmospheric and oceanic fluid motion Unique comparative analysis of the experimental and numerical approaches to modeling fluid flow Modeling Atmospheric and Oceanic Flows will be a valuable resource for graduate students, researchers, and professionals in the fields of geophysics, atmospheric sciences, oceanography, climate science, hydrology, and experimental geosciences.
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When using numerical simulation to make a decision, how can its reliability be determined? What are the common pitfalls and mistakes when assessing the trustworthiness of computed information, and how can they be avoided? Whenever numerical simulation is employed in connection with engineering decision-making, there is an implied expectation of reliability: one cannot base decisions on computed information without believing that information is reliable enough to support those decisions. Using mathematical models to show the reliability of computer-generated information is an essential part of any modelling effort. Giving users of finite element analysis (FEA) software an introduction to verification and validation procedures, this book thoroughly covers the fundamentals of assuring reliability in numerical simulation. The renowned authors systematically guide readers through the basic theory and algorithmic structure of the finite element method, using helpful examples and exercises throughout. Delivers the tools needed to have a working knowledge of the finite element method Illustrates the concepts and procedures of verification and validation Explains the process of conceptualization supported by virtual experimentation Describes the convergence characteristics of the h-, p- and hp-methods Covers the hierarchic view of mathematical models and finite element spaces Uses examples and exercises which illustrate the techniques and procedures of quality assurance Ideal for mechanical and structural engineering students, practicing engineers and applied mathematicians Includes parameter-controlled examples of solved problems in a companion website (www.wiley.com/go/szabo)
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As the Solutions Manual, this book is meant to accompany the main title, Nonlinear Programming: Theory and Algorithms, Third Edition. This book presents recent developments of key topics in nonlinear programming (NLP) using a logical and self-contained format. The volume is divided into three sections: convex analysis, optimality conditions, and dual computational techniques. Precise statements of algortihms are given along with convergence analysis. Each chapter contains detailed numerical examples, graphical illustrations, and numerous exercises to aid readers in understanding the concepts and methods discussed.
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Over the years, the numerical modeling of transport phenomena has been obtained a great portion in the solution of scientific and industrial problems. One of the new numerical techniques is Lattice Boltzmann Method. This method has a lot of advantages like easy implementation, flexible boundary condition, and fast convergence. Also, t is appropriate for simulation of complex geometries and domains like porous media, multiphase flow and etc. The present book provides an investigation of the transport phenomenon in porous media within a computational geometry using LBM. This book should help shed some light on the industrial and educational investigations of porous media and should be particularly useful to professionals in LBM modeling, or anyone else who may be considering employing of numerical techniques for porous and non-porous mediums.
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This book covers the design and optimization of computer networks applying a rigorous optimization methodology, applicable to any network technology. It is organized into two parts. In Part 1 the reader will learn how to model network problems appearing in computer networks as optimization programs, and use optimization theory to give insights on them. Four problem types are addressed systematically – traffic routing, capacity dimensioning, congestion control and topology design. Part 2 targets the design of algorithms that solve network problems like the ones modeled in Part 1. Two main approaches are addressed – gradient-like algorithms inspiring distributed network protocols that dynamically adapt to the network, or cross-layer schemes that coordinate the cooperation among protocols; and those focusing on the design of heuristic algorithms for long term static network design and planning problems. Following a hands-on approach, the reader will have access to a large set of examples in real-life technologies like IP, wireless and optical networks. Implementations of models and algorithms will be available in the open-source Net2Plan tool from which the user will be able to see how the lessons learned take real form in algorithms, and reuse or execute them to obtain numerical solutions. An accompanying link to the author’s own Net2plan software enables readers to produce numerical solutions to a multitude of real-life problems in computer networks (www.net2plan.com).
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Code of Federal Regulations Title 12, Volume 1, January 1, 2017 contains regulations governing Banks and Banking and may also be referenced as:- Code of Federal Regulations Title 12, Volume 1, January 1, 2017- CFR Title 12- CFR 12, Banks and Banking- CFR 12, Parts 1 to 199, Banks and BankingThis volume contains Parts 1 to 199:- Part 1; INVESTMENT SECURITIES- Part 2; SALES OF CREDIT LIFE INSURANCE- Part 3; CAPITAL ADEQUACY STANDARDS- Part 4; ORGANIZATION AND FUNCTIONS, AVAILABILITY AND RELEASE OF INFORMATION, CONTRACTING OUTREACH PROGRAM, POST-EMPLOYMENT RESTRICTIONS FOR SENIOR EXAMINERS- Part 5; RULES, POLICIES, AND PROCEDURES FOR CORPORATE ACTIVITIES- Part 6; PROMPT CORRECTIVE ACTION- Part 7; ACTIVITIES AND OPERATIONS- Part 8; ASSESSMENT OF FEES- Part 9; FIDUCIARY ACTIVITIES OF NATIONAL BANKS- Part 10; MUNICIPAL SECURITIES DEALERS- Part 11; SECURITIES EXCHANGE ACT DISCLOSURE RULES- Part 12; RECORDKEEPING AND CONFIRMATION REQUIREMENTS FOR SECURITIES TRANSACTIONS- Part 13; GOVERNMENT SECURITIES SALES PRACTICES- Part 14; CONSUMER PROTECTION IN SALES OF INSURANCE- Part 15; Reserved- Part 16; SECURITIES OFFERING DISCLOSURE RULES- Part 18; DISCLOSURE OF FINANCIAL AND OTHER INFORMATION BY NATIONAL BANKS- Part 19; RULES OF PRACTICE AND PROCEDURE- Part 21; MINIMUM SECURITY DEVICES AND PROCEDURES, REPORTS OF SUSPICIOUS ACTIVITIES, AND BANK SECRECY ACT COMPLIANCE PROGRAM- Part 22; LOANS IN AREAS HAVING SPECIAL FLOOD HAZARDS- Part 23; LEASING- Part 24; COMMUNITY AND ECONOMIC DEVELOPMENT...
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A comprehensive account of the theory and application of Monte Carlo methods Based on years of research in efficient Monte Carlo methods for estimation of rare-event probabilities, counting problems, and combinatorial optimization, Fast Sequential Monte Carlo Methods for Counting and Optimization is a complete illustration of fast sequential Monte Carlo techniques. The book provides an accessible overview of current work in the field of Monte Carlo methods, specifically sequential Monte Carlo techniques, for solving abstract counting and optimization problems. Written by authorities in the field, the book places emphasis on cross-entropy, minimum cross-entropy, splitting, and stochastic enumeration. Focusing on the concepts and application of Monte Carlo techniques, Fast Sequential Monte Carlo Methods for Counting and Optimization includes: Detailed algorithms needed to practice solving real-world problems Numerous examples with Monte Carlo method produced solutions within the 1-2% limit of relative error A new generic sequential importance sampling algorithm alongside extensive numerical results An appendix focused on review material to provide additional background information Fast Sequential Monte Carlo Methods for Counting and Optimization is an excellent resource for engineers, computer scientists, mathematicians, statisticians, and readers interested in efficient simulation techniques. The book is also useful for upper-undergraduate and graduate-level courses on Monte Carlo methods.
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An in-depth description of the state-of-the-art of 3D shape analysis techniques and their applications This book discusses the different topics that come under the title of «3D shape analysis». It covers the theoretical foundations and the major solutions that have been presented in the literature. It also establishes links between solutions proposed by different communities that studied 3D shape, such as mathematics and statistics, medical imaging, computer vision, and computer graphics. The first part of 3D Shape Analysis: Fundamentals, Theory, and Applications provides a review of the background concepts such as methods for the acquisition and representation of 3D geometries, and the fundamentals of geometry and topology. It specifically covers stereo matching, structured light, and intrinsic vs. extrinsic properties of shape. Parts 2 and 3 present a range of mathematical and algorithmic tools (which are used for e.g., global descriptors, keypoint detectors, local feature descriptors, and algorithms) that are commonly used for the detection, registration, recognition, classification, and retrieval of 3D objects. Both also place strong emphasis on recent techniques motivated by the spread of commodity devices for 3D acquisition. Part 4 demonstrates the use of these techniques in a selection of 3D shape analysis applications. It covers 3D face recognition, object recognition in 3D scenes, and 3D shape retrieval. It also discusses examples of semantic applications and cross domain 3D retrieval, i.e. how to retrieve 3D models using various types of modalities, e.g. sketches and/or images. The book concludes with a summary of the main ideas and discussions of the future trends. 3D Shape Analysis: Fundamentals, Theory, and Applications is an excellent reference for graduate students, researchers, and professionals in different fields of mathematics, computer science, and engineering. It is also ideal for courses in computer vision and computer graphics, as well as for those seeking 3D industrial/commercial solutions.
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Computational social choice is concerned with the design and analysis of methods for collective decision making. It is a research area that is located at the interface of Computer Science and Economics. This volume reports on a number of recent research trends in computational social choice. It has three parts. The first part presents novel scenarios in which methods for collective decision making are required. The second part introduces novel techniques for the analysis of such methods. The third part, finally, discusses a range of innovative applications enabled by recent research in computational social choice.
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Code of Federal Regulations Title 22, Volume 1, April 1, 2017 contains regulations governing Foreign Relations and may also be referenced as:- Code of Federal Regulations Title 22, Volume 1, April 1, 2017- CFR Title 22- CFR 22, Foreign Relations- CFR 22, Parts 1 to 299, Foreign RelationsThis volume contains Parts 1 to 299:- Part 1; INSIGNIA OF RANK- Part 2; PROTECTION OF FOREIGN DIGNITARIES AND OTHER OFFICIAL PERSONNEL- Part 3; GIFTS AND DECORATIONS FROM FOREIGN GOVERNMENTS- Part 3a; ACCEPTANCE OF EMPLOYMENT FROM FOREIGN GOVERNMENTS BY MEMBERS OF THE UNIFORMED SERVICES- Part 4; NOTIFICATION OF FOREIGN OFFICIAL STATUS- Part 5; ORGANIZATION- Part 7; Reserved- Part 9; SECURITY INFORMATION REGULATIONS- Part 9a; SECURITY INFORMATION REGULATIONS APPLICABLE TO CERTAIN INTERNATIONAL ENERGY PROGRAMS; RELATED MATERIAL- Part 9b; REGULATIONS GOVERNING DEPARTMENT OF STATE PRESS BUILDING PASSES- Part 11; APPOINTMENT OF FOREIGN SERVICE OFFICERS- Part 12; COMPLAINTS AGAINST EMPLOYEES BY ALLEGED CREDITORS- Part 13; PERSONNEL- Part 16; FOREIGN SERVICE GRIEVANCE SYSTEM- Part 17; OVERPAYMENTS FROM THE FOREIGN SERVICE RETIREMENT AND DISABILITY FUND UNDER THE FOREIGN SERVICE RETIREMENT AND DISABILITY SYSTEM (FSRDS) AND THE FOREIGN SERVICE PENSION SYSTEM (FSPS)- Part 18; REGULATIONS CONCERNING POST EMPLOYMENT CONFLICT OF INTEREST- Part 19; BENEFITS FOR SPOUSES AND FORMER SPOUSES OF PARTICIPANTS IN THE FOREIGN SERVICE RETIREMENT AND DISABILITY SYSTEM- Part 20; BENEFITS FOR CERTAIN FORMER SPOUSES- Pa...
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Code of Federal Regulations Title 16, Volume 2, January 1, 2017 contains regulations governing Commercial Practices and may also be referenced as:- Code of Federal Regulations Title 16, Volume 2, January 1, 2017- CFR Title 16- CFR 16, Commercial Practices- CFR 16, Part 1000 to End, Commercial PracticesThis volume contains Part 1000 to End:- Part 1000; COMMISSION ORGANIZATION AND FUNCTIONS- Part 1009; GENERAL STATEMENTS OF POLICY OR INTERPRETATION- Part 1010; Reserved- Part 1011; NOTICE OF AGENCY ACTIVITIES- Part 1012; MEETINGS POLICY-MEETINGS BETWEEN AGENCY PERSONNEL AND OUTSIDE PARTIES- Part 1013; GOVERNMENT IN THE SUNSHINE ACT, RULES FOR COMMISSION MEETINGS- Part 1014; POLICIES AND PROCEDURES IMPLEMENTING THE PRIVACY ACT OF 1974- Part 1015; PROCEDURES FOR DISCLOSURE OR PRODUCTION OF INFORMATION UNDER THE FREEDOM OF INFORMATION ACT- Part 1016; POLICIES AND PROCEDURES FOR INFORMATION DISCLOSURE AND COMMISSION EMPLOYEE TESTIMONY IN PRIVATE LITIGATION- Part 1017; Reserved- Part 1018; ADVISORY COMMITTEE MANAGEMENT- Part 1019; EXPORT OF NONCOMPLYING, MISBRANDED, OR BANNED PRODUCTS- Part 1020; SMALL BUSINESS- Part 1021; ENVIRONMENTAL REVIEW- Part 1025; RULES OF PRACTICE FOR ADJUDICATIVE PROCEEDINGS- Part 1027; SALARY OFFSET- Part 1028; PROTECTION OF HUMAN SUBJECTS- Part 1030; EMPLOYEE STANDARDS OF CONDUCT- Part 1031; COMMISSION PARTICIPATION AND COMMISSION EMPLOYEE INVOLVEMENT IN VOLUNTARY STANDARDS ACTIVITIES- Part 1033; DISPLAY OF CONTROL NUMBERS FOR COLLECTION OF INFORMATION RE...
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Code of Federal Regulations Title 25, Volume 1, April 1, 2017 contains regulations governing Indians and may also be referenced as:- Code of Federal Regulations Title 25, Volume 1, April 1, 2017- CFR Title 25- CFR 25, Indians- CFR 25, Parts 1 to 299, IndiansThis volume contains Parts 1 to 299:- Part 1; APPLICABILITY OF RULES OF THE BUREAU OF INDIAN AFFAIRS- Part 2; APPEALS FROM ADMINISTRATIVE ACTIONS- Part 5; PREFERENCE IN EMPLOYMENT- Part 10; INDIAN COUNTRY DETENTION FACILITIES AND PROGRAMS- Part 11; COURTS OF INDIAN OFFENSES AND LAW AND ORDER CODE- Part 12; INDIAN COUNTRY LAW ENFORCEMENT- Part 13; TRIBAL REASSUMPTION OF JURISDICTION OVER CHILD CUSTODY PROCEEDINGS- Part 15; PROBATE OF INDIAN ESTATES, EXCEPT FOR MEMBERS OF THE OSAGE NATION AND THE FIVE CIVILIZED TRIBES- Part 16; ESTATES OF INDIANS OF THE FIVE CIVILIZED TRIBES- Part 17; ACTION ON WILLS OF OSAGE INDIANS- Part 18; TRIBAL PROBATE CODES- Part 20; FINANCIAL ASSISTANCE AND SOCIAL SERVICES PROGRAMS- Part 23; INDIAN CHILD WELFARE ACT- Part 26; JOB PLACEMENT AND TRAINING PROGRAM- Part 30; ADEQUATE YEARLY PROGRESS- Part 31; FEDERAL SCHOOLS FOR INDIANS- Part 32; INDIAN EDUCATION POLICIES- Part 33; TRANSFER OF INDIAN EDUCATION FUNCTIONS- Part 36; MINIMUM ACADEMIC STANDARDS FOR THE BASIC EDUCATION OF INDIAN CHILDREN AND NATIONAL CRITERIA FOR DORMITORY SITUATIONS- Part 37; GEOGRAPHIC BOUNDARIES- Part 38; EDUCATION PERSONNEL- Part 39; THE INDIAN SCHOOL EQUALIZATION PROGRAM- Part 40; ADMINISTRATION OF EDUCATIONAL LOANS, GRANT...
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Code of Federal Regulations Title 9, Volume 2, January 1, 2017 contains regulations governing Animals and Animal Products and may also be referenced as:- Code of Federal Regulations Title 9, Volume 2, January 1, 2017- CFR Title 9- CFR 9, Animals and Animal Products- CFR 9, Part 200 to end, Animals and Animal ProductsThis volume contains Part 200 to end:- Part 200; Reserved- Part 201; REGULATIONS UNDER THE PACKERS AND STOCKYARDS ACT- Part 202; RULES OF PRACTICE GOVERNING PROCEEDINGS UNDER THE PACKERS AND STOCKYARDS ACT- Part 203; STATEMENTS OF GENERAL POLICY UNDER THE PACKERS AND STOCKYARDS ACT- Part 204; ORGANIZATION AND FUNCTIONS- Part 205; CLEAR TITLE-PROTECTION FOR PURCHASERS OF FARM PRODUCTS- Part 206; SWINE CONTRACT LIBRARY- Parts 207-299; Reserved- Part 300; AGENCY MISSION AND ORGANIZATION- Part 301; TERMINOLOGY; ADULTERATION AND MISBRANDING STANDARDS- Part 302; APPLICATION OF INSPECTION AND OTHER REQUIREMENTS- Part 303; EXEMPTIONS- Part 304; APPLICATION FOR INSPECTION; GRANT OF INSPECTION- Part 305; OFFICIAL NUMBERS; INAUGURATION OF INSPECTION; WITHDRAWAL OF INSPECTION; REPORTS OF VIOLATION- Part 306; ASSIGNMENT AND AUTHORITIES OF PROGRAM EMPLOYEES- Part 307; FACILITIES FOR INSPECTION- Part 308; Reserved- Part 309; ANTE-MORTEM INSPECTION- Part 310; POST-MORTEM INSPECTION- Part 311; DISPOSAL OF DISEASED OR OTHERWISE ADULTERATED CARCASSES AND PARTS- Part 312; OFFICIAL MARKS, DEVICES AND CERTIFICATES- Part 313; HUMANE SLAUGHTER OF LIVESTOCK- Part 314; HANDLING AND DISPOSA...
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Code of Federal Regulations Title 1, Volume 1, January 1, 2017 contains regulations governing General Provisions and may also be referenced as:- Code of Federal Regulations Title 1, Volume 1, January 1, 2017- CFR Title 1- CFR 1, General ProvisionsThis volume contains:- Part 1; DEFINITIONS- Part 2; GENERAL INFORMATION- Part 3; SERVICES TO THE PUBLIC- Part 5; GENERAL- Part 6; INDEXES AND ANCILLARIES- Part 8; CODE OF FEDERAL REGULATIONS- Part 9; THE UNITED STATES GOVERNMENT MANUAL- Part 10; PRESIDENTIAL PAPERS- Part 11; SUBSCRIPTIONS- Part 12; OFFICIAL DISTRIBUTION WITHIN FEDERAL GOVERNMENT- Part 15; SERVICES TO FEDERAL AGENCIES- Part 16; AGENCY REPRESENTATIVES- Part 17; FILING FOR PUBLIC INSPECTION AND PUBLICATION SCHEDULES- Part 18; PREPARATION AND TRANSMITTAL OF DOCUMENTS GENERALLY- Part 19; EXECUTIVE ORDERS AND PRESIDENTIAL PROCLAMATIONS- Part 20; HANDLING OF THE UNITED STATES GOVERNMENT MANUAL STATEMENTS- Part 21; PREPARATION OF DOCUMENTS SUBJECT TO CODIFICATION- Part 22; PREPARATION OF NOTICES AND PROPOSED RULES- Parts 23-49; Reserved- Part 50; Reserved- Part 51; INCORPORATION BY REFERENCE- Parts 52-299; Reserved- Part 300; Reserved- Part 301; ORGANIZATION AND PURPOSE- Parts 302-303; Reserved- Part 304; DISCLOSURE OF RECORDS OR INFORMATION- Parts 305-399; Reserved- Parts 400-424; Reserved- Part 425; PRESIDENT'S COMMISSION ON WHITE HOUSE FELLOWSHIPS- Part 455; NATIONAL CAPITAL PLANNING COMMISSION (PRIVACY ACT REGULATIONS)- Part 456; NATIONAL CAPITAL PLANNING COMMISSION ...
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The book not only offers scientists and engineers a clear inter-disciplinary introduction and orientation to all major EHL problems and their solutions but, most importantly, it also provides numerical programs on specific application in engineering. • A one-stop reference providing equations and their solutions to all major elastohydrodynamic lubrication (EHL) problems, plus numerical programs on specific applications in engineering • offers engineers and scientists a clear inter-disciplinary introduction and a concise program for practical engineering applications to most important EHL problems and their solutions • brings together a number of case studies in one text, each being solved using solution methods which share common features and methods
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Code of Federal Regulations Title 7, Volume 1, January 1, 2017 contains regulations governing Agriculture and may also be referenced as:- Code of Federal Regulations Title 7, Volume 1, January 1, 2017- CFR Title 7- CFR 7, Agriculture- CFR 7, Parts 1 to 26, AgricultureThis volume contains Parts 1 to 26:- Part 1; ADMINISTRATIVE REGULATIONS- Part 1a; LAW ENFORCEMENT AUTHORITIES- Part 1b; NATIONAL ENVIRONMENTAL POLICY ACT- Part 1c; PROTECTION OF HUMAN SUBJECTS- Part 2; DELEGATIONS OF AUTHORITY BY THE SECRETARY OF AGRICULTURE AND GENERAL OFFICERS OF THE DEPARTMENT- Part 3; DEBT MANAGEMENT- Part 4; Reserved- Part 5; DETERMINATION OF PARITY PRICES- Part 6; IMPORT QUOTAS AND FEES- Part 7; SELECTION AND FUNCTIONS OF FARM SERVICE AGENCY STATE AND COUNTY COMMITTEES- Part 8; 4-H CLUB NAME AND EMBLEM- Parts 9-10; Reserved- Part 11; NATIONAL APPEALS DIVISION- Part 12; HIGHLY ERODIBLE LAND CONSERVATION AND WETLAND CONSERVATION- Part 13; Reserved- Part 14; DETERMINING THE PRIMARY PURPOSE OF CERTAIN PAYMENTS FOR FEDERAL TAX PURPOSES- Part 15; NONDISCRIMINATION- Part 15a; EDUCATION PROGRAMS OR ACTIVITIES RECEIVING OR BENEFITTING FROM FEDERAL FINANCIAL ASSISTANCE- Part 15b; NONDISCRIMINATION ON THE BASIS OF HANDICAP IN PROGRAMS OR ACTIVITIES RECEIVING FEDERAL FINANCIAL ASSISTANCE- Part 15c; NONDISCRIMINATION ON THE BASIS OF AGE IN PROGRAMS OR ACTIVITIES RECEIVING FEDERAL FINANCIAL ASSISTANCE FROM THE UNITED STATES DEPARTMENT OF AGRICULTURE- Part 15d; NONDISCRIMINATION IN PROGRAMS OR ACTIVITIES ...
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The first comprehensive overview of preprocessing, mining, and postprocessing of biological data Molecular biology is undergoing exponential growth in both the volume and complexity of biological data—and knowledge discovery offers the capacity to automate complex search and data analysis tasks. This book presents a vast overview of the most recent developments on techniques and approaches in the field of biological knowledge discovery and data mining (KDD)—providing in-depth fundamental and technical field information on the most important topics encountered. Written by top experts, Biological Knowledge Discovery Handbook: Preprocessing, Mining, and Postprocessing of Biological Data covers the three main phases of knowledge discovery (data preprocessing, data processing—also known as data mining—and data postprocessing) and analyzes both verification systems and discovery systems. BIOLOGICAL DATA PREPROCESSING Part A: Biological Data Management Part B: Biological Data Modeling Part C: Biological Feature Extraction Part D Biological Feature Selection BIOLOGICAL DATA MINING Part E: Regression Analysis of Biological Data Part F Biological Data Clustering Part G: Biological Data Classification Part H: Association Rules Learning from Biological Data Part I: Text Mining and Application to Biological Data Part J: High-Performance Computing for Biological Data Mining Combining sound theory with practical applications in molecular biology, Biological Knowledge Discovery Handbook is ideal for courses in bioinformatics and biological KDD as well as for practitioners and professional researchers in computer science, life science, and mathematics.
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Cutting-edge solutions to current problems in orthopedics, supported by modeling and numerical analysis Despite the current successful methods and achievements of good joint implantations, it is essential to further optimize the shape of implants so they may better resist extreme long-term mechanical demands. This book provides the orthopedic, biomechanical, and mathematical basis for the simulation of surgical techniques in orthopedics. It focuses on the numerical modeling of total human joint replacements and simulation of their functions, along with the rigorous biomechanics of human joints and other skeletal parts. The book includes: An introduction to the anatomy and biomechanics of the human skeleton, biomaterials, and problems of alloarthroplasty The definition of selected simulated orthopedic problems Constructions of mathematical model problems of the biomechanics of the human skeleton and its parts Replacement parts of the human skeleton and corresponding mathematical model problems Detailed mathematical analyses of mathematical models based on functional analysis and finite element methods Biomechanical analyses of particular parts of the human skeleton, joints, and corresponding replacements A discussion of the problems of data processing from nuclear magnetic resonance imaging and computer tomography This timely book offers a wealth of information on the current research in this field. The theories presented are applied to specific problems of orthopedics. Numerical results are presented and discussed from both biomechanical and orthopedic points of view and treatment methods are also briefly addressed. Emphasis is placed on the variational approach to the investigated model problems while preserving the orthopedic nature of the investigated problems. The book also presents a study of algorithmic procedures based on these simulation models. This is a highly useful tool for designers, researchers, and manufacturers of joint implants who require the results of suggested experiments to improve existing shapes or to design new shapes. It also benefits graduate students in orthopedics, biomechanics, and applied mathematics.
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Code of Federal Regulations Title 7, Volume 2, January 1, 2017 contains regulations governing Agriculture and may also be referenced as:- Code of Federal Regulations Title 7, Volume 2, January 1, 2017- CFR Title 7- CFR 7, Agriculture- CFR 7, Parts 27 to 52, AgricultureThis volume contains Parts 27 to 52:- Part 27; COTTON CLASSIFICATION UNDER COTTON FUTURES LEGISLATION- Part 28; COTTON CLASSING, TESTING, AND STANDARDS- Part 29; TOBACCO INSPECTION- Part 30; TOBACCO STOCKS AND STANDARDS- Part 31; PURCHASE OF WOOL AND WOOL TOP SAMPLES- Part 32; PURCHASE OF GREASE MOHAIR AND MOHAIR TOP SAMPLES- Part 33; REGULATIONS ISSUED UNDER AUTHORITY OF THE EXPORT APPLE ACT- Part 34; Reserved- Part 35; EXPORT GRAPES AND PLUMS- Part 36; PROCEDURES BY WHICH THE AGRICULTURAL MARKETING SERVICE DEVELOPS, REVISES, SUSPENDS, OR TERMINATES VOLUNTARY OFFICIAL GRADE STANDARDS- Parts 37-41; Reserved- Part 42; STANDARDS FOR CONDITION OF FOOD CONTAINERS- Part 43; STANDARDS FOR SAMPLING PLANS- Parts 44-45; Reserved- Part 46; REGULATIONS (OTHER THAN RULES OF PRACTICE) UNDER THE PERISHABLE AGRICULTURAL COMMODITIES ACT, 1930- Part 47; RULES OF PRACTICE UNDER THE PERISHABLE AGRICULTURAL COMMODITIES ACT- Part 48; REGULATIONS OF THE SECRETARY OF AGRICULTURE FOR THE ENFORCEMENT OF THE PRODUCE AGENCY ACT- Part 50; RULES OF PRACTICE GOVERNING WITHDRAWAL OF INSPECTION AND GRADING SERVICES- Part 51; FRESH FRUITS, VEGETABLES AND OTHER PRODUCTS 1 2 (INSPECTION, CERTIFICATION, AND STANDARDS)- Part 52; PROCESSED FRUITS AN...
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This book presents a substantial description of the principles and applications of digital holography. The first part of the book deals with mathematical basics and the linear filtering theory necessary to approach the topic. The next part describes the fundamentals of diffraction theory and exhaustively details the numerical computation of diffracted fields using FFT algorithms. A thorough presentation of the principles of holography and digital holography, including digital color holography, is proposed in the third part. A special section is devoted to the algorithms and methods for the numerical reconstruction of holograms. There is also a chapter devoted to digital holographic interferometry with applications in holographic microscopy, quantitative phase contrast imaging, multidimensional deformation investigations, surface shape measurements, fluid mechanics, refractive index investigations, synthetic aperture imaging and information encrypting. Keys so as to understand the differences between digital holography and speckle interferometry and examples of software for hologram reconstructions are also treated in brief. Contents 1. Mathematical Prerequisites. 2. The Scalar Theory of Diffraction. 3. Calculating Diffraction by Fast Fourier Transform. 4. Fundamentals of Holography. 5. Digital Off-Axis Fresnel Holography. 6. Reconstructing Wavefronts Propagated through an Optical System. 7. Digital Holographic Interferometry and Its Applications. Appendix. Examples of Digital Hologram Reconstruction Programs
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High responsibility of hydraulic structures (HS) imposes to them increased requirements regarding the reliability of strength design and safety. This fundamental monograph incorporates 30 years of scientific researches of concrete underground culverts and dams conducted by the scientific school of Dr. Tech. Sci., Prof. M.I. Frolov. System analysis of HS stress state allows to save materials and money for HS constructing. For correct application of numerical methods for HS design it’s necessary the considerable scientific experience for creating high-quality models and subsequent correct interpretation of results in order to adequately reflect the work of real HS.
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Presents the methodology and applications of ODE and PDE models within biomedical science and engineering With an emphasis on the method of lines (MOL) for partial differential equation (PDE) numerical integration, Method of Lines PDE Analysis in Biomedical Science and Engineering demonstrates the use of numerical methods for the computer solution of PDEs as applied to biomedical science and engineering (BMSE). Written by a well-known researcher in the field, the book provides an introduction to basic numerical methods for initial/boundary value PDEs before moving on to specific BMSE applications of PDEs. Featuring a straightforward approach, the book’s chapters follow a consistent and comprehensive format. First, each chapter begins by presenting the model as an ordinary differential equation (ODE)/PDE system, including the initial and boundary conditions. Next, the programming of the model equations is introduced through a series of R routines that primarily implement MOL for PDEs. Subsequently, the resulting numerical and graphical solution is discussed and interpreted with respect to the model equations. Finally, each chapter concludes with a review of the numerical algorithm performance, general observations and results, and possible extensions of the model. Method of Lines PDE Analysis in Biomedical Science and Engineering also includes: Examples of MOL analysis of PDEs, including BMSE applications in wave front resolution in chromatography, VEGF angiogenesis, thermographic tumor location, blood-tissue transport, two fluid and membrane mass transfer, artificial liver support system, cross diffusion epidemiology, oncolytic virotherapy, tumor cell density in glioblastomas, and variable grids Discussions on the use of R software, which facilitates immediate solutions to differential equation problems without having to first learn the basic concepts of numerical analysis for PDEs and the programming of PDE algorithms A companion website that provides source code for the R routines Method of Lines PDE Analysis in Biomedical Science and Engineering is an introductory reference for researchers, scientists, clinicians, medical researchers, mathematicians, statisticians, chemical engineers, epidemiologists, and pharmacokineticists as well as anyone interested in clinical applications and the interpretation of experimental data with differential equation models. The book is also an ideal textbook for graduate-level courses in applied mathematics, BMSE, biology, biophysics, biochemistry, medicine, and engineering.
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This third book in a suite of four practical guides is an engineer's companion to using numerical methods for the solution of complex mathematical problems. The required software is provided by way of the freeware mathematical library BzzMath that is developed and maintained by the authors. The present volume focuses on optimization and nonlinear systems solution. The book describes numerical methods, innovative techniques and strategies that are all implemented in a well-established, freeware library. Each of these handy guides enables the reader to use and implement standard numerical tools for their work, explaining the theory behind the various functions and problem solvers, and showcasing applications in diverse scientific and engineering fields. Numerous examples, sample codes, programs and applications are proposed and discussed. The book teaches engineers and scientists how to use the latest and most powerful numerical methods for their daily work.
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Introduces both the fundamentals of time dependent differential equations and their numerical solutions Introduction to Numerical Methods for Time Dependent Differential Equations delves into the underlying mathematical theory needed to solve time dependent differential equations numerically. Written as a self-contained introduction, the book is divided into two parts to emphasize both ordinary differential equations (ODEs) and partial differential equations (PDEs). Beginning with ODEs and their approximations, the authors provide a crucial presentation of fundamental notions, such as the theory of scalar equations, finite difference approximations, and the Explicit Euler method. Next, a discussion on higher order approximations, implicit methods, multistep methods, Fourier interpolation, PDEs in one space dimension as well as their related systems is provided. Introduction to Numerical Methods for Time Dependent Differential Equations features: A step-by-step discussion of the procedures needed to prove the stability of difference approximations Multiple exercises throughout with select answers, providing readers with a practical guide to understanding the approximations of differential equations A simplified approach in a one space dimension Analytical theory for difference approximations that is particularly useful to clarify procedures Introduction to Numerical Methods for Time Dependent Differential Equations is an excellent textbook for upper-undergraduate courses in applied mathematics, engineering, and physics as well as a useful reference for physical scientists, engineers, numerical analysts, and mathematical modelers who use numerical experiments to test designs or predict and investigate phenomena from many disciplines. Uses mathematical, numerical, and programming tools to solve differential equations for physical phenomena and engineering problems Introduction to Computation and Modeling for Differential Equations, Second Edition features the essential principles and applications of problem solving across disciplines such as engineering, physics, and chemistry. The Second Edition integrates the science of solving differential equations with mathematical, numerical, and programming tools, specifically with methods involving ordinary differential equations; numerical methods for initial value problems (IVPs); numerical methods for boundary value problems (BVPs); partial differential equations (PDEs); numerical methods for parabolic, elliptic, and hyperbolic PDEs; mathematical modeling with differential equations; numerical solutions; and finite difference and finite element methods. The author features a unique “Five-M” approach: Modeling, Mathematics, Methods, MATLAB®, and Multiphysics, which facilitates a thorough understanding of how models are created and preprocessed mathematically with scaling, classification, and approximation and also demonstrates how a problem is solved numerically using the appropriate mathematical methods. With numerous real-world examples to aid in the visualization of the solutions, Introduction to Computation and Modeling for Differential Equations, Second Edition includes: New sections on topics including variational formulation, the finite element method, examples of discretization, ansatz methods such as Galerkin’s method for BVPs, parabolic and elliptic PDEs, and finite volume methods Numerous practical examples with applications in mechanics, fluid dynamics, solid mechanics, chemical engineering, heat conduction, electromagnetic field theory, and control theory, some of which are solved with computer programs MATLAB and COMSOL Multiphysics® Additional exercises that introduce new methods, projects, and problems to further illustrate possible applications A related website with select solutions to the exercises, as well as the MATLAB data sets for ordinary differential equations (ODEs) and PDEs Introduction to Computation and Modeling for Differential Equations, Second Edition is a useful textbook for upper-undergraduate and graduate-level courses in scientific computing, differential equations, ordinary differential equations, partial differential equations, and numerical methods. The book is also an excellent self-study guide for mathematics, science, computer science, physics, and engineering students, as well as an excellent reference for practitioners and consultants who use differential equations and numerical methods in everyday situations.