Classical mechanics Books

Book SynopsisBook Contents.- 1 Overview.- 2 Linear Structural Analysis.- 3 Exact Analysis of Trusses.- 4 Nonlinear Analysis of Plane Frames.- 5 Nonlinear Analysis of Space Frames.- 6 Nonlinear Analysis of Membranes.- 7 Cablenets and Fabric Structures.- 8 Three-Dimensional Beam-Columns.- 9 Nonlinear Analysis of Shells.- References.- Appendix 1 Member Stiffness When Beam-Column Effects are Included.- Appendix 2 Determinants.- Appendix 3 The Rotation Matrix.- Appendix 4 Perturbation Methods Applied to Plane Beams.- Appendix 5 Introduction to Computer Programs.- A5.1 Introduction.- A5.2 Space Trusses.- A5.3 Plane Frames.- A5.4 Listing for TR3D.FOR.- A5.5 Listing for FR2D.FOR.- Appendix 6 Graphics on a PC.- A6.1 Introduction.- A6.2 Plotting in 2-D.- A6.3 Drawing Lines in 2-D.Table of ContentsBook Contents.- 1 Overview.- 2 Linear Structural Analysis.- 3 “Exact” Analysis of Trusses.- 4 Nonlinear Analysis of Plane Frames.- 5 Nonlinear Analysis of Space Frames.- 6 Nonlinear Analysis of Membranes.- 7 Cablenets and Fabric Structures.- 8 Three-Dimensional Beam-Columns.- 9 Nonlinear Analysis of Shells.- References.- Appendix 1 Member Stiffness When Beam-Column Effects are Included.- Appendix 2 Determinants.- Appendix 3 The Rotation Matrix.- Appendix 4 Perturbation Methods Applied to Plane Beams.- Appendix 5 Introduction to Computer Programs.- A5.1 Introduction.- A5.2 Space Trusses.- A5.3 Plane Frames.- A5.4 Listing for TR3D.FOR.- A5.5 Listing for FR2D.FOR.- Appendix 6 Graphics on a PC.- A6.1 Introduction.- A6.2 Plotting in 2-D.- A6.3 Drawing Lines in 2-D.

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Book Synopsisto Turbulence in Fluid Mechanics.- Basic Fluid Dynamics.- Transition to Turbulence.- Shear Flow Turbulence.- Fourier Analysis of Homogeneous Turbulence.- Isotropic Turbulence: Phenomenology and Simulations.- Analytical Theories and Stochastic Models.- Two-Dimensional Turbulence.- Beyond Two-Dimensional Turbulence in GFD.- Statistical Thermodynamics of Turbulence.- Statistical Predictability Theory.- Large-Eddy Simulations.- Towards Real World Turbulence.Trade ReviewFrom the reviews of the fourth edition: "Turbulence in Fluids contains a wealth of information, and its author is a top-tier scientist. … The book is logically ordered and contains a comprehensive list of 738 references. … Lesieur’s monograph is recommended for those who already know quite a bit about turbulence, for the theoretically inclined, and in particular for those interested in homogeneous turbulence and geophysical flows and their numerical simulation." (Mohamed Gad-El-Hak, Siam Review, Vol. 51 (1), 2009)Table of Contentsto Turbulence in Fluid Mechanics.- Basic Fluid Dynamics.- Transition to Turbulence.- Shear Flow Turbulence.- Fourier Analysis of Homogeneous Turbulence.- Isotropic Turbulence: Phenomenology and Simulations.- Analytical Theories and Stochastic Models.- Two-Dimensional Turbulence.- Beyond Two-Dimensional Turbulence in GFD.- Statistical Thermodynamics of Turbulence.- Statistical Predictability Theory.- Large-Eddy Simulations.- Towards “Real World Turbulence”.

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Book SynopsisThe Compendium of Theoretical Physics contains the canonical curriculum of theoretical physics. From classical mechanics over electrodynamics, quantum mechanics and statistical physics/thermodynamics, all topics are treated axiomatic-deductively and confimed by exercises, solutions and short summaries.Table of ContentsPreface.- List of Applications.- 1.Mechanics: Newtonian Mechanics.- Lagrangian Mechanics.- Hamiltonian Mechanics.- Motion of Rigid Bodies.- Central Forces.- Relativistic Mechanics.- 2. Electrodynamics: Formalism of Electrodynamics.- Solutions of Maxwell’s Equations in the Form of Potentials.- Lorentz Covariant Formulation of Electrodynamics.- Radiation Theory.- Time-Independent Electrodynamics.- Electrodynamics in Matter.- Electromagnetic Waves.- Lagrange Formalism in Electrodynamics.- 3. Quantum Mechanics: Mathematical Foundations of Quantum Mechanics.- Formulation of Quantum Theory.- One-Dimensional Systems.- Quantum Mechanical Angular Momenta.- Schrödinger Equation in Three Dimensions.- Electromagnetic Interactions.- Perturbation Theory and Real Hydrogen Atom.- Atomic Transitions.- N-Particle Systems.- Scattering Theory.- 4. Statistical Physics and Thermodynamics: Foundations of Statistical Physics.- Ensemble Theory I: Microcanonical Ensemble and Entropy.- Ensemble Theory II: Canonical and Grand Canonical Ensemble.- Entropy and Information Theory.- Thermodynamics.- Classical Maxwell-Boltzmann Statistics.- Quantum Statistics.- Appendix A: Mathematical Appendix.- Appendix B: Literature List.- Index

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Book SynopsisFeaturing chapters on physics, structure, sound and design specifics, Technology of the Guitar also includes coverage of historical content, composition of strings and their effects on sound quality, and important designs.Table of Contents1. Guitar Overview.- 2. Basic Physics.- 3. The Structure of the Guitar.- 4. Electronics.- 5. Sound Quality.- 6. Design Specifics for Acoustic Guitars.- 7. Design Specifics for Electric Guitars.- 8. Hardware.- 9. Iconic Guitars.

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Book SynopsisFirst published in 1987, this text offers concise but clear explanations and derivations to give readers a confident grasp of the chain of argument that leads from Newton’s laws through Lagrange’s equations and Hamilton’s principle, to Hamilton’s equations and canonical transformations. This new edition has been extensively revised and updated to include: A chapter on symplectic geometry and the geometric interpretation of some of the coordinate calculations. A more systematic treatment of the conections with the phase-plane analysis of ODEs; and an improved treatment of Euler angles. A greater emphasis on the links to special relativity and quantum theory showing how ideas from this classical subject link into contemporary areas of mathematics and theoretical physics. A wealth of examples show the subject in action and a range of exercises – with solutions – are provided to help test understanding. Trade ReviewFrom the reviews of the second edition:“It is designed to teach analytical mechanics to second and third year undergraduates in the UK, and probably to third or fourth year undergraduates in the US. … This book offers a very attractive traditional introduction to the subject. … the author is well tuned to the difficulties even strong students encounter. … discusses the relevance of classical mechanics in modern physics, especially to relativity and quantum mechanics. This is a fine textbook. It would be a pleasure to teach or to learn from it.” (William J. Satzer, The Mathematical Association of America, March, 2010)Table of ContentsFrames of Reference.- One Degree of Freedom.- Lagrangian Mechanics.- Noether#x2019;s Theorem.- Rigid Bodies.- Oscillations.- Hamiltonian Mechanics.- Geometry of Classical Mechanics.- Epilogue: Relativity and Quantum Theory.

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Book SynopsisThis open access book, published in the Soft and Biological Matter series, presents an introduction to selected research topics in the broad field of flowing matter, including the dynamics of fluids with a complex internal structure -from nematic fluids to soft glasses- as well as active matter and turbulent phenomena. Flowing matter is a subject at the crossroads between physics, mathematics, chemistry, engineering, biology and earth sciences, and relies on a multidisciplinary approach to describe the emergence of the macroscopic behaviours in a system from the coordinated dynamics of its microscopic constituents. Depending on the microscopic interactions, an assembly of molecules or of mesoscopic particles can flow like a simple Newtonian fluid, deform elastically like a solid or behave in a complex manner. When the internal constituents are active, as for biological entities, one generally observes complex large-scale collective motions. Phenomenology is further complicated by the invariable tendency of fluids to display chaos at the large scales or when stirred strongly enough. This volume presents several research topics that address these phenomena encompassing the traditional micro-, meso-, and macro-scales descriptions, and contributes to our understanding of the fundamentals of flowing matter. This book is the legacy of the COST Action MP1305 “Flowing Matter”.Table of Contents1 Basic concepts of Stokes flows with particles; C. I. Trombley and M. L. Ekiel-Je˙zewska 2 Numerical approaches to complex fluids; Francesco Picano and Luca Brandt 3 Active fluids within the unified colored noise approximation; Umberto Marini Bettolo Marconi, Claudio Maggi and Alessandro Sarracino 4 Upscaling Flow and Transport Processes; M. Icardi 5 Quadrature-based lattice Boltzmann models for rarefied gas flow; Victor E. Ambrus and Victor Sofonea 6 Some recent developments in particle tracking diagnosis in Turbulence research; Mickael Bourgoin 7 Mesoscopic approach to nematic fluids; Miha Ravnik 8 Correlations and nonequilibrium transitions in flowing colloidal glasses; Peter Schall 9 The Finite Volume Approach to Lattice Boltzmann equation; Kalyan Shrestha and Enrico Calzavarini 10 Diffusion, Attachment and Self-Assembly of Janus Particles at Liquid-Liquid and Air-Liquid Interfaces; Andrei Honciuc

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Book SynopsisThis book unies the common tensor analytical aspects in engineering and physics. Using tensor analysis enables the reader to understand complex physical phenomena from the basic principles in continuum mechanics including the turbulence, its correlations and modeling to the complex Einstein' tensor equation. The development of General Theory of Relativity and the introduction of spacetime geometry would not have been possible without the use of tensor analysis. This textbook is primarily aimed at students of mechanical, electrical, aerospace, civil and other engineering disciplines as well as of theoretical physics. It also covers the special needs of practicing professionals who perform CFD-simulation on a routine basis and would like to know more about the underlying physics of the commercial codes they use. Furthermore, it is suitable for self-study, provided that the reader has a sufficient knowledge of differential and integral calculus. Particular attention was paid to selecting the application examples. The transformation of Cartesian coordinate system into curvilinear one and the subsequent applications to conservation laws of continuum mechanics and the turbulence physics prepares the reader for fully understanding the Einstein tensor equations, which exhibits one of the most complex tensor equation in theoretical physics.Table of ContentsVectors and Tensors.- Transformation of Tensors.- Differential Operators in Continuum Mechanics.- Tensors and Kinematics.- Differential Balances in Continuum Mechanics.- Tensor Operations in Orthogonal Curvilinear.- Tensor Application, Navier-Stokes Equation.- Curves, Curvature, Surfaces, Geodesics.- Turbulent Flow, Modeling.- Special Theory of Relativity.- Tensors In General Theory of Relativity.

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Book SynopsisThis exceptionally well-organized book uses solved problems and exercises to help readers understand the underlying concepts of classical mechanics; accordingly, many of the exercises included are of a conceptual rather than practical nature. A minimum of necessary background theory is presented, before readers are asked to solve the theoretical exercises. In this way, readers are effectively invited to discover concepts on their own. While more practical exercises are also included, they are always designed to introduce readers to something conceptually new. Special emphasis is placed on important but often-neglected concepts such as symmetries and invariance, especially when introducing vector analysis in Cartesian and curvilinear coordinates. More difficult concepts, including non-inertial reference frames, rigid body motion, variable mass systems, basic tensorial algebra, and calculus, are covered in detail. The equations of motion in non-inertial reference systems are derived in two independent ways, and alternative deductions of the equations of motion for variable mass problems are presented. Lagrangian and Hamiltonian formulations of mechanics are studied for non-relativistic cases, and further concepts such as inertial reference frames and the equivalence principle are introduced and elaborated on.Table of ContentsVector Analysis in Cartesian Coordinates.- Vector Analysis in Curvilinear Coordinates.- Kinematics.- Newton's Laws, Dynamics and Galilean Relativity.- Systems of Particles and Variable Mass.- One-Dimensional Potentials and Two-Dimensional Central Potentials.- Non Relativistic Collisions.- Continuous Mass Distributions. Gravitational Potential and Field.- Non-Inertial Reference Systems.- Rigid Body Dynamics.- Special Theory of Relativity.- Relativistic Collisions and Decays.- Non-Relativistic Lagrangian and Hamiltonian Mechanics.

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Book SynopsisThis book is intended to serve as a basic introduction to scientific computing by treating problems from various areas of physics - mechanics, optics, acoustics, and statistical reasoning in the context of the evaluation of measurements. After working through these examples, students are able to independently work on physical problems that they encounter during their studies. For every exercise, the author introduces the physical problem together with a data structure that serves as an interface to programming in Excel and Python. When a solution is achieved in one application, it can easily be translated into the other one and presumably any other platform for scientific computing. This is possible because the basic techniques of vector and matrix calculation and array broadcasting are also achieved with spreadsheet techniques, and logical queries and for-loops operate on spreadsheets from simple Visual Basic macros. So, starting to learn scientific calculation with Excel, e.g., at High School, is a targeted road to scientific computing. The primary target groups of this book are students with a major or minor subject in physics, who have interest in computational techniques and at the same time want to deepen their knowledge of physics. Math, physics and computer science teachers and Teacher Education students will also find a companion in this book to help them integrate computer techniques into their lessons. Even professional physicists who want to venture into Scientific Computing may appreciate this book.Table of Contents

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Book SynopsisThis textbook provides details of the derivation of Lagrange's planetary equations and of the closely related Gauss's variational equations, thereby covering a sorely needed topic in existing literature. Analytical solutions can help verify the results of numerical work, giving one confidence that his or her analysis is correct. The authors—all experienced experts in astrodynamics and space missions—take on the massive derivation problem step by step in order to help readers identify and understand possible analytical solutions in their own endeavors. The stages are elementary yet rigorous; suggested student research project topics are provided.After deriving the variational equations, the authors apply them to many interesting problems, including the Earth-Moon system, the effect of an oblate planet, the perturbation of Mercury's orbit due to General Relativity, and the perturbation due to atmospheric drag. Along the way, they introduce several useful techniques such as averaging, Poincaré's method of small parameters, and variation of parameters. In the end, this textbook will help students, practicing engineers, and professionals across the fields of astrodynamics, astronomy, dynamics, physics, planetary science, spacecraft missions, and others. “An extensive, detailed, yet still easy-to-follow presentation of the field of orbital perturbations.” - Prof. Hanspeter Schaub, Smead Aerospace Engineering Sciences Department, University of Colorado, Boulder “This book, based on decades of teaching experience, is an invaluable resource for aerospace engineering students and practitioners alike who need an in-depth understanding of the equations they use.” - Dr. Jean Albert Kéchichian, The Aerospace Corporation, Retired “Today we look at perturbations through the lens of the modern computer. But knowing the why and the how is equally important. In this well organized and thorough compendium of equations and derivations, the authors bring some of the relevant gems from the past back into the contemporary literature.” - Dr. David A Vallado, Senior Research Astrodynamicist, COMSPOC “The book presentation is with the thoroughness that one always sees with these authors. Their theoretical development is followed with a set of Earth orbiting and Solar System examples demonstrating the application of Lagrange’s planetary equations for systems with both conservative and nonconservative forces, some of which are not seen in orbital mechanics books.” - Prof. Kyle T. Alfriend, University Distinguished Professor, Texas A&M UniversityTable of Contents1 The n-Body Problem2 General Perturbations 3 Evaluation of Lagrange’s Brackets 4 Lagrange’s Planetary Equations 5 Expansion of the Perturbation Function 6 The Earth-Moon System 7 Potential of an Oblate Spheroid8 Effects of General Relativity9 Perturbations due to Atmospheric Drag 10 Periodic Solutions in Nonlinear OscillationsBibliography Projects

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Book SynopsisRubber based Bionanocomposites.- Cellulose based rubber nanocomposites.- Cellulose in rubber based blends and micro composites.- Chitin based rubber nanocomposites.- Chitin in rubber based blends and micro composites.- Starch based rubber nanocomposites.- Starch in rubber based blends and micro composites.- Soy Protein based Rubber composites and nanocomposites.- PLA based rubber composites and nanocomposites.- Bacterial Cellulose (BC)/ rubber composites and rubber nanocomposites.- Casein based rubber composites and nanocomposites.- Hemi Cellulose rubber composites and rubber nanocomposites.- PHA based rubber composites and nanocomposites.

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Book SynopsisSurface Electro Elastic Shear Waves in Piezo Electrical Half-Space with Semi Infinite Electrode.- Finite Amplitude Surface Waves in a Linear Electroacoustic (Piezoelectric) Waveguide.- Uniform Asymptotic Expansion for Gegenbauer Polynomials: New Approach.- Asymmetric Buckling of Circular and Annular Plates under Normal Pressure.- Comparison of Hyperelastic Corneal Models for Assessing Eye Deformations After MyoRing Implantation.- Mechanical Effect of Plastic Flow Instabilities at High Strain Rates.- On Possible Chirality and Black Holes of Acoustic Waves in Functionally Graded Rods.- The Effect of the Boundary Conditions on Free Vibrations of a String Resting on a Winkler Foundation.- On Dispersion Relations Within 1D Nonlocal Elasticity.- Analytically-Based Simulation of Guided Wave Scattering by Rectangular Delamination in an Anisotropic Composite Plate.- Bending Waves in Beams Lying on Generalized Deformable Foundations: Elastic, Viscoelastic and Nonlinear-Elastic Ones.- Effect of Curvature on Natural Frequencies of a Cylindrical Shell Closed with the Cap.- Large Torsional Deformations of a Cylindrical Tube Containing Screw Dislocations Under Internal Pressure.- Operator Algebra in Linear Viscoelasticity: Experimental Aspects.- On Flexural Oscillations of Pre-Stressed Circular Beams of Variable Radius Taking into Account Transverse Effects.- Surface Shear Horizontally Wave Propagation in a Half-Space Periodically Stratified with Interfaces of Imperfect Elastic Contact.- Dynamics of a Vortex in a Regulable Rectangular Channel.- On the Plane Contact Problem of a Punch with a Previously Unknown Contact Area in the Presence of Static Friction.- Magneto Electric Coefficients of Thermo-Magneto-Electro ElasticMultilayer Composites: Effective Properties for Nonperfect Connectivity Between Layers.- Diffraction of a Plane Shear Wave by Semi-Infinite Parallel Cracks in a Piezoelectric Space and Propagation of Surface Waves.- Influence of the Moisture Desorption Process on the Modulus of Elasticity and Strength of Lightweight Cement Concrete and Cement Soil Composite.- An Asymptotic Model for the Nonstationary Waves in the Shells of Revolution Initiated by the Longitudinal, Tangential Type Edge Shock Loading.- Modeling of Convective Flows in a Porous Circular Enclosure.- Effect of Nanosized Surface Roughness in Solids with the Account of Steigmann Ogden Mode.- Eigenvalues of a Lightly Loaded Lubricated Oscillating Contact.- Microstructure and Micro and Nano-Properties of Al-Cr-B-N Coatings.- On Model of Coupled Thermomechanics and Electrodynamics.- Numerical Analysis of Novel Composite Sandwich Panels with 3D Printed Cellular Core Under High Velocity Impact.- Investigation of the Effect of Magnetostriction in a Rectangular Dielectric Plate Under the Longitudinal Magnetic Field.- Investigation of the Effect of Magnetostriction in a Rectangular Dielectric Plate Under the Longitudinal Magnetic Field.- Discrimination of Propagating Weak Discontinuities Surfaces in Semi-Isotropic Micropolar Thermoelastic Media.- Three Dimensional Stream Functions and Monogenic Flow Potentials.- Detachment of the Elastic Half Plane from the Punch Attached to it.- The Problem of Interaction of Longitudinal Shear Waves with thin Defects in the Shape of a Broken Line.- Polarization Crosses of Transverse Plane Waves in Micropolar Elastic Media.- Mechanical Quadratures for Solution of the Problem of Torsion of an Inhomogeneous Ageing Viscoelastic Layer by a Round Rigid Washer.- Eigenstrains and Residual Stresses After Gradient Thermomechanical Treatment of Heavy Steel Plate: Numerical Modelling and Experiment.- Fuzzy-Set Methods of Parametric Uncertainty Accounting in the Investigation of Stability Thin-Walled Structures Models.- Development of the Boundary Equations Method for Wave Problems in 2D Domains with Irregularities of the Boundary Curve.- Increasing the Natural Frequency of Oscillations in Functionally Graded Material Rods.- On the Stress State of a Poroelastic Hollow Finite Cylinder.- The Boundary Value Problem of the Behavior of the Transverse Electromagnetic Wave.- Mechanics of Transformable Large Scale Space Structures with Shape Memory Actuator.

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Book SynopsisWolfgang Dreyer The Life of a Free-Spirited Scientist.- An Eulerian formulation for dissipative materials using Lie derivatives and GENERIC.- Reference map approach to Eulerian thermomechanics using GENERIC.- Pitfalls in the understanding of thermomechanics of continua.- Compressibility and volume variations due to composition in multicomponent fluids.- Incorporating dissipation in the Lagrange equations: Part I Theory.- Incorporating dissipation in the Lagrange equations: Part II Examples.- On Jump Conditions at Phase Boundaries for Ordered and Disordered Phases.- Balance Laws and Transport Theorems for Flows with Singular Interfaces.- Multi Velocity Sharp Interface Continuum Thermodynamics of Fluid Systems with Adsorption.- Damage Modeling in Batteries by Coupling Lithiation and Mechanics by Means of a Finite Element Method.- On the non constant dielectric susceptibility in continuum models for electrolytes.- Elastic Plastic Creep Deformation and Damage in Sn Ag Cu Solder Alloys.- Constitutive theory and simulation of entropy and enthalpy relaxation in the glass transition regime.- Constitutive equations for non linear isotropic limited compressible elastic solids.- Phase field Cosserat modelling of grain boundary pore interaction.- Phase field modeling and sharp interface limits of multi component gas liquid flows with electrochemical reactions and phase transition effects.- Hyperbolic relaxation of the chemical potential in the viscous Cahn Hilliard equation.- A new approach to thermodynamically consistent models for SMAs.- Which frequency bands are responsible for noise-induced triggering of thermoacoustic instabilities?.- A model for tidal effects on a planet.- Mass transport in Fokker Planck equations with general potentials.- Distortion and Residual Stresses in an Additively Manufactured Disc Stack: Continuum Modeling and FEM Simulation for Polyamide 12.- Approaches to conservative Smoothed Particle Hydrodynamics with entropy.- Martensitic nucleation a phonon thermodynamics approach.- The Maximum Entropy Principle in Nonequilibrium Thermodynamics: A Brief History and the Contributions of Wolfgang Dreyer.- Phonon Hydrodynamics Revisited.- On the visual explanation of the isotherm dilute atmosphere.

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Book SynopsisThis textbook covers all fundamental concepts of physics and describes how different theories are developed from physical observations and phenomena. After some essential calculus the author presents the complete classical mechanics giving numerous examples and with a clear focus on problem-solving techniques. Due to the high number of exercises at the end of each chapter and their solutions the work is valuable for self-study.

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Book SynopsisThe work shows, by means of examples coming from different corners of physics, how physical and mathematical questions can be answered using a computer. Starting with maps and neural networks, applications from Newton's mechanics described by ordinary differential equations come into the focus, like the computation of planetary orbits or classical molecular dynamics. A large part of the textbook is dedicated to deterministic chaos normally encountered in systems with sufficiently many degrees of freedom. Partial differential equations are studied considering (nonlinear) field theories like quantum mechanics, thermodynamics or fluid mechanics. In the second edition, a new chapter gives a detailed survey on delay or memory systems with a direct application to epidemic and road traffic models. Most of the algorithms are realized in FORTRAN, a language most suitable for effectively solving the discussed problems. On the other hand, the codes given and presented on the book’s homepage can be easily translated into other languages. Moreover, several MATLAB examples are presented, mainly for didactic reasons. The book is addressed to advanced Bachelor or Master students of physics, applied mathematics and mechanical engineering.

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Book SynopsisPrecision and uniformity are indispensable when working with physical quantities, units and formula symbols. Only through unambiguous and authoritative notation is interdisciplinary cooperation possible. The book gives an overview of all common quantities and units, which are needed in studies and teaching as well as in everyday work. All printed quantities and units are currently valid and standardized in ISO/IEC. The book includes: _brief introduction to the development of the system of units _overview on the system of quantities and units _calculating with quantity values _units (international system of units, SI) _notation of numbers _mathematical symbols _Standardized symbols for quantities (mechanics, space and time, radiation, solid state physics, etc.), elements, nuclides, particles and quantum states. _Appendix: conversion to the U.S. customary system of units.

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Book SynopsisThis book covers the major problems of turbulence and turbulent processes, including physical phenomena, their modeling and their simulation.After a general introduction in Chapter 1 illustrating many aspects dealing with turbulent flows, averaged equations and kinetic energy budgets are provided in Chapter 2. The concept of turbulent viscosity as a closure of the Reynolds stress is also introduced. Wall-bounded flows are presented in Chapter 3 and aspects specific to boundary layers and channel or pipe flows are also pointed out. Free shear flows, namely free jets and wakes, are considered in Chapter 4. Chapter 5 deals with vortex dynamics. Homogeneous turbulence, isotropy and dynamics of isotropic turbulence are presented in Chapters 6 and 7. Turbulence is then described both in the physical space and in the wave number space. Time dependent numerical simulations are presented in Chapter 8, where an introduction to large eddy simulation is offered. The last three chapters of the book summarize remarkable digital techniques current and experimental. Many results are presented in a practical way, based on both experiments and numerical simulations.The book is written for a advanced engineering students as well as postgraduate engineers and researchers. For students, it contains the essential results as well as details and demonstrations whose oral transmission is often tedious. At a more advanced level, the text provides numerous references which allow readers to find quickly further study regarding their work and to acquire a deeper knowledge on topics of interest.Table of Contents Introduction to turbulence.- Statistical description of turbulent flows.- Wall-bounded turbulent flows.- Free turbulent flows: jets and wakes.- Vortex dynamics.- Homogeneous and isotropic turbulence.- The dynamics of isotropic turbulence.- Direct and large eddy simulation of turbulent flows.- Turbulence models.- Experimental methods.

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Book SynopsisThis book – specifically developed as a novel textbook on elementary classical mechanics – shows how analytical and numerical methods can be seamlessly integrated to solve physics problems. This approach allows students to solve more advanced and applied problems at an earlier stage and equips them to deal with real-world examples well beyond the typical special cases treated in standard textbooks.Another advantage of this approach is that students are brought closer to the way physics is actually discovered and applied, as they are introduced right from the start to a more exploratory way of understanding phenomena and of developing their physical concepts.While not a requirement, it is advantageous for the reader to have some prior knowledge of scientific programming with a scripting-type language. This edition of the book uses Python, and a chapter devoted to the basics of scientific programming with Python is included. A parallel edition using Matlab instead of Python is also available.Last but not least, each chapter is accompanied by an extensive set of course-tested exercises and solutions.Table of ContentsIntroduction.- Getting started with programming.- Units and measurement.- Motion in one dimension.- Forces in one dimension.- Motion in two and three dimensions.- Forces in two and three dimensions.- Constrained motion.- Forces and constrained motion.- Work.- Energy.- Momentum, impulse, and collisions.- Multiparticle systems.- Rotational motion.- Rotation of rigid bodies.- Dynamics of rigid bodies.- Proofs.- Solutions.- Index.

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Book SynopsisTable of ContentsComputational aerodynamics and design.- Numerical computations of explosions in gases.- Two-dimensional separated flows.- Numerical simulation of wall-bounded turbulent shear flows.- Shock capturing, fitting and recovery.- Flow simulation by discrete vortex method.- A grid interfacing zonal algorithm for three-dimensional transonic flows about aircraft configurations.- An accurate and efficient finite element Euler equation algorithm.- Numerical computation of large-scale fire-induced flows.- Simulation of the fluctuating field of a forced Jet.- Modeling of gasdynamic processes in neutron stars with phase transitions.- Adaptation of flux-corrected transport algorithms for Modelina blast waves.- A local-relaxation method for solving convection-diffusion equations.- A numerical treatment of two-dimensional flow in a branching channel.- Finite element least square method for solving full steady Euler equations in a plane nozzle.- Analysis of separated boundary-layer flows.- Numerical modelling of inviscid shocked flows of real gases.- An overrelaxation method for transonic flow calculations by Euler equations.- A Dorodnitsyn finite element boundary layer formulation.- Large eddy simulation of a turbulent wall-bounded shear layer with longitudinal curvature.- Mixed initial and boundary value problems: Upwind schemes and their application.- An Eulerian method for calculation of gas motion in a varying region.- Computation of inviscid transonic internal flow.- Random element method for numerical modeling of diffusional processes.- A high Reynolds number flow with closed streamlines.- Compressible swirling flow into a constant volume cylinder.- Techniques for efficient implementation of pseudo-spectral methods and comparisons with finite difference solutions of the Navier-Stokes equations.- Numerical simulation of the fluid flow in front of the scoop of a gas centrifuge.- Study of incompressible turbulent channel flow by large eddy simulation.- Numerical solution and boundary conditions for boundary layer like flows.- Relaxation solution of the full Euler equations.- Spectral simulations of laminar-turbulent transition in plane Poiseuille flow and comparison with experiments.- Transonic-flow computation using an explicit-implicit method.- Numerical modeling of viscous flows in approximation of full and simplified Navier-Stokes equations.- Numerical solution of transonic shear flows past thin bodies.- Transonic potential flow calculation about complex bodies by a technique of overlapping subdomains.- Calculation method for transonic separated flows over airfoils including spoiler effects.- On the use of several compact methods for the study of unsteady incompressible viscous flow for outer problems (II).- Mesh generation strategies for CFD on complex configurations.- A new numerical method for the simulation of three-dimensional flow in a pipe.- An implicit finite-volume method for solving the Euler equations.- Finite difference computation of pressure and wave-drag of slender bodies of revolution at transonic speeds with zero-lift.- Numerical solution of viscous flow in unbounded fluid.- A natural conservative flux difference splitting for the hyperbolic systems of gasdynamics.- Simulation of cylindrical Couette flow.- Solution-adaptive grid for the calculation of three-dimensional laminar and turbulent boundary layers.- Calculation of pressure statistics in turbulent free shear flows by direct numerical simulation.- An implicit finite difference method for chemical nonequilibrium flow through an axisymmetric supersonic nozzle.- Noniterative grid generation using parabolic difference equations for fuselage-wing flow calculations.- The numerical calculation of rotating fluid flows at low Rossby numbers.- Numerical techniques for multidimensional modeling of shock-generated turbulence.- Adaptive curvilinear grids for large Reynolds number viscous flows.- Simulation of large turbulent vortex structures with the parabolic Navier-Stokes equations.- Unigrid projection method to solve the Euler equations for steady transonic flow.- Numerical solution of viscous flow around arbitrary airfoils in a straight cascade.- Numerical simulation of homogeneous anisotropic turbulence.- A composite velocity procedure for the incompressible Navier-Stokes equations.- On calculation accuracy in gas flow problems with shock type discontinuities.- Shock-fitted Euler solutions to shock-vortex interactions.- Euler solutions as limit of infinite Reynolds number for separation flows and flows with vortices.- Branching of Navier-Stokes equations in a spherical gap.- On the construction of adaptive algorithms for unsteady problems of gas dynamics in arbitrary coordinate systems.- Analytical tests for numerical methods in gas dynamics.- Discrete models of the kinetic Boltzman equation.- Application of a polynomial spline in higher-order accurate viscous-flow computations.- Flux-vector splitting for the Euler equations.- Numerical solution of the problem of supersonic flow past wings of arbitrary form with a detached shock wave.- Solution of three-dimensional time-dependent viscous flows.- A minimal residual method for transonic potential flows.- Application of two-point difference schemes to the conservative Euler equations for one-dimensional flows.- Numerical solution of the Euler equation for a compressible flow problem.- A high-resolution numerical technique for inviscid gas-dynamic problems with weak solutions.- Some new developments of the singularity-separating difference method.

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Book SynopsisSoliton theory, the theory of nonlinear waves in lattices composed of particles interacting by nonlinear forces, is treated rigorously in this book. The presentation is coherent and self-contained, starting with pioneering work and extending to the most recent advances in the field. Special attention is focused on exact methods of solution of nonlinear problems and on the exact mathematical treatment of nonlinear lattice vibrations. This new edition updates the material to take account of important new advances.Table of Contents1. Introduction.- 1.1 The Fermi-Pasta-Ulam Problem.- 1.2 Hénon-Heiles Calculation.- 1.3 Discovery of Solitons.- 1.4 Dual Systems.- 2. The Lattice with Exponential Interaction.- 2.1 Finding of an Integrable Lattice.- 2.2 The Lattice with Exponential Interaction.- 2.3 Periodic Solutions.- 2.4 Solitary Waves.- 2.5 Two-Soliton Solutions.- 2.6 Hard-Sphere Limit.- 2.7 Continuum Approximation and Recurrence Time.- 2.8 Applications and Extensions.- 2.9 Poincaré Mapping.- 2.10 Conserved Quantities.- 3. The Spectrum and Construction of Solutions.- 3.1 Matrix Formalism.- 3.2 Infinite Lattice.- 3.3 Scattering and Bound States.- 3.4 The Gel’fand-Levitan Equation.- 3.5 The Initial Value Problem.- 3.6 Soliton Solutions.- 3.7 The Relationship Between the Conserved Quantities and the Transmission Coefficient.- 3.8 Extensions of the Equations of Motion and the Kac-Moerbeke System.- 3.9 The Bäcklund Transformation.- 3.10 A Finite Lattice.- 3.11 Continuum Approximation.- 4. Periodic Systems.- 4.1 Discrete Hill’s Equation.- 4.2 Auxiliary Spectrum.- 4.3 Relation Between ?j (k) and ?j (0).- 4.4 Related Integrals on the Riemann Surface.- 4.5 Solution to the Inverse Problem.- 4.6 Time Evolution.- 4.7 A Simple Example (A Cnoidal Wave).- 4.8 Periodic System of Three-Particles.- 5. Application of the Hamilton-Jacobi Theory.- 5.1 Canonically Conjugate Variables.- 5.2 Action Variables.- 6. Recent Advances in the Theory of Nonlinear Lattices.- 6.1 The KdV Equation as a Limit of the TL Equation.- 6.2 Interacting Soliton Equations.- 6.3 Integrability.- 6.4 Generalization of the TL Equation.- 6.5 Two-Dimensional TL.- 6.6 Bethe Ansatz.- 6.7 The Thermodynamic Limit.- 6.8 Hierarchy of Nonlinear Equations.- 6.9 Some Numerical Results.- Appendices.- Simplified Answers to Main Problems.- References.- List of Authors Cited in Text.

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Book SynopsisSpontaneous pattern formation in nonlinear dissipative systems far from equilibrium occurs in a variety of settings in nature and technology, and has applications ranging from nonlinear optics through solid and fluid mechanics, physical chemistry and chemical engineering to biology. This book explores the forefront of current research, describing in-depth the analytical methods that elucidate the complex evolution of nonlinear dissipative systems.Trade ReviewFrom the reviews: "This book presents thorough descriptions of analytical methods divulging the complex evolution of nonlinear dissipative systems, and introduces the reader to the forefront of current research. … This book addresses graduate students and non-specialists from the many related areas of applied mathematics, physical chemistry, chemical engineering and biology, as well as the seasoned scientist in search of a modern source of reference." (Ömer Kavaklioglu, Zentralblatt MATH, Vol. 1098 (24), 2006) "This substantial monograph summarizes a broad selection of results concerning the dynamics of model nonlinear dissipative partial differential equations. … The layout and figures are generally very clear and the material is well-organised. … Overall I recommend this book as a very useful reference and guide to the literature. It will undoubtedly be of use to those working in very different areas of nonlinear science." (Jonathan Dawes, Fluid Mechanics, Vol. 584, 2007) "The book begins with a brief overview of dynamical systems theory, which is helpful for understanding the bulk of the book. … In summary, this book is a clear and comprehensive review of this interesting area of pattern formation, and usefully complements existing texts. It is particularly useful as a reference to the development of the theory of stability of fronts and defects." (Alastair M. Rucklidge, Mathematical Reviews, Issue 2008 f)Table of ContentsDynamics, Stability and Bifurcations.- Fronts and Interfaces.- Systems with Separated Scales.- Amplitude Equations for Patterns.- Amplitude Equations for Waves.

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Book SynopsisThis is the first textbook in this field of increasing importance for the food and cosmetics industries. It is indispensable for future students of food technology and food chemistry as well as for engineers, technologists and technicians in the food industries. It describes the principles of food physics starting with the very basics – and focuses on the needs of practitioners without omitting important basic principles. It will be indispensable for future students of food technology and food chemistry as well as for engineers, technologists and technicians in the food industries. Food Physics deals with the physical properties of food, food ingredients and their measurement.Table of ContentsWater Activity.- Mass and Density.- Geometric Properties: Size and Shape.- Rheological Properties.- Interfacial Phenomena.- Permeability.- Thermal Properties.- Electrical Properties.- Magnetic Properties.- Electromagnetic Properties.- Optical Properties.- Acoustical Properties.- Radioactivity.- On-Line Sensing.- Appendices.-

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Book SynopsisWave propagation is an important topic in engineering sciences, especially, in the field of solid mechanics. A description of wave propagation phenomena is given by Graff [98]: The effect of a sharply applied, localized disturbance in a medium soon transmits or 'spreads' to other parts of the medium. These effects are familiar to everyone, e.g., transmission of sound in air, the spreading of ripples on a pond of water, or the transmission of radio waves. From all wave types in nature, here, attention is focused only on waves in solids. Thus, solely mechanical disturbances in contrast to electro-magnetic or acoustic disturbances are considered. of waves - the compression wave similar to the In solids, there are two types pressure wave in fluids and, additionally, the shear wave. Due to continual reflec­ tions at boundaries and propagation of waves in bounded solids after some time a steady state is reached. Depending on the influence of the inertia terms, this state is governed by a static or dynamic equilibrium in frequency domain. However, if the rate of onset of the load is high compared to the time needed to reach this steady state, wave propagation phenomena have to be considered.Table of Contents1. Introduction.- 2. Convolution quadrature method.- 2.1 Basic theory of the convolution quadrature method.- 2.2 Numerical tests.- 2.2.1 Series expansion of the test functions f1 and f2.- 2.2.2 Computing the integration weights ?n.- 2.2.3 Numerical convolution.- 3. Viscoelastically supported Euler-Bernoulli beam.- 3.1 Integral equation for a beam resting on viscoelastic foundation.- 3.1.1 Fundamental solutions.- 3.1.2 Integral equation.- 3.2 Numerical example.- 3.2.1 Fixed-simply supported beam.- 3.2.2 Fixed-free viscoelastic supported beam.- 4. Time domain boundary element formulation.- 4.1 Integral equation for elastodynamics.- 4.2 Boundary element formulation for elastodynamics.- 4.3 Validation of proposed method: Wave propagation in a rod.- 4.3.1 Influence of the spatial and time discretization.- 4.3.2 Comparison with the “classical” time domain BE formulation.- 5. Viscoelastodynamic boundary element formulation.- 5.1 Viscoelastic constitutive equation.- 5.2 Boundary integral equation.- 5.3 Boundary element formulation.- 5.4 Validation of the method and parameter study.- 5.4.1 Three-dimensional rod.- 5.4.2 Elastic foundation on viscoelastic half space.- 6. Poroelastodynamic boundary element formulation.- 6.1 Biot’s theory of poroelasticity.- 6.1.1 Elastic skeleton.- 6.1.2 Viscoelastic skeleton.- 6.2 Fundamental solutions.- 6.3 Poroelastic Boundary Integral Formulation.- 6.3.1 Boundary integral equation.- 6.3.2 Boundary element formulation.- 6.4 Numerical studies.- 6.4.1 Influence of time step size and mesh size.- 6.4.2 Poroelastic half space.- 7. Wave propagation.- 7.1 Wave propagation in poroelastic one-dimensional column.- 7.1.1 Analytical solution.- 7.1.2 Poroelastic results.- 7.1.3 Poroviscoelastic results.- 7.2 Waves in half space.- 7.2.1 Rayleigh surface wave.- 7.2.2 Slow compressional wave in poroelastic half space.- 8. Conclusions — Applications.- 8.1 Summary.- 8.2 Outlook on further applications.- A. Mathematic preliminaries.- A.1 Distributions or generalized functions.- A.2 Convolution integrals.- A.3 Laplace transform.- A.4 Linear multistep method.- B. BEM details.- B.1 Fundamental solutions.- B.1.1 Visco- and elastodynamic fundamental solutions.- B.1.2 Poroelastodynamic fundamental solutions.- B.2 “Classical” time domain BE formulation.- Notation Index.- References.

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Book SynopsisThis is a book about spectral methods for partial differential equations: when to use them, how to implement them, and what can be learned from their of spectral methods has evolved rigorous theory. The computational side vigorously since the early 1970s, especially in computationally intensive of the more spectacular applications are applications in fluid dynamics. Some of the power of these discussed here, first in general terms as examples of the methods have been methods and later in great detail after the specifics covered. This book pays special attention to those algorithmic details which are essential to successful implementation of spectral methods. The focus is on algorithms for fluid dynamical problems in transition, turbulence, and aero­ dynamics. This book does not address specific applications in meteorology, partly because of the lack of experience of the authors in this field and partly because of the coverage provided by Haltiner and Williams (1980). The success of spectral methods in practical computations has led to an increasing interest in their theoretical aspects, especially since the mid-1970s. Although the theory does not yet cover the complete spectrum of applications, the analytical techniques which have been developed in recent years have facilitated the examination of an increasing number of problems of practical interest. In this book we present a unified theory of the mathematical analysis of spectral methods and apply it to many of the algorithms in current use.Table of Contents1. Introduction.- 1.1. Historical Background.- 1.2. Some Examples of Spectral Methods.- 1.2.1. A Fourier Galerkin Method for the Wave Equation.- 1.2.2. A Chebyshev Collocation Method for the Heat Equation.- 1.2.3. A Legendre Tau Method for the Poisson Equation.- 1.2.4. Basic Aspects of Galerkin, Tau and Collocation Methods.- 1.3. The Equations of Fluid Dynamics.- 1.3.1. Compressible Navier-Stokes.- 1.3.2. Compressible Euler.- 1.3.3. Compressible Potential.- 1.3.4. Incompressible Flow.- 1.3.5. Boundary Layer.- 1.4. Spectral Accuracy for a Two-Dimensional Fluid Calculation.- 1.5. Three-Dimensional Applications in Fluids.- 2. Spectral Approximation.- 2.1. The Fourier System.- 2.1.1. The Continuous Fourier Expansion.- 2.1.2. The Discrete Fourier Expansion.- 2.1.3. Differentiation.- 2.1.4. The Gibbs Phenomenon.- 2.2. Orthogonal Polynomials in ( — 1, 1).- 2.2.1. Sturm—Liouville Problems.- 2.2.2. Orthogonal Systems of Polynomials.- 2.2.3. Gauss-Type Quadratures and Discrete Polynomial Transforms.- 2.3. Legendre Polynomials.- 2.3.1. Basic Formulas.- 2.3.2. Differentiation.- 2.4. Chebyshev Polynomials.- 2.4.1. Basic Formulas.- 2.4.2. Differentiation.- 2.5. Generalizations.- 2.5.1. Jacobi Polynomials.- 2.5.2. Mapping.- 2.5.3. Semi-Infinite Intervals.- 2.5.4. Infinite Intervals.- 3. Fundamentals of Spectral Methods for PDEs.- 3.1. Spectral Projection of the Burgers Equation.- 3.1.1. Fourier Galerkin.- 3.1.2. Fourier Collocation.- 3.1.3. Chebyshev Tau.- 3.1.4. Chebyshev Collocation.- 3.2. Convolution Sums.- 3.2.1. Pseudospectral Transform Methods.- 3 2 2 Aliasing Removal by Padding or Truncation.- 3.2.3. Aliasing Removal by Phase Shifts.- 3.2.4. Convolution Sums in Chebyshev Methods.- 3.2.5. Relation Between Collocation and Pseudospectral Methods.- 3.3. Boundary Conditions.- 3.4. Coordinate Singularities.- 3.4.1. Polar Coordinates.- 3.4.2. Spherical Polar Coordinates.- 3.5. Two-Dimensional Mapping.- 4. Temporal Discretization.- 4.1. Introduction.- 4.2. The Eigenvalues of Basic Spectral Operators.- 4.2.1. The First-Derivative Operator.- 4.2.2. The Second-Derivative Operator.- 4.3. Some Standard Schemes.- 4.3.1. Multistep Schemes.- 4.3.2. Runge—Kutta Methods.- 4.4. Special Purpose Schemes.- 4.4.1. High Resolution Temporal Schemes.- 4.4.2. Special Integration Techniques.- 4.4.3. Lerat Schemes.- 4.5. Conservation Forms.- 4.6. Aliasing.- 5. Solution Techniques for Implicit Spectral Equations.- 5.1. Direct Methods.- 5.1.1. Fourier Approximations.- 5.1.2. Chebyshev Tau Approximations.- 5.1.3. Schur-Decomposition and Matrix-Diagonalization.- 5.2. Fundamentals of Iterative Methods.- 5.2.1. Richardson Iteration.- 5.2.2. Preconditioning.- 5.2.3. Non-Periodic Problems.- 5.2.4. Finite-Element Preconditioning.- 5.3. Conventional Iterative Methods.- 5.3.1. Descent Methods for Symmetric, Positive-Definite Systems.- 5.3.2. Descent Methods for Non-Symmetric Problems.- 5.3.3. Chebyshev Acceleration.- 5.4. Multidimensional Preconditioning.- 5.4.1. Finite-Difference Solvers.- 5.4.2. Modified Finite-Difference Preconditioners.- 5.5. Spectral Multigrid Methods.- 5.5.1. Model Problem Discussion.- 5.5.2. Two-Dimensional Problems.- 5.5.3. Interpolation Operators.- 5.5.4. Coarse-Grid Operators.- 5.5.5. Relaxation Schemes.- 5.6. A Semi-Implicit Method for the Navier—Stokes Equations.- 6. Simple Incompressible Flows.- 6.1. Burgers Equation.- 6.2. Shear Flow Past a Circle.- 6.3. Boundary-Layer Flows.- 6.4. Linear Stability.- 7. Some Algorithms for Unsteady Navier—Stokes Equations.- 7.1. Introduction.- 7.2. Homogeneous Flows.- 7.2.1. A Spectral Galerkin Solution Technique.- 7.2.2. Treatment of the Nonlinear Terms.- 7.2.3. Refinements.- 7.2.4. Pseudospectral and Collocation Methods.- 7.3. Inhomogeneous Flows.- 7.3.1. Coupled Methods.- 7.3.2. Splitting Methods.- 7.3.3. Galerkin Methods.- 7.3.4. Other Confined Flows.- 7.3.5. Unbounded Flows.- 7.3.6. Aliasing in Transition Calculations.- 7.4. Flows with Multiple Inhomogeneous Directions.- 7.4.1. Choice of Mesh.- 7.4.2. Coupled Methods.- 7.4.3. Splitting Methods.- 7.4.4. Other Methods.- 7.5. Mixed Spectral/Finite-Difference Methods.- 8. Compressible Flow.- 8.1. Introduction.- 8.2. Boundary Conditions for Hyperbolic Problems.- 8.3. Basic Results for Scalar Nonsmooth Problems.- 8.4. Homogeneous Turbulence.- 8.5. Shock-Capturing.- 8.5.1. Potential Flow.- 8.5.2. Ringleb Flow.- 8.5.3. Astrophysical Nozzle.- 8.6. Shock-Fitting.- 8.7. Reacting Flows.- 9. Global Approximation Results.- 9.1. Fourier Approximation.- 9.1.1. Inverse Inequalities for Trigonometric Polynomials.- 9.1.2. Estimates for the Truncation and Best Approximation Errors.- 9.1.3. Estimates for the Interpolation Error.- 9.2. Sturm—Liouville Expansions.- 9.2.1. Regular Sturm—Liouville Problems.- 9.2.2. Singular Sturm—Liouville Problems.- 9.3. Discrete Norms.- 9.4. Legendre Approximations.- 9.4.1. Inverse Inequalities for Algebraic Polynomials.- 9.4.2. Estimates for the Truncation and Best Approximation Errors.- 9.4.3. Estimates for the Interpolation Error.- 9.5. Chebyshev Approximations.- 9.5.1. Inverse Inequalities for Polynomials.- 9.5.2. Estimates for the Truncation and Best Approximation Errors.- 9.5.3. Estimates for the Interpolation Error.- 9.5.4. Proofs of Some Approximation Results.- 9.6. Other Polynomial Approximations.- 9.6.1. Jacobi Polynomials.- 9.6.2. Laguerre and Hermite Polynomials.- 9.7. Approximation Results in Several Dimensions.- 9.7.1. Fourier Approximations.- 9.7.2. Legendre Approximations.- 9.7.3. Chebyshev Approximations.- 9.7.4. Blended Fourier and Chebyshev Approximations.- 10. Theory of Stability and Convergence for Spectral Methods.- 10.1. The Three Examples Revisited.- 10.1.1. A Fourier Galerkin Method for the Wave Equation.- 10.1.2. A Chebyshev Collocation Method for the Heat Equation.- 10.1.3. A Legendre Tau Method for the Poisson Equation.- 10.2. Towards a General Theory.- 10.3. General Formulation of Spectral Approximations to Linear Steady Problems.- 10.4. Galerkin, Collocation and Tau Methods.- 10.4.1. Galerkin Methods.- 10.4.2. Tau Methods.- 10.4.3. Collocation Methods.- 10.5. General Formulation of Spectral Approximations to Linear Evolution Equations.- 10.5.1. Conditions for Stability and Convergence: The Parabolic Case.- 10.5.2. Conditions for Stability and Convergence: The Hyperbolic Case.- 10.6. The Error Equation.- 11. Steady, Smooth Problems.- 11.1. The Poisson Equation.- 11.1.1. Legendre Methods.- 11.1.2. Chebyshev Methods.- 11.1.3. Other Boundary Value Problems.- 11.2. Advection-Diffusion Equation.- 11.2.1. Linear Advection-Diffusion Equation.- 11.2.2. Steady Burgers Equation.- 11.3. Navier—Stokes Equations.- 11.3.1. Compatibility Conditions Between Velocity and Pressure.- 11.3.2. Direct Discretization of the Continuity Equation: The “inf-sup” Condition.- 11.3.3. Discretizations of the Continuity Equation by an Influence-Matrix Technique: The Kleiser—Schumann Method.- 11.3.4. Navier—Stokes Equations in Streamfunction Formulation.- 11.4. The Eigenvalues of Some Spectral Operators.- 11.4.1. The Discrete Eigenvalues for Lu = ? uxx.- 11.4.2. The Discrete Eigenvalues for Lu = ? vuxx + bux.- 11.4.3. The Discrete Eigenvalues for Lu = ux.- 12. Transient, Smooth Problems.- 12.1. Linear Hyperbolic Equations.- 12.1.1. Periodic Boundary Conditions.- 12.1.2. Non-Periodic Boundary Conditions.- 12.1.3. Hyperbolic Systems.- 12.1.4. Spectral Accuracy for Non-Smooth Solutions.- 12.2. Heat Equation.- 12.2.1. Semi-Discrete Approximation.- 12.2.2. Fully Discrete Approximation.- 12.3. Advection-Diffusion Equation.- 12.3.1. Semi-Discrete Approximation.- 12.3.2. Fully Discrete Approximation.- 13. Domain Decomposition Methods.- 13.1. Introduction.- 13.2. Patching Methods.- 13.2.1. Notation.- 13.2.2. Discretization.- 13.2.3. Solution Techniques.- 13.2.4. Examples.- 13.3. Variational Methods.- 13.3.1. Formulation.- 13.3.2. The Spectral-Element Method.- 13.4. The Alternating Schwarz Method.- 13.5. Mathematical Aspects of Domain Decomposition Methods.- 13.5.1. Patching Methods.- 13.5.2. Equivalence Between Patching and Variational Methods.- 13.6. Some Stability and Convergence Results.- 13.6.1. Patching Methods.- 13.6.2. Variational Methods.- Appendices.- A. Basic Mathematical Concepts.- B. Fast Fourier Transforms.- C. Jacobi—Gauss—Lobatto Roots.- References.

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