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3879 руб.
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The present monography is dedicated to a fashionable trend in nonlinear analysis - the theories of blow-up of solutions for final time. In this book nonlinear Sobolev type equations are systematically studied. The book will be interesting both to experts in the field of nonlinear analysis and to students and post-graduate students of the corresponding specialties.
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8767.77 руб.
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A modern approach to mathematical modeling, featuring unique applications from the field of mechanics An Introduction to Mathematical Modeling: A Course in Mechanics is designed to survey the mathematical models that form the foundations of modern science and incorporates examples that illustrate how the most successful models arise from basic principles in modern and classical mathematical physics. Written by a world authority on mathematical theory and computational mechanics, the book presents an account of continuum mechanics, electromagnetic field theory, quantum mechanics, and statistical mechanics for readers with varied backgrounds in engineering, computer science, mathematics, and physics. The author streamlines a comprehensive understanding of the topic in three clearly organized sections: Nonlinear Continuum Mechanics introduces kinematics as well as force and stress in deformable bodies; mass and momentum; balance of linear and angular momentum; conservation of energy; and constitutive equations Electromagnetic Field Theory and Quantum Mechanics contains a brief account of electromagnetic wave theory and Maxwell's equations as well as an introductory account of quantum mechanics with related topics including ab initio methods and Spin and Pauli's principles Statistical Mechanics presents an introduction to statistical mechanics of systems in thermodynamic equilibrium as well as continuum mechanics, quantum mechanics, and molecular dynamics Each part of the book concludes with exercise sets that allow readers to test their understanding of the presented material. Key theorems and fundamental equations are highlighted throughout, and an extensive bibliography outlines resources for further study. Extensively class-tested to ensure an accessible presentation, An Introduction to Mathematical Modeling is an excellent book for courses on introductory mathematical modeling and statistical mechanics at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for professionals working in the areas of modeling and simulation, physics, and computational engineering.
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7837.86 руб.
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Features a solid foundation of mathematical and computational tools to formulate and solve real-world ODE problems across various fields With a step-by-step approach to solving ordinary differential equations (ODEs), Differential Equation Analysis in Biomedical Science and Engineering: Ordinary Differential Equation Applications with R successfully applies computational techniques for solving real-world ODE problems that are found in a variety of fields, including chemistry, physics, biology, and physiology. The book provides readers with the necessary knowledge to reproduce and extend the computed numerical solutions and is a valuable resource for dealing with a broad class of linear and nonlinear ordinary differential equations. The author’s primary focus is on models expressed as systems of ODEs, which generally result by neglecting spatial effects so that the ODE dependent variables are uniform in space. Therefore, time is the independent variable in most applications of ODE systems. As such, the book emphasizes details of the numerical algorithms and how the solutions were computed. Featuring computer-based mathematical models for solving real-world problems in the biological and biomedical sciences and engineering, the book also includes: R routines to facilitate the immediate use of computation for solving differential equation problems without having to first learn the basic concepts of numerical analysis and programming for ODEs Models as systems of ODEs with explanations of the associated chemistry, physics, biology, and physiology as well as the algebraic equations used to calculate intermediate variables Numerical solutions of the presented model equations with a discussion of the important features of the solutions Aspects of general ODE computation through various biomolecular science and engineering applications Differential Equation Analysis in Biomedical Science and Engineering: Ordinary Differential Equation Applications with R is an excellent reference for researchers, scientists, clinicians, medical researchers, engineers, statisticians, epidemiologists, and pharmacokineticists who are interested in both clinical applications and interpretation of experimental data with mathematical models in order to efficiently solve the associated differential equations. The book is also useful as a textbook for graduate-level courses in mathematics, biomedical science and engineering, biology, biophysics, biochemistry, medicine, and engineering.
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9631.26 руб.
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Innovative developments in science and technology require a thorough knowledge of applied mathematics, particularly in the field of differential equations and special functions. These are relevant in modeling and computing applications of electromagnetic theory and quantum theory, e.g. in photonics and nanotechnology. The problem of solving partial differential equations remains an important topic that is taught at both the undergraduate and graduate level. Separable Boundary-Value Problems in Physics is an accessible and comprehensive treatment of partial differential equations in mathematical physics in a variety of coordinate systems and geometry and their solutions, including a differential geometric formulation, using the method of separation of variables. With problems and modern examples from the fields of nano-technology and other areas of physics. The fluency of the text and the high quality of graphics make the topic easy accessible. The organization of the content by coordinate systems rather than by equation types is unique and offers an easy access. The authors consider recent research results which have led to a much increased pedagogical understanding of not just this topic but of many other related topics in mathematical physics, and which like the explicit discussion on differential geometry shows – yet have not been treated in the older texts. To the benefit of the reader, a summary presents a convenient overview on all special functions covered. Homework problems are included as well as numerical algorithms for computing special functions. Thus this book can serve as a reference text for advanced undergraduate students, as a textbook for graduate level courses, and as a self-study book and reference manual for physicists, theoretically oriented engineers and traditional mathematicians.
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4317.46 руб.
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Detailed guidance on the mathematics behind equity derivatives Problems and Solutions in Mathematical Finance Volume II is an innovative reference for quantitative practitioners and students, providing guidance through a range of mathematical problems encountered in the finance industry. This volume focuses solely on equity derivatives problems, beginning with basic problems in derivatives securities before moving on to more advanced applications, including the construction of volatility surfaces to price exotic options. By providing a methodology for solving theoretical and practical problems, whilst explaining the limitations of financial models, this book helps readers to develop the skills they need to advance their careers. The text covers a wide range of derivatives pricing, such as European, American, Asian, Barrier and other exotic options. Extensive appendices provide a summary of important formulae from calculus, theory of probability, and differential equations, for the convenience of readers. As Volume II of the four-volume Problems and Solutions in Mathematical Finance series, this book provides clear explanation of the mathematics behind equity derivatives, in order to help readers gain a deeper understanding of their mechanics and a firmer grasp of the calculations. Review the fundamentals of equity derivatives Work through problems from basic securities to advanced exotics pricing Examine numerical methods and detailed derivations of closed-form solutions Utilise formulae for probability, differential equations, and more Mathematical finance relies on mathematical models, numerical methods, computational algorithms and simulations to make trading, hedging, and investment decisions. For the practitioners and graduate students of quantitative finance, Problems and Solutions in Mathematical Finance Volume II provides essential guidance principally towards the subject of equity derivatives.
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10292.17 руб.
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Nonlinear problems are of interest to engineers, physicists and mathematicians and many other scientists because most systems are inherently nonlinear in nature. As nonlinear equations are difficult to solve, nonlinear systems are commonly approximated by linear equations. This works well up to some accuracy and some range for the input values, but some interesting phenomena such as chaos and singularities are hidden by linearization and perturbation analysis. It follows that some aspects of the behavior of a nonlinear system appear commonly to be chaotic, unpredictable or counterintuitive. Although such a chaotic behavior may resemble a random behavior, it is absolutely deterministic. Analytical Routes to Chaos in Nonlinear Engineering discusses analytical solutions of periodic motions to chaos or quasi-periodic motions in nonlinear dynamical systems in engineering and considers engineering applications, design, and control. It systematically discusses complex nonlinear phenomena in engineering nonlinear systems, including the periodically forced Duffing oscillator, nonlinear self-excited systems, nonlinear parametric systems and nonlinear rotor systems. Nonlinear models used in engineering are also presented and a brief history of the topic is provided. Key features: Considers engineering applications, design and control Presents analytical techniques to show how to find the periodic motions to chaos in nonlinear dynamical systems Systematically discusses complex nonlinear phenomena in engineering nonlinear systems Presents extensively used nonlinear models in engineering Analytical Routes to Chaos in Nonlinear Engineering is a practical reference for researchers and practitioners across engineering, mathematics and physics disciplines, and is also a useful source of information for graduate and senior undergraduate students in these areas.
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2194.57 руб.
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Features a balance between theory, proofs, and examples and provides applications across diverse fields of study Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order.
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6907.94 руб.
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A simplified, yet rigorous treatment of scattering theory methods and their applications Dispersion Decay and Scattering Theory provides thorough, easy-to-understand guidance on the application of scattering theory methods to modern problems in mathematics, quantum physics, and mathematical physics. Introducing spectral methods with applications to dispersion time-decay and scattering theory, this book presents, for the first time, the Agmon-Jensen-Kato spectral theory for the Schr?dinger equation, extending the theory to the Klein-Gordon equation. The dispersion decay plays a crucial role in the modern application to asymptotic stability of solitons of nonlinear Schr?dinger and Klein-Gordon equations. The authors clearly explain the fundamental concepts and formulas of the Schr?dinger operators, discuss the basic properties of the Schr?dinger equation, and offer in-depth coverage of Agmon-Jensen-Kato theory of the dispersion decay in the weighted Sobolev norms. The book also details the application of dispersion decay to scattering and spectral theories, the scattering cross section, and the weighted energy decay for 3D Klein-Gordon and wave equations. Complete streamlined proofs for key areas of the Agmon-Jensen-Kato approach, such as the high-energy decay of the resolvent and the limiting absorption principle are also included. Dispersion Decay and Scattering Theory is a suitable book for courses on scattering theory, partial differential equations, and functional analysis at the graduate level. The book also serves as an excellent resource for researchers, professionals, and academics in the fields of mathematics, mathematical physics, and quantum physics who would like to better understand scattering theory and partial differential equations and gain problem-solving skills in diverse areas, from high-energy physics to wave propagation and hydrodynamics.
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11291.83 руб.
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The Duffing Equation: Nonlinear Oscillators and their Behaviour brings together the results of a wealth of disseminated research literature on the Duffing equation, a key engineering model with a vast number of applications in science and engineering, summarizing the findings of this research. Each chapter is written by an expert contributor in the field of nonlinear dynamics and addresses a different form of the equation, relating it to various oscillatory problems and clearly linking the problem with the mathematics that describe it. The editors and the contributors explain the mathematical techniques required to study nonlinear dynamics, helping the reader with little mathematical background to understand the text. The Duffing Equation provides a reference text for postgraduate and students and researchers of mechanical engineering and vibration / nonlinear dynamics as well as a useful tool for practising mechanical engineers. Includes a chapter devoted to historical background on Georg Duffing and the equation that was named after him. Includes a chapter solely devoted to practical examples of systems whose dynamic behaviour is described by the Duffing equation. Contains a comprehensive treatment of the various forms of the Duffing equation. Uses experimental, analytical and numerical methods as well as concepts of nonlinear dynamics to treat the physical systems in a unified way.
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8435.66 руб.
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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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8767.77 руб.
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Features a balance between theory, proofs, and examples and provides applications across diverse fields of study Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order. The book transitions smoothly from first-order to higher-order equations, allowing readers to develop a complete understanding of the related theory. Featuring diverse and interesting applications from engineering, bioengineering, ecology, and biology, the book anticipates potential difficulties in understanding the various solution steps and provides all the necessary details. Topical coverage includes: First-Order Differential Equations Higher-Order Linear Equations Applications of Higher-Order Linear Equations Systems of Linear Differential Equations Laplace Transform Series Solutions Systems of Nonlinear Differential Equations In addition to plentiful exercises and examples throughout, each chapter concludes with a summary that outlines key concepts and techniques. The book's design allows readers to interact with the content, while hints, cautions, and emphasis are uniquely featured in the margins to further help and engage readers. Written in an accessible style that includes all needed details and steps, Ordinary Differential Equations is an excellent book for courses on the topic at the upper-undergraduate level. The book also serves as a valuable resource for professionals in the fields of engineering, physics, and mathematics who utilize differential equations in their everyday work. An Instructors Manual is available upon request. Email [email protected] for information. There is also a Solutions Manual available. The ISBN is 9781118398999.
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10494.76 руб.
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Praise for the Second Edition «This book is an excellent introduction to the wide field of boundary value problems.»—Journal of Engineering Mathematics «No doubt this textbook will be useful for both students and research workers.»—Mathematical Reviews A new edition of the highly-acclaimed guide to boundary value problems, now featuring modern computational methods and approximation theory Green's Functions and Boundary Value Problems, Third Edition continues the tradition of the two prior editions by providing mathematical techniques for the use of differential and integral equations to tackle important problems in applied mathematics, the physical sciences, and engineering. This new edition presents mathematical concepts and quantitative tools that are essential for effective use of modern computational methods that play a key role in the practical solution of boundary value problems. With a careful blend of theory and applications, the authors successfully bridge the gap between real analysis, functional analysis, nonlinear analysis, nonlinear partial differential equations, integral equations, approximation theory, and numerical analysis to provide a comprehensive foundation for understanding and analyzing core mathematical and computational modeling problems. Thoroughly updated and revised to reflect recent developments, the book includes an extensive new chapter on the modern tools of computational mathematics for boundary value problems. The Third Edition features numerous new topics, including: Nonlinear analysis tools for Banach spaces Finite element and related discretizations Best and near-best approximation in Banach spaces Iterative methods for discretized equations Overview of Sobolev and Besov space linear Methods for nonlinear equations Applications to nonlinear elliptic equations In addition, various topics have been substantially expanded, and new material on weak derivatives and Sobolev spaces, the Hahn-Banach theorem, reflexive Banach spaces, the Banach Schauder and Banach-Steinhaus theorems, and the Lax-Milgram theorem has been incorporated into the book. New and revised exercises found throughout allow readers to develop their own problem-solving skills, and the updated bibliographies in each chapter provide an extensive resource for new and emerging research and applications. With its careful balance of mathematics and meaningful applications, Green's Functions and Boundary Value Problems, Third Edition is an excellent book for courses on applied analysis and boundary value problems in partial differential equations at the graduate level. It is also a valuable reference for mathematicians, physicists, engineers, and scientists who use applied mathematics in their everyday work.
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14214.42 руб.
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A unified and coherent treatment of analytical, computational and experimental techniques of nonlinear dynamics with numerous illustrative applications. Features a discourse on geometric concepts such as Poincare maps. Discusses chaos, stability and bifurcation analysis for systems of differential and algebraic equations. Includes scores of examples to facilitate understanding.
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7103.89 руб.
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This is an introduction to stochastic integration and stochastic differential equations written in an understandable way for a wide audience, from students of mathematics to practitioners in biology, chemistry, physics, and finances. The presentation is based on the naïve stochastic integration, rather than on abstract theories of measure and stochastic processes. The proofs are rather simple for practitioners and, at the same time, rather rigorous for mathematicians. Detailed application examples in natural sciences and finance are presented. Much attention is paid to simulation diffusion processes. The topics covered include Brownian motion; motivation of stochastic models with Brownian motion; Itô and Stratonovich stochastic integrals, Itô’s formula; stochastic differential equations (SDEs); solutions of SDEs as Markov processes; application examples in physical sciences and finance; simulation of solutions of SDEs (strong and weak approximations). Exercises with hints and/or solutions are also provided.
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4317.46 руб.
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Mathematical finance requires the use of advanced mathematical techniques drawn from the theory of probability, stochastic processes and stochastic differential equations. These areas are generally introduced and developed at an abstract level, making it problematic when applying these techniques to practical issues in finance. Problems and Solutions in Mathematical Finance Volume I: Stochastic Calculus is the first of a four-volume set of books focusing on problems and solutions in mathematical finance. This volume introduces the reader to the basic stochastic calculus concepts required for the study of this important subject, providing a large number of worked examples which enable the reader to build the necessary foundation for more practical orientated problems in the later volumes. Through this application and by working through the numerous examples, the reader will properly understand and appreciate the fundamentals that underpin mathematical finance. Written mainly for students, industry practitioners and those involved in teaching in this field of study, Stochastic Calculus provides a valuable reference book to complement one’s further understanding of mathematical finance.
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10627.6 руб.
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In this introductory treatment Ali Nayfeh presents different concepts from dynamical systems theory and nonlinear dynamics in a rigorous yet plan way. He systematically introduces models and techniques and states the relevant ranges of validity and applicability. The reader is provided with a clear operational framework for consciously use rather than focused on the underlying mathematical apparatus. The exposition is largely by means of examples, dealt with up to their final outcome. For most of the examples, the results obtained with the method of normal forms are equivalent to those obtained with other perturbation methods, such as the method of multiple scales and the method of averaging. The previous edition had a remarkable success by researchers from all over the world working in the area of nonlinear dynamics and their applications in engineering. Additions to this new edition concern major topics of current interest. In particular, the author added three new chapters dedicated to Maps, Bifurcations of Continuous Systems, and Retarded Systems. In particular the latter has become of major importance in several applications, both in mechanics and in different areas. Accessible to engineers and applied scientist involved with nonlinear dynamics and their applications in a wide variety of fields. It is assumed that readers have a knowledge of basic calculus as well as the elementary properties of ordinary-differential equations.
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10627.6 руб.
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A distinctive discussion of the nonlinear dynamical phenomena of semiconductor lasers. The book combines recent results of quantum dot laser modeling with mathematical details and an analytic understanding of nonlinear phenomena in semiconductor lasers and points out possible applications of lasers in cryptography and chaos control. This interdisciplinary approach makes it a unique and powerful source of knowledge for anyone intending to contribute to this field of research. By presenting both experimental and theoretical results, the distinguished authors consider solitary lasers with nano-structured material, as well as integrated devices with complex feedback sections. In so doing, they address such topics as the bifurcation theory of systems with time delay, analysis of chaotic dynamics, and the modeling of quantum transport. They also address chaos-based cryptography as an example of the technical application of highly nonlinear laser systems.
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10295.49 руб.
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Illustrates theories and associated mathematical expressions with numerical examples using various methods, leading to exact solutions, more accurate results, and more computationally efficient techniques This book presents the derivations of the equations of motion for all structure foundations using either the continuous model or the discrete model. This mathematical display is a strong feature of the book as it helps to explain in full detail how calculations are reached and interpreted. In addition to the simple 'uniform' and 'straight' beams, the book introduces solution techniques for the complicated ‘non uniform’ beams (including linear or non-linear tapered beams), and curved beams. Most of the beams are analyzed by taking account of the effects of shear deformation and rotary inertia of the beams themselves as well as the eccentricities and mass moments of inertia of the attachments. Demonstrates approaches which dramatically cut CPU times to a fraction of conventional FEM Presents «mode shapes» in addition to natural frequencies, which are critical for designers Gives detailed derivations for continuous and discrete model equations of motions Summarizes the analytical and numerical methods for the natural frequencies, mode shapes, and time histories of straight structures rods shafts Euler beams strings Timoshenko beams membranes/thin plates Conical rods and shafts Tapered beams Curved beams Has applications for students taking courses including vibration mechanics, dynamics of structures, and finite element analyses of structures, the transfer matrix method, and Jacobi method This book is ideal for graduate students in mechanical, civil, marine, aeronautical engineering courses as well as advanced undergraduates with a background in General Physics, Calculus, and Mechanics of Material. The book is also a handy reference for researchers and professional engineers.
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9299.15 руб.
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An authoritative view of Maxwell's Equations that takes theory to practice Maxwell's Equations is a practical guide to one of the most remarkable sets of equations ever devised. Professor Paul Huray presents techniques that show the reader how to obtain analytic solutions for Maxwell's equations for ideal materials and boundary conditions. These solutions are then used as a benchmark for solving real-world problems. Coverage includes: An historical overview of electromagnetic concepts before Maxwell and how we define fundamental units and universal constants today A review of vector analysis and vector operations of scalar, vector, and tensor products Electrostatic fields and the interaction of those fields with dielectric materials and good conductors A method for solving electrostatic problems through the use of Poisson's and Laplace's equations and Green's function Electrical resistance and power dissipation; superconductivity from an experimental perspective; and the equation of continuity An introduction to magnetism from the experimental inverse square of the Biot-Savart law so that Maxwell's magnetic flux equations can be deduced Maxwell's Equations serves as an ideal textbook for undergraduate students in junior/senior electromagnetics courses and graduate students, as well as a resource for electrical engineers.
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8767.77 руб.
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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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8502.08 руб.
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Structural dynamics is a subset of structural analysis which covers the behavior of structures subjected to dynamic loading. The subject has seen rapid growth and also change in how the basic concepts can be interpreted. For instance, the classical notions of discretizing the operator of a dynamic structural model have given way to a set-theoretic, function-space based framework, which is more conducive to implementation with a computer. This modern perspective, as adopted in this book, is also helpful in putting together the various tools and ideas in a more integrated style. Elements of Structural Dynamics: A New Perspective is devoted to covering the basic concepts in linear structural dynamics, whilst emphasizing their mathematical moorings and the associated computational aspects that make their implementation in software possible. Key features: Employs a novel ‘top down’ approach to structural dynamics. Contains an insightful treatment of the computational aspects, including the finite element method, that translate into numerical solutions of the dynamic equations of motion. Consistently touches upon the modern mathematical basis for the theories and approximations involved. Elements of Structural Dynamics: A New Perspective is a holistic treatise on structural dynamics and is an ideal textbook for senior undergraduate and graduate students in Mechanical, Aerospace and Civil engineering departments. This book also forms a useful reference for researchers and engineers in industry.
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7701.69 руб.
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This book will provide insight into the principles and applications of nonlinear effects in fibers for students, researchers, and developers who have a basic understanding of electromagnetic theory under their belts. It will explore the physics, limitations, applications, and research results surrounding nonlinear effects in fiber optics. In addition to communications, optical fibers are already used in medical procedures, automobiles, and aircraft and are expected to have many other applications. This will expand the range of industry workers who will find a book of this type useful.
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11690.36 руб.
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Filling the gap for a book covering vibronic, nonadiabatic and diabatic couplings as well as radiationless processes in context, this monograph compiles classic and cutting-edge work from numerous researchers into one handy source. Alongside a description of radiationless processes in statistical large molecules and calculational methods for intramolecular distributions, the authors also investigate the nuclear coordinate dependence of matrix elements. Whole chapters are devoted to the mathematical description of the lifetime and decay of a prepared states as well as miscellaneous applications. The text is supplemented by a number of appendices for optimum usability. With its integration of the necessary mathematical rigor, this is primarily intended for graduate students in theoretical physics and chemistry, but is also indispensable reading for those working in molecular physics, physical chemistry and laser physics.
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10361.91 руб.
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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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10831.22 руб.
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This book is issued from a 30 years’ experience on the presentation of variational methods to successive generations of students and researchers in Engineering. It gives a comprehensive, pedagogical and engineer-oriented presentation of the foundations of variational methods and of their use in numerical problems of Engineering. Particular applications to linear and nonlinear systems of equations, differential equations, optimization and control are presented. MATLAB programs illustrate the implementation and make the book suitable as a textbook and for self-study. The evolution of knowledge, of the engineering studies and of the society in general has led to a change of focus from students and researchers. New generations of students and researchers do not have the same relations to mathematics as the previous ones. In the particular case of variational methods, the presentations used in the past are not adapted to the previous knowledge, the language and the centers of interest of the new generations. Since these methods remain a core knowledge – thus essential – in many fields (Physics, Engineering, Applied Mathematics, Economics, Image analysis …), a new presentation is necessary in order to address variational methods to the actual context.
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7705.01 руб.
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A new and unique way of understanding the translation of concepts and natural language into mathematical expressions Transforming a body of text into corresponding mathematical expressions and models is traditionally viewed and taught as a mathematical problem; it is also a task that most find difficult. The Language of Mathematics: Utilizing Math in Practice reveals a new way to view this process—not as a mathematical problem, but as a translation, or language, problem. By presenting the language of mathematics explicitly and systematically, this book helps readers to learn mathematics¿and improve their ability to apply mathematics more efficiently and effectively to practical problems in their own work. Using parts of speech to identify variables and functions in a mathematical model is a new approach, as is the insight that examining aspects of grammar is highly useful when formulating a corresponding mathematical model. This book identifies the basic elements of the language of mathematics, such as values, variables, and functions, while presenting the grammatical rules for combining them into expressions and other structures. The author describes and defines different notational forms for expressions, and also identifies the relationships between parts of speech and other grammatical elements in English and components of expressions in the language of mathematics. Extensive examples are used throughout that cover a wide range of real-world problems and feature diagrams and tables to facilitate understanding. The Language of Mathematics is a thought-provoking book of interest for readers who would like to learn more about the linguistic nature and aspects of mathematical notation. The book also serves as a valuable supplement for engineers, technicians, managers, and consultants who would like to improve their ability to apply mathematics effectively, systematically, and efficiently to practical problems.
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14878.64 руб.
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The present book introduces and develops mathematical techniques for the treatment of nonlinear waves and singular perturbation methods at a level that is suitable for graduate students, researchers and faculty throughout the natural sciences and engineering. The practice of implementing these techniques and their value are largely realized by showing their application to problems of nonlinear wave phenomena in electronic transport in solid state materials, especially bulk semiconductors and semiconductor superlattices. The authors are recognized leaders in this field, with more than 30 combined years of contributions.
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11690.36 руб.
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The building blocks of MEMS design through closed-form solutions Microelectromechanical Systems, or MEMS, is the technology of very small systems; it is found in everything from inkjet printers and cars to cell phones, digital cameras, and medical equipment. This book describes the principles of MEMS via a unified approach and closed-form solutions to micromechanical problems, which have been recently developed by the author and go beyond what is available in other texts. The closed-form solutions allow the reader to easily understand the linear and nonlinear behaviors of MEMS and their design applications. Beginning with an overview of MEMS, the opening chapter also presents dimensional analysis that provides basic dimensionless parameters existing in large- and small-scale worlds. The book then explains microfabrication, which presents knowledge on the common fabrication process to design realistic MEMS. From there, coverage includes: Statics/force and moment acting on mechanical structures in static equilibrium Static behaviors of structures consisting of mechanical elements Dynamic responses of the mechanical structures by the solving of linear as well as nonlinear governing equations Fluid flow in MEMS and the evaluation of damping force acting on the moving structures Basic equations of electromagnetics that govern the electrical behavior of MEMS Combining the MEMS building blocks to form actuators and sensors for a specific purpose All chapters from first to last use a unified approach in which equations in previous chapters are used in the derivations of closed-form solutions in later chapters. This helps readers to easily understand the problems to be solved and the derived solutions. In addition, theoretical models for the elements and systems in the later chapters are provided, and solutions for the static and dynamic responses are obtained in closed-forms. This book is designed for senior or graduate students in electrical and mechanical engineering, researchers in MEMS, and engineers from industry. It is ideal for radio frequency/electronics/sensor specialists who, for design purposes, would like to forego numerical nonlinear mechanical simulations. The closed-form solution approach will also appeal to device designers interested in performing large-scale parametric analysis.
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6838.2 руб.
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Modelling of Engineering Materials presents the background that is necessary to understand the mathematical models that govern the mechanical response of engineering materials. The book provides the basics of continuum mechanics and helps the reader to use them to understand the development of nonlinear material response of solids and fluids used in engineering applications. A brief review of simplistic and linear models used to characterize the mechanical response of materials is presented. This is followed by a description of models that characterize the nonlinear response of solids and fluids from first principles. Emphasis is given to popular models that characterize the nonlinear response of materials. The book also presents case studies of materials, where a comprehensive discussion of material characterization, experimental techniques and constitutive model development, is presented. Common principles that govern material response of both solids and fluids within a unified framework are outlined. Mechanical response in the presence of non-mechanical fields such as thermal and electrical fields applied to special materials such as shape memory materials and piezoelectric materials is also explained within the same framework.
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1329.38 руб.
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The fun and easy way to understand and solve complex equations Many of the fundamental laws of physics, chemistry, biology, and economics can be formulated as differential equations. This plain-English guide explores the many applications of this mathematical tool and shows how differential equations can help us understand the world around us. Differential Equations For Dummies is the perfect companion for a college differential equations course and is an ideal supplemental resource for other calculus classes as well as science and engineering courses. It offers step-by-step techniques, practical tips, numerous exercises, and clear, concise examples to help readers improve their differential equation-solving skills and boost their test scores.
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24772.27 руб.
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Systems biology is a relatively new biological study field that focuses on the systematic study of complex interactions in biological systems, thus using a new perspective (integration instead of reduction) to study them. Particularly from year 2000 onwards, the term is used widely in the biosciences, and in a variety of contexts. Systems biology is the study of the interconnected aspect of molecular, cellular, tissue, whole animal and ecological processes, and comprises mathematical and mechanistic studies of dynamical, mesoscopic, open, spatiotemporally defined, nonlinear, complex systems that are far from thermodynamic equilibrium.
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9896.95 руб.
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Groundbreaking, long-ranging research in this emergent field that enables solutions to complex biological problems Computational systems biology is an emerging discipline that is evolving quickly due to recent advances in biology such as genome sequencing, high-throughput technologies, and the recent development of sophisticated computational methodologies. Elements of Computational Systems Biology is a comprehensive reference covering the computational frameworks and techniques needed to help research scientists and professionals in computer science, biology, chemistry, pharmaceutical science, and physics solve complex biological problems. Written by leading experts in the field, this practical resource gives detailed descriptions of core subjects, including biological network modeling, analysis, and inference; presents a measured introduction to foundational topics like genomics; and describes state-of-the-art software tools for systems biology. Offers a coordinated integrated systems view of defining and applying computational and mathematical tools and methods to solving problems in systems biology Chapters provide a multidisciplinary approach and range from analysis, modeling, prediction, reasoning, inference, and exploration of biological systems to the implications of computational systems biology on drug design and medicine Helps reduce the gap between mathematics and biology by presenting chapters on mathematical models of biological systems Establishes solutions in computer science, biology, chemistry, and physics by presenting an in-depth description of computational methodologies for systems biology Elements of Computational Systems Biology is intended for academic/industry researchers and scientists in computer science, biology, mathematics, chemistry, physics, biotechnology, and pharmaceutical science. It is also accessible to undergraduate and graduate students in machine learning, data mining, bioinformatics, computational biology, and systems biology courses.
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4061.71 руб.
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Pick up any hydrology textbook and it will not be long before you encounter pages listing sequences of equations representing complex mathematical concepts. Students and practitioners of hydrology will not find this very helpful, as their aim, generally, is to study and understand hydrology, and not to find themselves confronted with material that even students of mathematics would find challenging. Often, equations appear to be copied and pasted into hydrological texts in an attempt to give a more rigorous scientific basis to the narrative. However, they are commonly wrong, poorly explained, without context or background, and more likely to confuse and distance the reader than to enlighten and engage them in the topic. Understanding Mathematical and Statistical Techniques in Hydrology provides full and detailed expositions of such equations and mathematical concepts, commonly used in hydrology. In contrast to other hydrological texts, instead of presenting abstract mathematical hydrology, the essential mathematics is explained with the help of real-world hydrological examples.
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11690.36 руб.
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A comprehensive and readily accessible work for studying the physics of ionized gases, based on «Physics of Ionized Gases». The focus remains on fundamentals rather than on the details required for interesting but difficult applications, such as magnetic confinement fusion, or the phenomena that occur with extremely high-intensity short-pulse lasers. However, this new work benefits from much rearranging of the subject matter within each topic, resulting in a more coherent structure. There are also some significant additions, many of which relate to clusters, while other enlarged sections include plasmas in the atmosphere and their applications. In each case, the emphasis is on a clear and unified understanding of the basic physics that underlies all plasma phenomena. Thus, there are chapters on plasma behavior from the viewpoint of atomic and molecular physics, as well as on the macroscopic phenomena involved in physical kinetics of plasmas and the transport of radiation and of charged particles within plasmas. With this grounding in the fundamental physics of plasmas, the notoriously difficult subjects of nonlinear phenomena and of instabilities in plasmas can then be treated with comprehensive clarity. The work is rounded off with appendices containing information and data of great importance and relevance that are not easily found in other books. Valuable reading for graduate and PhD physics students, and a reference for researchers in low-temperature ionized gases-plasma processing, edge region fusion plasma physics, and atmospheric plasmas.
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40 руб.
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The book offers a new approach to the calculation of economic processes. This approach allows to obtain very interesting data: – to define a generic mathematical description of the goods. In book gives a mathematical market model, it is shown that calculations of the parameters of the market can be carried out according to the formulas of the Queuing theory, in particular according to the formulas of erlang, Engset, etc; to define formulas that reflect the relationship between supply and demand
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11690.36 руб.
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This revised and enlarged second edition of the popular textbook and reference contains comprehensive treatments of both the established foundations of magnetic fusion plasma physics and of the newly developing areas of active research. It concludes with a look ahead to fusion power reactors of the future. The well-established topics of fusion plasma physics – basic plasma phenomena, Coulomb scattering, drifts of charged particles in magnetic and electric fields, plasma confinement by magnetic fields, kinetic and fluid collective plasma theories, plasma equilibria and flux surface geometry, plasma waves and instabilities, classical and neoclassical transport, plasma-materials interactions, radiation, etc. – are fully developed from first principles through to the computational models employed in modern plasma physics. The new and emerging topics of fusion plasma physics research – fluctuation-driven plasma transport and gyrokinetic/gyrofluid computational methodology, the physics of the divertor, neutral atom recycling and transport, impurity ion transport, the physics of the plasma edge (diffusive and non-diffusive transport, MARFEs, ELMs, the L-H transition, thermal-radiative instabilities, shear suppression of transport, velocity spin-up), etc. – are comprehensively developed and related to the experimental evidence. Operational limits on the performance of future fusion reactors are developed from plasma physics and engineering constraints, and conceptual designs of future fusion power reactors are discussed.
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1846.57 руб.
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Bringing the concepts of dimensional analysis, self-similarity, and fractal dimensions together in a logical and self-contained manner, this book reveals the close links between modern theoretical physics and applied mathematics. The author focuses on the classic applications of self-similar solutions within astrophysical systems, with some general theory of self-similar solutions, so as to provide a framework for researchers to apply the principles across all scientific disciplines. He discusses recent advances in theoretical techniques of scaling while presenting a uniform technique that encompasses these developments, as well as applications to almost any branch of quantitative science. The result is an invaluable reference for active scientists, featuring examples of dimensions and scaling in condensed matter physics, astrophysics, fluid mechanics, and general relativity, as well as in mathematics and engineering.
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320 руб.
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The book contains 80 different types of algebra equations together with explanations, answers and solutions. It helps a learner to understand the logic behind algebra equations and to build their self confidence. It is also a basic refresher for parents who are helping their children with math homework.
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12022.47 руб.
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The capability to predict the nonlinear response of beams, plates and shells when subjected to thermal and mechanical loads is of prime interest to structural analysis. In fact, many structures are subjected to high load levels that may result in nonlinear load-deflection relationships due to large deformations. One of the important problems deserving special attention is the study of their nonlinear response to large deflection, postbuckling and nonlinear vibration. A two-step perturbation method is firstly proposed by Shen and Zhang (1988) for postbuckling analysis of isotropic plates. This approach gives parametrical analytical expressions of the variables in the postbuckling range and has been generalized to other plate postbuckling situations. This approach is then successfully used in solving many nonlinear bending, postbuckling, and nonlinear vibration problems of composite laminated plates and shells, in particular for some difficult tasks, for example, shear deformable plates with four free edges resting on elastic foundations, contact postbuckling of laminated plates and shells, nonlinear vibration of anisotropic cylindrical shells. This approach may be found its more extensive applications in nonlinear analysis of nano-scale structures. Concentrates on three types of nonlinear analyses: vibration, bending and postbuckling Presents not only the theoretical aspect of the techniques, but also engineering applications of the method A Two-Step Perturbation Method in Nonlinear Analysis of Beams, Plates and Shells is an original and unique technique devoted entirely to solve geometrically nonlinear problems of beams, plates and shells. It is ideal for academics, researchers and postgraduates in mechanical engineering, civil engineering and aeronautical engineering.
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9960.05 руб.
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Teaches the fundamentals of mass transport with a unique approach emphasizing engineering principles in a biomedical environment Includes a basic review of physiology, chemical thermodynamics, chemical kinetics, mass transport, fluid mechanics and relevant mathematical methods Teaches engineering principles and mathematical modelling useful in the broad range of problems that students will encounter in their academic programs as well as later on in their careers Illustrates principles with examples taken from physiology and medicine or with design problems involving biomedical devices Stresses the simplification of problem formulations based on key geometric and functional features that permit practical analyses of biomedical applications Offers a web site of homework problems associated with each chapter and solutions available to instructors Homework problems related to each chapter are available from a supplementary website (
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1858.74 руб.
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The goal of this book is to teach undergraduate students how to use Scientific Notebook (SNB) to solve physics problems. SNB software combines word processing and mathematics in standard notation with the power of symbolic computation. As its name implies, SNB can be used as a notebook in which students set up a math or science problem, write and solve equations, and analyze and discuss their results. Written by a physics teacher with over 20 years experience, this text includes topics that have educational value, fit within the typical physics curriculum, and show the benefits of using SNB. This easy-to-read text: Provides step-by-step instructions for using Scientific Notebook (SNB) to solve physics problems Features examples in almost every section to enhance the reader's understanding of the relevant physics and to provide detailed instructions on using SNB Follows the traditional physics curriculum, so it can be used to supplement teaching at all levels of undergraduate physics Includes many problems taken from the author’s class notes and research Aimed at undergraduate physics and engineering students, this text teaches readers how to use SNB to solve some everyday physics problems.
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1858.74 руб.
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Written by a well-known author in the field, this book presents a modern understanding of the universe based on relativity, quantum physics and their elusive combination. It introduces the crucial theoretical ingredients in an accessible way, starting from the physics of Newton and developing subsequent theories all the way to the modern enigma of quantum gravity. The intermediate level presentation assumes only a general knowledge of math and physics, adopting a «two-level» approach: equations are retained throughout the chapters but set apart from the main text in boxes to allow for lay readers to understand the book. For scientists, researchers, students and lecturers in cosmology, astronomy, gravitation, quantum and theoretical physics; as well as mathematicians, students, lecturers, academics and non-experts in related fields with an interest in the subject.
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6572.51 руб.
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Thermal Physics of the Atmosphere offers a concise and thorough introduction on how basic thermodynamics naturally leads on to advanced topics in atmospheric physics. The book starts by covering the basics of thermodynamics and its applications in atmospheric science. The later chapters describe major applications, specific to more specialized areas of atmospheric physics, including vertical structure and stability, cloud formation, and radiative processes. The book concludes with a discussion of non-equilibrium thermodynamics as applied to the atmosphere. This book provides a thorough introduction and invaluable grounding for specialised literature on the subject. Introduces a wide range of areas associated with atmospheric physics Starts from basic level thermal physics Ideally suited for readers with a general physics background Self-assessment questions included for each chapter Supplementary website to accompany the book
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979 руб.
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The present book contains one hundred and sixty problems, most of them simple, in nonrelativistic quantum mechanics. Some of these problems were used previously by the authors in their courses at the Moscow Institute of Engineering and Physics. However, the majority were drawn up or selected in the course of work on the book. This book is designed for physics students who are studying quantum mechanics approximately at the level of D.I.Blokhintsev's book or Part II of "Theoretical Physics" by A.S.Kompaneyts. A number of problems is intended primarily for students who are beginning to specialize in theoretical physics and who are partially familiar with the contents of "Quantum Mechanics" by L.D.Landau and Ye.M.Lifshits. Some problems illustrate individual theoretical questions which have scarcely been considered in textbooks: sudden and adiabatic changes; Heisenberg representation of operators; probability relations in addition of momenta; isotopic spin; parity; and others. The authors have tried to use relatively elementary mathematical tools of quantum mechanics to facilitate use of the book by nontheoretical physicists. With a few exceptions, the authors have not included in this book problems which are considered in sufficient detail in the basic textbooks mentioned above and in the problem book on quantum mechanics written by V.G.Levich. Therefore, this book should be regarded chiefly as an auxiliary textbook in the study of the above books.
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10624.28 руб.
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This book deals with electromagnetic theory and its applications at the level of a senior-level undergraduate course for science and engineering. The basic concepts and mathematical analysis are clearly developed and the important applications are analyzed. Each chapter contains numerous problems ranging in difficulty from simple applications to challenging. The answers for the problems are given at the end of the book. Some chapters which open doors to more advanced topics, such as wave theory, special relativity, emission of radiation by charges and antennas, are included. The material of this book allows flexibility in the choice of the topics covered. Knowledge of basic calculus (vectors, differential equations and integration) and general physics is assumed. The required mathematical techniques are gradually introduced. After a detailed revision of time-independent phenomena in electrostatics and magnetism in vacuum, the electric and magnetic properties of matter are discussed. Induction, Maxwell equations and electromagnetic waves, their reflection, refraction, interference and diffraction are also studied in some detail. Four additional topics are introduced: guided waves, relativistic electrodynamics, particles in an electromagnetic field and emission of radiation. A useful appendix on mathematics, units and physical constants is included. Contents 1. Prologue. 2. Electrostatics in Vacuum. 3. Conductors and Currents. 4. Dielectrics. 5. Special Techniques and Approximation Methods. 6. Magnetic Field in Vacuum. 7. Magnetism in Matter. 8. Induction. 9. Maxwell’s Equations. 10. Electromagnetic Waves. 11. Reflection, Interference, Diffraction and Diffusion. 12. Guided Waves. 13. Special Relativity and Electrodynamics. 14. Motion of Charged Particles in an Electromagnetic Field. 15. Emission of Radiation.
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10959.71 руб.
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A readable little book assisting the student in understanding, in a nonmathematical way, the essentials of the different bonds occurring in chemistry. Starting with a short, self-contained,introduction, Chapter 1 presents the essential elements of the variation approach to either total or second-order molecular energies, the system of atomic units (au) necessary to simplify all mathematical expressions, and an introductory description of the electron distribution in molecules. Using mostly 2x2 Hückel secular equations, Chapter 2, by far the largest part of the book because of the many implications of the chemical bond, introduces a model of bonding in homonuclear and heteronuclear diatomics, multiple and delocalized bonds in hydrocarbons, and the stereochemistry of chemical bonds in polyatomic molecules, in a word, a model of the strong first-order interactions originating the chemical bond. In Chapter 3 the Hückel model of the linear polyene chain is used to explain the origin of band structure in the 1-dimensional crystal. Chapter 4 deals with a simple two-state model of weak interactions, introducing the reader to understand second-order electric properties of molecules and VdW bonding between closed shells. Lastly, Chapter 5 studies the structure of H-bonded dimers and the nature of the hydrogen bond, which has a strength intermediate between a VdW bond and a weak chemical bond. Besides a qualitative MO approach based on HOMO-LUMO charge transfer from an electron donor to an electron acceptor molecule, a quantitative electrostatic approach is presented yielding an electrostatic model working even at its simplest pictorial level. A list of alphabetically ordered references, author and subject indices complete the book.
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10627.6 руб.
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The first book to focus on the electromagnetic basis of signal integrity The Foundations of Signal Integrity is the first of its kind—a reference that examines the physical foundation of system integrity based on electromagnetic theory derived from Maxwell's Equations. Drawing upon the cutting-edge research of Professor Paul Huray's team of industrial engineers and graduate students, it develops the physical theory of wave propagation using methods of solid state and high-energy physics, mathematics, chemistry, and electrical engineering before addressing its application to modern high-speed systems. Coverage includes: All the necessary electromagnetic theory needed for a complete understanding of signal integrity Techniques for obtaining analytic solutions to Maxwell's Equations for ideal materials and boundary conditions Plane electromagnetic waves Plane waves in compound media Transmission lines and waveguides Ideal models vs. real-world systems Complex permittivity of propagating media Surface roughness Advanced signal integrity Signal integrity simulations Problem sets for each chapter With its thorough coverage of this relatively new discipline, the book serves as an ideal textbook for senior undergraduate and junior graduate students, as well as a resource for practicing engineers in this burgeoning field. At the end of each section, it typically stimulates the reader with open-ended questions that might lead to future theses or dissertation research.
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13085.23 руб.
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Filling the gap for a treatment of the subject as an advanced course in theoretical physics with a huge potential for future applications, this monograph discusses aspects of these applications and provides theoretical methods and tools for their investigation. Throughout this coherent and up-to-date work the main emphasis is on classical plasmas at high-temperatures, drawing on the experienced author's specialist background. As such, it covers the key areas of magnetic fusion plasma, laser-plasma-interaction and astrophysical plasmas, while also including nonlinear waves and phenomena. For master and PhD students as well as researchers interested in the theoretical foundations of plasma models.
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10295.49 руб.
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Mechanics and Physics of Porous Solids addresses the mechanics and physics of deformable porous materials whose porous space is filled by one or several fluid mixtures interacting with the solid matrix. Coussy uses the language of thermodynamics to frame the discussion of this topic and bridge the gap between physicists and engineers, and organises the material in such a way that individual phases are explored, followed by coupled problems of increasing complexity. This structure allows the reader to build a solid understanding of the physical processes occurring in the fluids and then porous solids. Mechanics and Physics of Porous Solids offers a critical reference on the physics of multiphase porous materials – key reading for engineers and researchers in structural and material engineering, concrete, wood and materials science, rock and soil mechanics, mining and oil prospecting, biomechanics.
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619 руб.
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How do you apply game theory to select who should be on your Christmas shopping list? Can you predict Her Majesty's Christmas Message? Will calculations show Santa is getting steadily thinner - shimmying up and down chimneys for a whole night - or fatter - as he tucks into a mince pie and a glass of sherry in billions of houses across the world?Full of diagrams, sketches and graphs, beautiful equations, Markov chains and matrices, The Indisputable Existence of Santa Claus brightens up the bleak midwinter with stockingfuls of mathematical marvels. And proves once and for all that maths isn't just for old men with white hair and beards who associate with elves.Maths has never been merrier.
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7701.69 руб.
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Mathematical Methods for Physical and Analytical Chemistry presents mathematical and statistical methods to students of chemistry at the intermediate, post-calculus level. The content includes a review of general calculus; a review of numerical techniques often omitted from calculus courses, such as cubic splines and Newton’s method; a detailed treatment of statistical methods for experimental data analysis; complex numbers; extrapolation; linear algebra; and differential equations. With numerous example problems and helpful anecdotes, this text gives chemistry students the mathematical knowledge they need to understand the analytical and physical chemistry professional literature.
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2744 руб.
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This book contributes substantively to the current state of art of macroeconomic modeling by providing a method for modeling large collections of possibly heterogeneous agents subject to nonpairwise externality called field effects, that is, feedback of aggregate effects on individual agents or agents using state-dependent strategies. By adopting a level of microeconomic description that keeps track of compositions of fractions of agents by types or strategies, time evolution of the microeconomic states is described by (backward) Chapman-Kolmogorov equations. Macroeconomic dynamics naturally arise from these equations by expansion of the solutions in some power series of the number of participants. Specification of the microeconomic transition rates thus leads to macroeconomic dynamic models. This approach provides a consistent way for dealing with multiple equilibria of macroeconomic dynamics by ergodic decomposition and associated calculations of mean first passage times, and stationary probabilities of equilibria provide further useful information on macroeconomic behavior. This book ends with a set of elaborations, sketches of further topics of research, and a collection of supporting materials in the Appendix.
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11690.36 руб.
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This self-contained introduction discusses the evolution of the notion of coherent states, from the early works of Schrodinger to the most recent advances, including signal analysis. An integrated and modern approach to the utility of coherent states in many different branches of physics, it strikes a balance between mathematical and physical descriptions. Split into two parts, the first introduces readers to the most familiar coherent states, their origin, their construction, and their application and relevance to various selected domains of physics. Part II, mostly based on recent original results, is devoted to the question of quantization of various sets through coherent states, and shows the link to procedures in signal analysis.
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1895.31 руб.
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Emanuel Derman was a quantitative analyst (Quant) at Goldman Sachs, one of the financial engineers whose mathematical models became crucial for Wall Street. The reliance investors put on such quantitative analysis was catastrophic for the economy, setting off the ongoing string of financial crises that began with the mortgage market in 2007 and continues through today. Here Derman looks at why people – bankers in particular – still put so much faith in these models, and why it's a terrible mistake to do so. Though financial models imitate the style of physics and employ the language of mathematics, ultimately they deal with human beings. There is a fundamental difference between the aims and potential achievements of physics and those of finance. In physics, theories aim for a description of reality; in finance, at best, models can shoot only for a simplistic and very limited approximation to it. When we make a model involving human beings, we are trying to force the ugly stepsister's foot into Cinderella's pretty glass slipper. It doesn't fit without cutting off some of the essential parts. Physicists and economists have been too enthusiastic to acknowledge the limits of their equations in the sphere of human behavior–which of course is what economics is all about. Models.Behaving.Badly includes a personal account of Derman's childhood encounters with failed models–the oppressions of apartheid and the utopia of the kibbutz. He describes his experience as a physicist on Wall Street, the models quants generated, the benefits they brought and the problems, practical and ethical, they caused. Derman takes a close look at what a model is, and then highlights the differences between the successes of modeling in physics and its failures in economics. Describing the collapse of the subprime mortgage CDO market in 2007, Derman urges us to stop the naïve reliance on these models, and offers suggestions for mending them. This is a fascinating, lyrical, and very human look behind the curtain at the intersection between mathematics and human nature.
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11291.83 руб.
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This textbook brings together the fundamentals of the macroscopic and microscopic aspects of thermal physics by presenting thermodynamics and statistical mechanics as complementary theories based on small numbers of postulates. The book is designed to give the instructor flexibility in structuring courses for advanced undergraduates and/or beginning graduate students and is written on the principle that a good text should also be a good reference. The presentation of thermodynamics follows the logic of Clausius and Kelvin while relating the concepts involved to familiar phenomena and the modern student's knowledge of the atomic nature of matter. Another unique aspect of the book is the treatment of the mathematics involved. The essential mathematical concepts are briefly reviewed before using them, and the similarity of the mathematics to that employed in other fields of physics is emphasized. The text gives in depth treatments of low density gases, harmonic solids, magnetic and dielectric materials, phase transitions, and the concept of entropy. The microcanonical, canonical, and grand canonical ensembles of statistical mechanics are derived and used as the starting point for the analysis of fluctuations, blackbody radiation, the Maxwell distribution, Fermi-Dirac statistics, Bose-Einstein condensation, and the statistical basis of computer simulations. Supplementary material including PowerPoint slides and detailed worked solutions can be downloaded online at http://booksupport.wiley.com
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1329.38 руб.
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Hands-on practice in solving quantum physics problems Quantum Physics is the study of the behavior of matter and energy at the molecular, atomic, nuclear, and even smaller microscopic levels. Like the other titles in our For Dummies Workbook series, Quantum Physics Workbook For Dummies allows you to hone your skills at solving the difficult and often confusing equations you encounter in this subject. Explains equations in easy-to-understand terms Harmonic Oscillator Operations, Angular Momentum, Spin, Scattering Theory Using a proven practice-and-review approach, Quantum Physics Workbook For Dummies is all you need to get up to speed in problem solving!
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9299.15 руб.
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Now updated—the leading single-volume introduction to solid state and soft condensed matter physics This Second Edition of the unified treatment of condensed matter physics keeps the best of the first, providing a basic foundation in the subject while addressing many recent discoveries. Comprehensive and authoritative, it consolidates the critical advances of the past fifty years, bringing together an exciting collection of new and classic topics, dozens of new figures, and new experimental data. This updated edition offers a thorough treatment of such basic topics as band theory, transport theory, and semiconductor physics, as well as more modern areas such as quasicrystals, dynamics of phase separation, granular materials, quantum dots, Berry phases, the quantum Hall effect, and Luttinger liquids. In addition to careful study of electron dynamics, electronics, and superconductivity, there is much material drawn from soft matter physics, including liquid crystals, polymers, and fluid dynamics. Provides frequent comparison of theory and experiment, both when they agree and when problems are still unsolved Incorporates many new images from experiments Provides end-of-chapter problems including computational exercises Includes more than fifty data tables and a detailed forty-page index Offers a solutions manual for instructors Featuring 370 figures and more than 1,000 recent and historically significant references, this volume serves as a valuable resource for graduate and undergraduate students in physics, physics professionals, engineers, applied mathematicians, materials scientists, and researchers in other fields who want to learn about the quantum and atomic underpinnings of materials science from a modern point of view.
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79.9 руб.
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In this paper, we examine nonlinear interrelationship between energy consumption and output level for a panel of G7 countries. For this purpose, we propose a nonlinear cointegration test in heterogeneous panels for testing the presence of a cointegrating relationship that follows a globally stationary exponential smooth transition (ESTR) process, and apply our test for investigating long-run relationship between energy use and economic growth in the case of the G7 countries. Our results suggest the presence of a long-run relationship between these two variables whereas adjustment to the equilibrium is inherently nonlinear. After establishing long-run relationship between energy consumption and output, we estimate a Panel Smooth Transition Vector Error Correction Model and apply nonlinear Granger causality tests in order to analyze the direction of the causality between these variables. We find that the causality between energy consumption and output level is dependent on the phases of business cycle. Our results highlight importance of taking account of possible nonlinearities in analysing output-energy causality nexus and designing energy policies.
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1528.89 руб.
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The easy way to shed light on Optics In general terms, optics is the science of light. More specifically, optics is a branch of physics that describes the behavior and properties of light?including visible, infrared, and ultraviolet?and the interaction of light with matter. Optics For Dummies gives you an approachable introduction to optical science, methods, and applications. You'll get plain-English explanations of the nature of light and optical effects; reflection, refraction, and diffraction; color dispersion; optical devices, industrial, medical, and military applications; as well as laser light fundamentals. Tracks a typical undergraduate optics course Detailed explanations of concepts and summaries of equations Valuable tips for study from college professors If you're taking an optics course for your major in physics or engineering, let Optics For Dummies shed light on the subject and help you succeed!
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902 руб.
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The Solutions Second Edition Workbook and Audio CD Pack supports the Student's Book content with plenty of extra practice and revision, while the CD provides a huge number of extra listening opportunities. A new, refreshed edition of the five-level English course for teenagers, with a clear structure, supported approach to speaking, practice, and exam preparation still at its heart. Solutions has been thoroughly modernized with 80% new content to draw in students, embed the grammar and vocabulary presented, and engage them in the tasks. Its guided approach builds up every student's confidence, through step-by-step objectives, lots of practice, meaningful personalization activities, and exam preparation tasks. The course now embraces a wide range of teaching methods, furnishing the teacher with a flexible pick-and-choose package for use in the classroom, at home, and on the move. The digital elements of the course enliven the material and allow teachers to vary the pace and focus of their lessons. Solutions turns all students into active learners, by offering a rich variety of learning opportunities for a whole range of abilities through extension and revision activities in all components - giving everyone a sense of achievement whatever their level. The Solutions Second Edition DVD-ROM material and worksheets bring the language to life by taking it out of the classroom and into authentic settings. Praise for the Second Edition «This book is an excellent introduction to the wide field of boundary value problems.»—Journal of Engineering Mathematics «No doubt this textbook will be useful for both students and research workers.»—Mathematical Reviews A new edition of the highly-acclaimed guide to boundary value problems, now featuring modern computational methods and approximation theory Green's Functions and Boundary Value Problems, Third Edition continues the tradition of the two prior editions by providing mathematical techniques for the use of differential and integral equations to tackle important problems in applied mathematics, the physical sciences, and engineering. This new edition presents mathematical concepts and quantitative tools that are essential for effective use of modern computational methods that play a key role in the practical solution of boundary value problems. With a careful blend of theory and applications, the authors successfully bridge the gap between real analysis, functional analysis, nonlinear analysis, nonlinear partial differential equations, integral equations, approximation theory, and numerical analysis to provide a comprehensive foundation for understanding and analyzing core mathematical and computational modeling problems. Thoroughly updated and revised to reflect recent developments, the book includes an extensive new chapter on the modern tools of computational mathematics for boundary value problems. The Third Edition features numerous new topics, including: Nonlinear analysis tools for Banach spaces Finite element and related discretizations Best and near-best approximation in Banach spaces Iterative methods for discretized equations Overview of Sobolev and Besov space linear Methods for nonlinear equations Applications to nonlinear elliptic equations In addition, various topics have been substantially expanded, and new material on weak derivatives and Sobolev spaces, the Hahn-Banach theorem, reflexive Banach spaces, the Banach Schauder and Banach-Steinhaus theorems, and the Lax-Milgram theorem has been incorporated into the book. New and revised exercises found throughout allow readers to develop their own problem-solving skills, and the updated bibliographies in each chapter provide an extensive resource for new and emerging research and applications. With its careful balance of mathematics and meaningful applications, Green's Functions and Boundary Value Problems, Third Edition is an excellent book for courses on applied analysis and boundary value problems in partial differential equations at the graduate level. It is also a valuable reference for mathematicians, physicists, engineers, and scientists who use applied mathematics in their everyday work.