Maths for engineers Books

Book SynopsisUse this book to nudge your brain~mind into its metastable mode again and again, to better perceive the complementary dances of contraries, and to transcend the detrimental narrow-mindedness of polarized, either/or thinking.

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Book SynopsisIn this book the dynamics of the non-ideal oscillatory system, in which the excitation is influenced by the response of the oscillator, is presented. Linear and nonlinear oscillators with one or more degrees of freedom interacting with one or more energy sources are treated. This concerns for example oscillating systems excited by a deformed elastic connection, systems excited by an unbalanced rotating mass, systems of parametrically excited oscillator and an energy source, frictionally self-excited oscillator and an energy source, energy harvesting system, portal frame – non-ideal source system, non-ideal rotor system, planar mechanism – non-ideal source interaction. For the systems the regular and irregular motions are tested. The effect of self-synchronization, chaos and methods for suppressing chaos in non-ideal systems are considered. In the book various types of motion control are suggested. The most important property of the non-ideal system connected with the jump-like transition from a resonant state to a non-resonant one is discussed. The so called ‘Sommerfeld effect’, resonant unstable state and jumping of the system into a new stable state of motion above the resonant region is explained. A mathematical model of the system is solved analytically and numerically. Approximate analytical solving procedures are developed. Besides, simulation of the motion of the non-ideal system is presented. The obtained results are compared with those for the ideal case. A significant difference is evident. The book aims to present the established results and to expand the literature in non-ideal vibrating systems. A further intention of the book is to give predictions of the effects for a system where the interaction between an oscillator and the energy source exist. The book is targeted at engineers and technicians dealing with the problem of source-machine system, but is also written for PhD students and researchers interested in non-linear and non-ideal problems. Table of ContentsPREFACE1. INTRODUCTION2. LINEAR OSCILLATOR AND A NON-IDEAL ENERGY SOURCE2.1. Simple degree of freedom oscillator coupled with a non-ideal energy source 2.1.1. Analytical solving procedure 2.1.2. Sommerfeld effect 2.1.3. Model analogy and numerical simulation2.1.4. Stability analysis2.2. Oscillator with clearance coupled with a non-ideal source 2.2.1. Model of the system 2.2.2. Transient motion of the system2.2.3. Steady-state motion of the system2.2.4. Chaotic motion2.2.5. Chaos control 2.3. Conclusion2.4. References3. NONLINEAR ONE-DEGREE-OF-FREEDOM OSCILLATOR INTERACTING WITH A NON-IDEAL ENEGY SOURCE3.1. Stable Duffing oscillator coupled with a non-ideal energy source3.2. Bistable Duffing oscillator coupled with a non-ideal energy source3.3. Pure strong nonlinear oscillator coupled with a non-ideal energy source3.4. Conclusion3.5. References4. NON-IDEAL VIBRATING SYSTEMS WITH DAMPERS 4.1. System with electromechanical vibration absorber 4.2. System with magnetically levitated vibrating system 4.3. System with magnetic rheological damper (MRD) 4.4. References5. TWO-DEGREE-OF-FREEDOM OSCILLATOR INTERACTING WITH A NON-IDEAL ENEGY SOURCE 5.1. Non-ideal energy source on the vibrating foundation 5.2. Non-ideal vibrating system coupled to a magneto-rheological damper 5.3. References6. VIBRATION OF A NON-IDEAL ROTOR SYSTEM7. PORTAL FRAME SUPPORTING NON-IDEAL ENERGY SOURCES 7.1. Regular and chaotic motion in a non-ideal portal frame system 7.2. Self-synchronization of two non-ideal sources supported by a portal frame 7.3. Self-synchronization of four non-ideal exciters7.4. References8. APPLICATION OF NON-IDEAL SYSTEMS IN ENERGY HARVESTING8.1. Non-ideal energy harvesting8.2. Energy harvesting system with piezoelectric coupling8.3. Non-ideal portal frame in energy harvester9. APPENDIXINDEX

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Book SynopsisThis book introduces readers to essential tools for the measurement and analysis of information loss in signal processing systems. Employing a new information-theoretic systems theory, the book analyzes various systems in the signal processing engineer’s toolbox: polynomials, quantizers, rectifiers, linear filters with and without quantization effects, principal components analysis, multirate systems, etc. The user benefit of signal processing is further highlighted with the concept of relevant information loss. Signal or data processing operates on the physical representation of information so that users can easily access and extract that information. However, a fundamental theorem in information theory—data processing inequality—states that deterministic processing always involves information loss. These measures form the basis of a new information-theoretic systems theory, which complements the currently prevailing approaches based on second-order statistics, such as the mean-squared error or error energy. This theory not only provides a deeper understanding but also extends the design space for the applied engineer with a wide range of methods rooted in information theory, adding to existing methods based on energy or quadratic representations.Table of ContentsIntroduction.- Part I: Random Variables.- Piecewise Bijective Functions and Continuous Inputs.- General Input Distributions.- Dimensionality-Reducing Functions.- Relevant Information Loss.- II. Part II: Stationary Stochastic Processes.- Discrete-Valued Processes.- Piecewise Bijective Functions and Continuous Inputs.- Dimensionality-Reducing Functions.- Relevant Information Loss Rate.- Conclusion and Outlook.

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Book SynopsisThe aim of this book is to gather the most recent works that address issues related to the concept of mining complex data. The whole knowledge discovery process being involved, our goal is to provide researchers dealing with each step of this process by key entries. Actually, managing complex data within the KDD process implies to work on every step, starting from the pre-processing (e.g. structuring and organizing) to the visualization and interpretation (e.g. sorting or filtering) of the results, via the data mining methods themselves (e.g. classification, clustering, frequent patterns extraction, etc.). The papers presented here are selected from the workshop papers held yearly since 2006. Table of ContentsGeneral Aspects of Complex Data.- Using Layout Data for the Analysis of Scientific Literature.- Extracting a Fuzzy System by Using Genetic Algorithms for Imbalanced Datasets Classification: Application on Down’s Syndrome Detection.- A Hybrid Approach of Boosting Against Noisy Data.- Dealing with Missing Values in a Probabilistic Decision Tree during Classification.- Kernel-Based Algorithms and Visualization for Interval Data Mining.- Rules Extraction.- Evaluating Learning Algorithms Composed by a Constructive Meta-learning Scheme for a Rule Evaluation Support Method.- Mining Statistical Association Rules to Select the Most Relevant Medical Image Features.- From Sequence Mining to Multidimensional Sequence Mining.- Tree-Based Algorithms for Action Rules Discovery.- Graph Data Mining.- Indexing Structure for Graph-Structured Data.- Full Perfect Extension Pruning for Frequent Subgraph Mining.- Parallel Algorithm for Enumerating Maximal Cliques in Complex Network.- Community Finding of Scale-Free Network: Algorithm and Evaluation Criterion.- The k-Dense Method to Extract Communities from Complex Networks.- Data Clustering.- Efficient Clustering for Orders.- Exploring Validity Indices for Clustering Textual Data.

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Book SynopsisWhen a new extraordinary and outstanding theory is stated, it has to face criticism and skeptism, because it is beyond the usual concept. The fractional calculus though not new, was not discussed or developed for a long time, particularly for lack of its application to real life problems. It is extraordinary because it does not deal with ‘ordinary’ differential calculus. It is outstanding because it can now be applied to situations where existing theories fail to give satisfactory results. In this book not only mathematical abstractions are discussed in a lucid manner, with physical mathematical and geometrical explanations, but also several practical applications are given particularly for system identification, description and then efficient controls. The normal physical laws like, transport theory, electrodynamics, equation of motions, elasticity, viscosity, and several others of are based on ‘ordinary’ calculus. In this book these physical laws are generalized in fractional calculus contexts; taking, heterogeneity effect in transport background, the space having traps or islands, irregular distribution of charges, non-ideal spring with mass connected to a pointless-mass ball, material behaving with viscous as well as elastic properties, system relaxation with and without memory, physics of random delay in computer network; and several others; mapping the reality of nature closely. The concept of fractional and complex order differentiation and integration are elaborated mathematically, physically and geometrically with examples. The practical utility of local fractional differentiation for enhancing the character of singularity at phase transition or characterizing the irregularity measure of response function is deliberated. Practical results of viscoelastic experiments, fractional order controls experiments, design of fractional controller and practical circuit synthesis for fractional order elements are elaborated in this book. The book also maps theory of classical integer order differential equations to fractional calculus contexts, and deals in details with conflicting and demanding initialization issues, required in classical techniques. The book presents a modern approach to solve the ‘solvable’ system of fractional and other differential equations, linear, non-linear; without perturbation or transformations, but by applying physical principle of action-and-opposite-reaction, giving ‘approximately exact’ series solutions.Historically, Sir Isaac Newton and Gottfried Wihelm Leibniz independently discovered calculus in the middle of the 17th century. In recognition to this remarkable discovery, J.von Neumann remarked, “…the calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more equivocally than anything else the inception of modern mathematical analysis which is logical development, still constitute the greatest technical advance in exact thinking.”This XXI century has thus started to ‘think-exactly’ for advancement in science & technology by growing application of fractional calculus, and this century has started speaking the language which nature understands the best.Trade ReviewFrom the reviews of the second edition:“This is a book that ought be read by any applied or theoretical researcher interesting in this topic, because the book is plenty of good work. It is possible to learn from it, especially, from the applications included, and finally, because the reader will get a lot of ideas to produce new works in the area of the fractional calculus.” (Juan J. Trujillo, Zentralblatt MATH, Vol. 1225, 2012)“The author has developed this subject without mathematical details but with correct mathematics and proper explanation of the generalization of the integer order to fractional order calculus … . This applied and innovative approach of presentation is really appreciable for understanding an application oriented subject to the scientists and engineers. … the author has elaborated each concept herein via very relevant examples of practical utility, is real novelty. … this book is highly illuminating to the researchers of different fields of science and engineering.” (Susmita Sarkar, International Journal of Mathematics and Computation, Vol. 18 (1), 2013)“This book is a very timely addition to the existing literature in this subject … . The book may be considered as a textbook for students of mathematics and recommended as a useful reference and guidebook for researchers in other streams of science and technology. A proof of acceptance of the book by the scientific community is quite evident from over 200 citations it has already received within such a short time span after publication.” (Sujata Tarafdar, International Journal of Mathematics and Computation, Vol. 18 (1), 2013)Table of ContentsCHAPTER 1 INTRODUCTION TO FRACTIONAL CALCULUS.- CHAPTER 2FUNCTIONS USED IN FRACTIONAL CALCULUS.- CHAPTER 3 OBSERVATION OF FRACTIONAL CALCULUS IN PHYSICAL SYSTEM DESCRIPTION.- CHAPTER-4 CONCEPT OF FRACTIONAL DIVERGENCE AND FRACTIONAL CURLCHAPTER-5.- FRACTIONAL DIFFERINTEGRATIONS INSIGHT CONCEPTS.-CHAPTER-6 INITIALIZED DIFFERINTEGRALS AND GENERALIZED CALCULUS.- CHAPTER-7 GENERALIZED LAPLACE TRANSFORM FOR FRACTIONAL DIFFERINTEGRALS.-CHAPTER-8 APPLICATION OF GENERALIZED FRACTIONAL CALCULUS IN ELECTRICAL CIRCUIT ANALYSIS & ELECTROMAGNETICS.- CHAPTER-9 APPLICATION OF GENERALIZED FRACTIONAL CALCULUS IN OTHER SCIENCE AND ENGINEERING FIELDS.- CHAPTER-10 SYSTEM ORDER IDENTIFICATION AND CONTROL.- CHAPTER-11 SOLUTION OF GENERALIZED DIFFERENTIAL EQUATION SYSTEMS .

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Book SynopsisThis book provides an inter-disciplinary introduction to the theory of random fields and its applications. Spatial models and spatial data analysis are integral parts of many scientific and engineering disciplines. Random fields provide a general theoretical framework for the development of spatial models and their applications in data analysis. The contents of the book include topics from classical statistics and random field theory (regression models, Gaussian random fields, stationarity, correlation functions) spatial statistics (variogram estimation, model inference, kriging-based prediction) and statistical physics (fractals, Ising model, simulated annealing, maximum entropy, functional integral representations, perturbation and variational methods). The book also explores links between random fields, Gaussian processes and neural networks used in machine learning. Connections with applied mathematics are highlighted by means of models based on stochastic partial differential equations. An interlude on autoregressive time series provides useful lower-dimensional analogies and a connection with the classical linear harmonic oscillator. Other chapters focus on non-Gaussian random fields and stochastic simulation methods. The book also presents results based on the author’s research on Spartan random fields that were inspired by statistical field theories originating in physics. The equivalence of the one-dimensional Spartan random field model with the classical, linear, damped harmonic oscillator driven by white noise is highlighted. Ideas with potentially significant computational gains for the processing of big spatial data are presented and discussed. The final chapter concludes with a description of the Karhunen-Loève expansion of the Spartan model. The book will appeal to engineers, physicists, and geoscientists whose research involves spatial models or spatial data analysis. Anyone with background in probability and statistics can read at least parts of the book. Some chapters will be easier to understand by readers familiar with differential equations and Fourier transforms.Trade Review“I would say … that the author’s use of an interdisciplinary approach in presenting the field of spatial data modeling is what makes this book truly unique. … I believe anyone who is willing to learn about and understand concepts, assumptions and methods behind spatial data modeling would benefit from having a copy of this outstanding book.” (Sandra De Iaco, Mathematical Geosciences, February 12, 2021)Table of ContentsIntroduction.- Preliminary Remarks.- Why Random Fields?.- Notation and Definitions.- Noise and Errors.- Spatial Data and Basic Processing Procedures.- A Personal Selection of Relevant Books.- Trend Models and Estimation.- Empirical Trend Estimation.- Regression Analysis.- Global Trend Models.- Local Trend Models.- Trend Estimation based on Physical Information.- Trend Based on the Laplace Equation.- Basic Notions of Random Fields.- Introduction.- Single-Point Description.- Stationarity and Statistical Homogeneity.- Variogram versus Covariance.- Permissibility of Covariance Functions.- Permissibility of Variogram Functions.- Additional Topics of Random Field Modeling.- Ergodicity.- Statistical Isotropy.- Anisotropy.- Anisotropic Spectral Densities.- Multipoint Description of Random Fields.- Geometric Properties of Random Fields.- Local Properties.- Covariance Hessian Identity and Geometric Anisotropy.- Spectral Moments.- Length Scales of Random Fields.- Fractal Dimension.- Long-Range Dependence.- Intrinsic Random Fields.- Fractional Brownian Motion.- Classification of Random Fields.- Gaussian Random Fields.- Multivariate Normal Distribution.- Field Integral Formulation.- Useful Properties of Gaussian Random Fields.- Perturbation Theory for Non-Gaussian Probability Densities.- Non-stationary Covariance Functions.- Further Reading.- Random Fields based on Local Interactions.- Spartan Spatial Random Fields.- Two-point Functions and Realizations.- Statistical and Geometric Properties.- Bessel-Lommel Covariance Functions.- Lattice Representations of Spartan Random Fields.- Introduction to Gauss-Markov Random Fields.- From Spartan Random Fields to Gauss-Markov Random Fields.- Lattice Spectral Density.- SSRF Lattice Moments.- SSRF Inverse Covariance Operator on Lattices.- Spartan Random Fields and Langevin Equations.- Introduction to Stochastic Differential Equations.- Classical Harmonic Oscillator.- Stochastic Partial Differential Equations.- Spartan Random Fields and Stochastic Partial Differential Equations.- Covariance and Green’s functions.- Whittle-Matérn Stochastic Partial Differential Equation.- Diversion in Time Series.- Spatial Prediction Fundamentals.- General Principles of Linear Prediction.- Deterministic Interpolation.- Stochastic Methods.- Simple Kriging.- Ordinary Kriging.- Properties of the Kriging Predictor.- Topics Related to the Application of Kriging.- Evaluating Model Performance.- More on Spatial Prediction.- Linear Generalizations of Kriging.- Nonlinear Extensions of Kriging.- Connections with Gaussian Process Regression.- Bayesian Kriging.- Continuum Formulation of Linear Prediction.- The “Local-Interaction” Approach.- Big Spatial Data.- Basic Concepts and Methods of Estimation.- Estimator Properties.- Estimating the Mean with Ordinary Kriging.- Variogram Estimation.- Maximum Likelihood Estimation.- Cross Validation.- More on Estimation.- The Method of Normalized Correlations.- The Method of Maximum Entropy.- Stochastic Local Interactions.- Measuring Ergodicity.- Beyond the Gaussian Models.- Trans-Gaussian Random Fields.- Gaussian Anamorphosis.- Tukey g-h Random Fields.- Transformations based on Kappa Exponentials.- Hermite Polynomials.- Multivariate Student’s t-distribution.- Copula Models.- The Replica Method.- Binary Random Fields.- The Indicator Random Field.- Ising Model.- Generalized Linear Models.- Simulations.- Introduction.- Covariance Matrix Factorization.- Spectral Simulation Methods.- Fast-Fourier-Transform Simulation.- Randomized Spectral Sampling.- Conditional Simulation based on Polarization Method.- Conditional Simulation based on Covariance Matrix Factorization.- Monte Carlo Methods.- Sequential Simulation of Random Fields.- Simulated Annealing.- Karhunen-Loève Expansion.- Karhunen-Loève Expansion of Spartan Random Fields.- Epilogue.- A Jacobi’s Transformation Theorems.- B Tables of SSRF Properties.- C Linear Algebra Facts.- D Kolmogorov-Smirnov Test.- Glossary.- References.- Index.

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Book SynopsisThis Finite Element Method offers a fundamental and practical introduction to the finite element method, its variants, and their applications in engineering. Every concept is introduced in the simplest possible setting, while maintaining a level of treatment that is as rigorous as possible without being unnecessarily abstract. Various finite elements in one, two, and three space dimensions are introduced, and their applications to elliptic, parabolic, hyperbolic, and nonlinear equations and to solid mechanics, fluid mechanics, and porous media flow problems are addressed. The variants include the control volume, multipoint flux approximation, nonconforming, mixed, discontinuous, characteristic, adaptive, and multiscale finite element methods. Illustrative computer programs in Fortran and C++ are described. An extensive set of exercises are provided in each chapter. This book serves as a text a for one-semester course for upper-level undergraduates and beginning graduate students and as a professional reference for engineers, mathematicians, and scientists.Table of ContentsOne-Dimensional Model Problems; Two-Dimensional Model Problems; General Variational Formulation; One-Dimensional Elements and Their Properties; Two-Dimensional Elements and Their Properties; Three-Dimensional Elements and Their Properties; Finite Elements for Transient and Nonlinear Problems; Application to Solid Mechanics; Application to Fluid Mechanics; Application to Porous Media Flow; Other Finite Element Methods.

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Book SynopsisDiscrete Signals and Inverse Problems Discrete Signals and Inverse Problems examines fundamental concepts necessary to engineers and scientists working with discrete signal processing and inverse problem solving, and places emphasis on the clear understanding of algorithms within the context of application needs. Based on the original Introduction to Discrete Signals and Inverse Problems in Civil Engineering', this expanded and enriched version: combines discrete signal processing and inverse problem solving in one book covers the most versatile tools that are needed to process engineering and scientific data presents step-by-step implementation procedures' for the most relevant algorithms provides instructive figures, solved examples and insightful exercises Discrete Signals and Inverse Problems is essential reading for experimental researchers and practicing engineers in civil, mechanical and electrical engineTable of ContentsPreface xi Brief Comments on Notation xiii 1 Introduction 1 1.1 Signals, Systems, and Problems 1 1.2 Signals and Signal Processing – Application Examples 3 1.3 Inverse Problems – Application Examples 8 1.4 History – Discrete Mathematical Representation 10 1.5 Summary 12 Solved Problems 12 Additional Problems 14 2 Mathematical Concepts 17 2.1 Complex Numbers and Exponential Functions 17 2.2 Matrix Algebra 21 2.3 Derivatives – Constrained Optimization 28 2.4 Summary 29 Further Reading 29 Solved Problems 30 Additional Problems 33 3 Signals and Systems 35 3.1 Signals: Types and Characteristics 35 3.2 Implications of Digitization – Aliasing 40 3.3 Elemental Signals and Other Important Signals 45 3.4 Signal Analysis with Elemental Signals 49 3.5 Systems: Characteristics and Properties 53 3.6 Combination of Systems 57 3.7 Summary 59 Further Reading 59 Solved Problems 60 Additional Problems 63 4 Time Domain Analyses of Signals and Systems 65 4.1 Signals and Noise 65 4.2 Cross- and Autocorrelation: Identifying Similarities 77 4.3 The Impulse Response – System Identification 85 4.4 Convolution: Computing the Output Signal 89 4.5 Time Domain Operations in Matrix Form 94 4.6 Summary 96 Further Reading 96 Solved Problems 97 Additional Problems 99 5 Frequency Domain Analysis of Signals (Discrete Fourier Transform) 103 5.1 Orthogonal Functions – Fourier Series 103 5.2 Discrete Fourier Analysis and Synthesis 107 5.3 Characteristics of the Discrete Fourier Transform 112 5.4 Computation in Matrix Form 119 5.5 Truncation, Leakage, and Windows 121 5.6 Padding 123 5.7 Plots 125 5.8 The Two-Dimensional Discrete Fourier Transform 127 5.9 Procedure for Signal Recording 128 5.10 Summary 130 Further Reading and References 131 Solved Problems 131 Additional Problems 134 6 Frequency Domain Analysis of Systems 137 6.1 Sinusoids and Systems – Eigenfunctions 137 6.2 Frequency Response 138 6.3 Convolution 142 6.4 Cross-Spectral and Autospectral Densities 147 6.5 Filters in the Frequency Domain – Noise Control 151 6.6 Determining H with Noiseless Signals (Phase Unwrapping) 156 6.7 Determining H with Noisy Signals (Coherence) 160 6.8 Summary 168 Further Reading and References 169 Solved Problems 169 Additional Problems 172 7 Time Variation and Nonlinearity 175 7.1 Nonstationary Signals: Implications 175 7.2 Nonstationary Signals: Instantaneous Parameters 179 7.3 Nonstationary Signals: Time Windows 184 7.4 Nonstationary Signals: Frequency Windows 188 7.5 Nonstationary Signals: Wavelet Analysis 191 7.6 Nonlinear Systems: Detecting Nonlinearity 197 7.7 Nonlinear Systems: Response to Different Excitations 200 7.8 Time-Varying Systems 204 7.9 Summary 207 Further Reading and References 209 Solved Problems 209 Additional Problems 212 8 Concepts in Discrete Inverse Problems 215 8.1 Inverse Problems – Discrete Formulation 215 8.2 Linearization of Nonlinear Problems 227 8.3 Data-Driven Solution – Error Norms 228 8.4 Model Selection – Ockham’s Razor 234 8.5 Information 238 8.6 Data and Model Errors 240 8.7 Nonconvex Error Surfaces 241 8.8 Discussion on Inverse Problems 242 8.9 Summary 243 Further Reading and References 244 Solved Problems 244 Additional Problems 246 9 Solution by Matrix Inversion 249 9.1 Pseudoinverse 249 9.2 Classification of Inverse Problems 250 9.3 Least Squares Solution (LSS) 253 9.4 Regularized Least Squares Solution (RLSS) 255 9.5 Incorporating Additional Information 262 9.6 Solution Based on Singular Value Decomposition 265 9.7 Nonlinearity 267 9.8 Statistical Concepts – Error Propagation 268 9.9 Experimental Design for Inverse Problems 272 9.10 Methodology for the Solution of Inverse Problems 274 9.11 Summary 275 Further Reading 276 Solved Problems 277 Additional Problems 282 10 Other Inversion Methods 285 10.1 Transformed Problem Representation 286 10.2 Iterative Solution of System of Equations 293 10.3 Solution by Successive Forward Simulations 298 10.4 Techniques from the Field of Artificial Intelligence 301 10.5 Summary 308 Further Reading 308 Solved Problems 309 Additional Problems 312 11 Strategy for Inverse Problem Solving 315 11.1 Step 1: Analyze the Problem 315 11.2 Step 2: Pay Close Attention to Experimental Design 320 11.3 Step 3: Gather High-quality Data 321 11.4 Step 4: Preprocess the Data 321 11.5 Step 5: Select an Adequate Physical Model 327 11.6 Step 6: Explore Different Inversion Methods 330 11.7 Step 7: Analyze the Final Solution 338 11.8 Summary 338 Solved Problems 339 Additional Problems 342 Index 347

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Book SynopsisThe objective of this book is to motivate an appreciation of contemporary statistical techniques within the context of engineering. The author presents an optimum blend between statistical thinking and statistical methodology through emphasis of a broad sweep of tools rather than endless streams of seemingly unrelated methods and formulae.Trade Review"Overall this is an excellent book, which defines a broader mandate than many of its competing texts. By providing, clear, understandable discussion of the basics of statistics through to more advanced methods commonly used by engineers, this book is an essential reference for practitioners, and an ideal text for a two semester course introducing engineers to the power and utility of statistics." (The American Statistician, August 2008) "In this book on modern engineering statistics, Ryan does an excellent job of providing the appropriate statistical concepts and tools using engineering resources.... Highly recommended. Lower- and upper-division undergraduates" (CHOICE, April 2008) "This self-contained volume motivates an appreciation of statistical techniques within the context of engineering; many datasets that are used in the chapters and exercises are from engineering sources. This book is ideal for either a one- or two-semester course in engineering statistics." (Computing Reviews, April 2008)Table of ContentsPreface xvii 1. Methods of Collecting and Presenting Data 1 1.1 Observational Data and Data from Designed Experiments 3 1.2 Populations and Samples 5 1.3 Variables 6 1.4 Methods of Displaying Small Data Sets 7 1.5 Methods of Displaying Large Data Sets 16 1.6 Outliers 22 1.7 Other Methods 22 1.8 Extremely Large Data Sets: Data Mining 23 1.9 Graphical Methods: Recommendations 23 1.10 Summary 24 References 24 Exercises 25 2. Measures of Location and Dispersion 45 2.1 Estimating Location Parameters 46 2.2 Estimating Dispersion Parameters 50 2.3 Estimating Parameters from Grouped Data 55 2.4 Estimates from a Boxplot 57 2.5 Computing Sample Statistics with MINITAB 58 2.6 Summary 58 Reference 58 Exercises 58 3. Probability and Common Probability Distributions 68 3.1 Probability: From the Ethereal to the Concrete 68 3.3 Common Discrete Distributions 76 3.4 Common Continuous Distributions 92 3.5 General Distribution Fitting 106 3.6 How to Select a Distribution 107 3.7 Summary 108 References 109 Exercises 109 4. Point Estimation 121 4.1 Point Estimators and Point Estimates 121 4.2 Desirable Properties of Point Estimators 121 4.3 Distributions of Sampling Statistics 125 4.4 Methods of Obtaining Estimators 128 4.5 Estimating σθ 132 4.6 Estimating Parameters Without Data 133 4.7 Summary 133 References 134 Exercises 134 5. Confidence Intervals and Hypothesis Tests—One Sample 140 5.1 Confidence Interval for μ: Normal Distribution σ Not Estimated from Sample Data 140 5.2 Confidence Interval for μ: Normal Distribution σ Estimated from Sample Data 146 5.3 Hypothesis Tests for μ: Using Z and t 147 5.4 Confidence Intervals and Hypothesis Tests for a Proportion 157 5.5 Confidence Intervals and Hypothesis Tests for σ2 and σ 161 5.6 Confidence Intervals and Hypothesis Tests for the Poisson Mean 164 5.7 Confidence Intervals and Hypothesis Tests When Standard Error Expressions are Not Available 166 5.8 Type I and Type II Errors 168 5.9 Practical Significance and Narrow Intervals: The Role of n 172 5.10 Other Types of Confidence Intervals 173 5.11 Abstract of Main Procedures 174 5.12 Summary 175 Appendix: Derivation 176 References 176 Exercises 177 6. Confidence Intervals and Hypothesis Tests—Two Samples 189 6.1 Confidence Intervals and Hypothesis Tests for Means: Independent Samples 189 6.2 Confidence Intervals and Hypothesis Tests for Means: Dependent Samples 197 6.3 Confidence Intervals and Hypothesis Tests for Two Proportions 200 6.4 Confidence Intervals and Hypothesis Tests for Two Variances 202 6.5 Abstract of Procedures 204 6.6 Summary 205 References 205 Exercises 205 7. Tolerance Intervals and Prediction Intervals 214 7.1 Tolerance Intervals: Normality Assumed 215 7.2 Tolerance Intervals and Six Sigma 219 7.3 Distribution-Free Tolerance Intervals 219 7.4 Prediction Intervals 221 7.5 Choice Between Intervals 227 7.6 Summary 227 References 228 Exercises 229 8. Simple Linear Regression Correlation and Calibration 232 8.1 Introduction 232 8.2 Simple Linear Regression 232 8.3 Correlation 254 8.4 Miscellaneous Uses of Regression 256 8.5 Summary 264 References 264 Exercises 265 9. Multiple Regression 276 9.1 How Do We Start? 277 9.2 Interpreting Regression Coefficients 278 9.3 Example with Fixed Regressors 279 9.4 Example with Random Regressors 281 9.5 Example of Section 8.2.4 Extended 291 9.6 Selecting Regression Variables 293 9.7 Transformations 299 9.8 Indicator Variables 300 9.9 Regression Graphics 300 9.10 Logistic Regression and Nonlinear Regression Models 301 9.11 Regression with Matrix Algebra 302 9.12 Summary 302 References 303 Exercises 304 10. Mechanistic Models 314 10.1 Mechanistic Models 315 10.2 Empirical–Mechanistic Models 316 10.3 Additional Examples 324 10.4 Software 325 10.5 Summary 326 References 326 Exercises 327 11. Control Charts and Quality Improvement 330 11.1 Basic Control Chart Principles 330 11.2 Stages of Control Chart Usage 331 11.3 Assumptions and Methods of Determining Control Limits 334 11.4 Control Chart Properties 335 11.5 Types of Charts 336 11.6 Shewhart Charts for Controlling a Process Mean and Variability (Without Subgrouping) 336 11.7 Shewhart Charts for Controlling a Process Mean and Variability (With Subgrouping) 344 11.8 Important Use of Control Charts for Measurement Data 349 11.9 Shewhart Control Charts for Nonconformities and Nonconforming Units 349 11.10 Alternatives to Shewhart Charts 356 11.11 Finding Assignable Causes 359 11.12 Multivariate Charts 362 11.13 Case Study 362 11.14 Engineering Process Control 364 11.15 Process Capability 365 11.16 Improving Quality with Designed Experiments 366 11.17 Six Sigma 367 11.18 Acceptance Sampling 368 11.19 Measurement Error 368 11.20 Summary 368 References 369 Exercises 370 12. Design and Analysis of Experiments 382 12.1 Processes Must be in Statistical Control 383 12.2 One-Factor Experiments 384 12.3 One Treatment Factor and at Least One Blocking Factor 392 12.4 More Than One Factor 395 12.5 Factorial Designs 396 12.6 Crossed and Nested Designs 405 12.7 Fixed and Random Factors 406 12.8 ANOM for Factorial Designs 407 12.9 Fractional Factorials 409 12.10 Split-Plot Designs 413 12.11 Response Surface Designs 414 12.12 Raw Form Analysis Versus Coded Form Analysis 415 12.13 Supersaturated Designs 416 12.14 Hard-to-Change Factors 416 12.15 One-Factor-at-a-Time Designs 417 12.16 Multiple Responses 418 12.17 Taguchi Methods of Design 419 12.18 Multi-Vari Chart 420 12.19 Design of Experiments for Binary Data 420 12.20 Evolutionary Operation (EVOP) 421 12.21 Measurement Error 422 12.22 Analysis of Covariance 422 12.23 Summary of MINITAB and Design-Expert® Capabilities for Design of Experiments 422 12.24 Training for Experimental Design Use 423 12.25 Summary 423 Appendix A Computing Formulas 424 Appendix B Relationship Between Effect Estimates and Regression Coefficients 426 References 426 Exercises 428 13. Measurement System Appraisal 441 13.1 Terminology 442 13.2 Components of Measurement Variability 443 13.3 Graphical Methods 449 13.4 Bias and Calibration 449 13.5 Propagation of Error 454 13.6 Software 455 13.7 Summary 456 References 456 Exercises 457 14. Reliability Analysis and Life Testing 460 14.1 Basic Reliability Concepts 461 14.2 Nonrepairable and Repairable Populations 463 14.3 Accelerated Testing 463 14.4 Types of Reliability Data 466 14.5 Statistical Terms and Reliability Models 467 14.6 Reliability Engineering 473 14.7 Example 474 14.8 Improving Reliability with Designed Experiments 474 14.9 Confidence Intervals 477 14.10 Sample Size Determination 478 14.11 Reliability Growth and Demonstration Testing 479 14.12 Early Determination of Product Reliability 480 14.13 Software 480 14.14 Summary 481 References 481 Exercises 482 15. Analysis of Categorical Data 487 15.1 Contingency Tables 487 15.2 Design of Experiments: Categorical Response Variable 497 15.3 Goodness-of-Fit Tests 498 15.4 Summary 500 References 500 Exercises 501 16. Distribution-Free Procedures 507 16.1 Introduction 507 16.2 One-Sample Procedures 508 16.3 Two-Sample Procedures 512 16.4 Nonparametric Analysis of Variance 514 16.5 Exact Versus Approximate Tests 519 16.6 Nonparametric Regression 519 16.7 Nonparametric Prediction Intervals and Tolerance Intervals 521 16.8 Summary 521 References 521 Exercises 522 17. Tying It All Together 525 17.1 Review of Book 525 17.2 The Future 527 17.3 Engineering Applications of Statistical Methods 528 Reference 528 Exercises 528 Answers to Selected Excercises 533 Appendix: Statistical Tables 562 Table A Random Numbers 562 Table B Normal Distribution 564 Table C t-Distribution 566 Table D F-Distribution 567 Table E Factors for Calculating Two-Sided 99% Statistical Intervals for a Normal Population to Contain at Least 100p% of the Population 570 Table F Control Chart Constants 571 Author Index 573 Subject Index 579

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Book SynopsisThe objective of this book is to motivate an appreciation of contemporary statistical techniques within the context of engineering. The author presents an optimum blend between statistical thinking and statistical methodology through emphasis of a broad sweep of tools rather than endless streams of seemingly unrelated methods and formulae.Table of Contents1. Methods of Collecting and Presenting Data. 2. Measures of Location and Dispersion. 3. Probability and Common Probability Distributions. 4. Point Estimation. 5. Confidence Intervals an Hypothesis test - One Sample. 6. Confidence intervals and Hypothesis Tests-Two Samples. 7. Tolerance Intervals an Prediction Intervals. 8. Simple Linear Regression, Correlation and Calibration. 9. Multiple Regression. 10. Mechanistic Models. 11. Control Charts and Quality Improvement. 12. Design and Analysis of Experiments. 13. Measurement System Appraisal. 14. Reliability Analysis and Life Testing. 15. Analysis of Categorical Data. 16. Distribution-Free Procedures. 17. Tying It All Together.

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Book SynopsisThe only handbook of mathematical relations with a focus on particulate materials processing The National Science Foundation estimates that over 35% of materials-related funding is now directed toward modeling. In part, this reflects the increased knowledge and the high cost of experimental work.Trade Review"Suited for quick reference with stand alone definitions. It is the perfect complement to existing textbooks since it will simply cut to the key relations. " (Alamogordo Daily News, 16 March 2011) Table of ContentsPARTIAL TABLE OF CONTENTS Foreword. About the Authors. A Abnormal Grain Growth. Abrasive Wearâ??See Friction and Wear Testing. Acceleration of Free-settling Particles. Activated Sintering, Early-stage Shrinkage. Activation Energyâ??See Arrhenius Relation. Adsorptionâ??See BET Specific Surface Area. Agglomerate Strength. Agglomeration Force. Agglomeration of Nanoscale Particlesâ??See Nanoparticle Agglomeration. Andreasen Size Distribution. B Ball Millingâ??See Jar Milling. Bearing Strength. Bell Curveâ??See Gaussian Distribution. Bending-beam Viscosity. Bending Test. BET Equivalent Spherical-particle Diameter. BET Specific Surface Area. Bimodal Powder Packing. Bimodal Powder Sintering. Binder Burnoutâ??See Polymer Pyrolysis. C Cantilever-beam Testâ??See Bending-beam Viscosity. Capillarity. Capillarity-induced Sinteringâ??See Surface Curvature-Driven Mass Flow in Sintering. Capillary Pressure during Liquid-phase Sinteringâ??See Mean Capillary Pressure. Capillary Riseâ??See Washburn Equation. Capillary Stressâ??See Laplace Equation. Case Carburization. Casson Model. Cemented-carbide Hardness. Centrifugal Atomization Droplet Size. D Darcyâ??s Law. Debindingâ??See Polymer Pyrolysis, Solvent Debinding Time, Thermal Debinding Time, Vacuum Thermal Debinding Time, and Wicking. Debinding Master Curveâ??See Master Decomposition Curve. Debinding Temperature. Debinding Timeâ??See Solvent Debinding Time, Thermal Debinding Time, Vacuum Thermal Debinding Time, and Wicking. Debinding by Solvent Immersionâ??See Solvent Debinding Time. Debinding Weight Loss. Delubricationâ??See Polymer Pyrolysis. Densification. Densification in Liquid-phase Sinteringâ??See Dissolution-induced Densification. E Effective Pressure. Ejection Stressâ??See Maximum Ejection Stress. Elastic Behaviorâ??See Hookeâ??s Law. Elastic deformation Neck-size Ratio. Elastic-modulus Variation with Density. Elastic-property Variation with Porosity. Electrical-conductivity Variation with Porosity. Electromigration Contributions to Spark Sintering. Elongation. Elongation Variation with Densityâ??See Sintered Ductility. F Feedstock Formulation. Feedstock Viscosityâ??See Suspension Viscosity and Viscosity Model for Infection-molding Feedstock. Feedstock Viscosity as a Function of Shear Rateâ??See Cross Model. Feedstock Yield Strengthâ??See Yield Strength of Particle-Polymer Feedstock. Fiber-fracture from Buckling. Fiber-fracture Probability. Fiber Packing Density. Fickâ??s First Law. Fickâ??s Second Law. Field-activated Sintering. G Gas-absorption Surface Areaâ??See BET Specific Surface Area. Gas-atomization Cooling Rate. Gas-atomization Melt Flow Rate. Gas-atomization Particle Size. Gas-generated Final Pores. Gas Permeabilityâ??See Kozeny-Carman Equation. Gate Strain Rate in Injection Molding. Gaudin-Schuhmann distribution. Gaussian Distribution. Gel-densification Model. H Hall-Petch Relation. Hardenability Factor. Hardness. Hardness Variation with Grain Size in Cemented Carbides. Heating-rate Effect in Transient Liquid-phase Sintering. Heat Transfer in Sintered Materials. Heat-transfer Rate in Modelingâ??See Cooling Rate in Molding. Herring Scaling Law. Hertzian stressâ??See Elastic Deformation Neck-size Ratio. Heterodiffusionâ??See Mixed-powder Sintering Shrinkage. I Impregnationâ??See Infiltration Pressure. Inertial-flow Equation. Infiltration Depth. Infiltration Pressure. Infiltration Rate. Inhibited Grain Growthâ??See Zener Relation. Initial-stage Liquid-phase Sintering Stressâ??See Sintering Stress in Initial-stage Liquid-phase Sintering. Initial-stage Neck Growth. Initial-stage Sinteringâ??See Surface Diffusion-Controlled Neck Growth. Initial-stage Sintering Modelâ??See Kuczynski Neck-growth Model. J Jar Milling. Jet Mixing Time. K Kawakita Equation. Kelvin Equation. Kelvin Modelâ??See Viscoelastic Model for Powder-Polymer Mixtures. K-Factor. Kingery Intermediate-stage Liquid-phase Sintering Modelâ??See Intermediateâ??stage Liquid-phase Sintering Model. Kingery Model for Pressure-assisted Liquid-phase Sinteringâ??See Pressure-assisted Liquid-phase Sintering. Kingery Rearrangement Shrinkage Kineticsâ??See Rearrangement Kinetics in Initial-stage Liquid-phase Sintering. Kissinger Method. Knoop Hardness. Knudsen Diffusionâ??See Vapor Mean Free Path. L Laminar Flow Settlingâ??See Stokesâ?? Law. Laplace Equation. Laplace Numberâ??See Suratman Number. Laser Sintering. Lattice Diffusionâ??See Vacancy Diffusion. Lifschwiz, Slyozov, Wagner Model. Ligament Pinchingâ??See Raleigh Instability. Limiting Neck Size. Limiting Size for Sedimentation Analysis. Liquid and Solid Compositions in Prealloy Particle Melting. M Macroscopic Sintering Model Constitutive Equations. Magnetic Coercivity Correlation in Cemented Carbides. Mass Flow Rate in Atomizationâ??See Gas-atomization Melt Flow Rate. Master Decomposition Curve. Master Sintering Curve. Master Sintering Curve for Grain Growthâ??See Grain-growth Master Curve. Maximum Density in Pressure-assisted Sintering. Maximum Ejection Stress. Maximum Grain Size in Sintering. Maximum Lubricant Content. N Nabarro-Herring Creep-controlled Pressure-assisted Densification. Nanoparticle Agglomeration. Nanoparticle Melting-point Depression. Nanoscale Particle-Agglomerate Spheroidization. Nanoscale Particle-size Effect on Surface Energyâ??See Surface-energy variation with Droplet Size. Neck-curvature Stress. Neck Growth Early in Liquid-phase Sintering. Neck Growth-induced Shrinkageâ??See Shrinkage Relation to Neck Size. Neck Growth Limited by Grain Growth. Neck-growth Modelâ??See Kuczynski neck-growth Model. O Open-pore Content. Optimal Packing Particle-size Distributionâ??See Andreasen Size Distribution. Optimal Mixer Rotational Speed. Ordered Packing. Osprey Processâ??See Spray Deposition. Ostwald Ripening. Oxide Reduction. P Packing Density for Log-normal Particles. Particle Cooling in Atomizationâ??See Newtonian Cooling Approximation. Particle Coordination Numberâ??See Coordination Number and Density. Particle Diffusion in Mixing. Particle Fracture in Milling. Particle Packing. Particle-shape Index. Particle Sizeâ??See Equivalent Spherical Diameter and Mean Particle Size. Particle-size Analysisâ??See Sieve Progression. Particle size and Apparent Density. Q Quantitative-microscopy Determination of Surface Areaâ??See Surface Area by Quantitative Microscopy. Quasi-3-dimensional Energy-governing Equation for Powder Injection Moldingâ??See Energy-governing Equation for Powder Injection Molding. Quasi-3-dimensional Pressure-governing Equation for Powder Injection Modelingâ??See Pressure-governing Equation in Powder Injection Molding. Quasi-3-dimensional Pressure-governing Equation for Powder Injection Molding with Slip-layer Modelâ??See Pressure-governing Equation in Powder Injection Molding with Slip-layer Model. Quasi-3-dimensional Pressure-governing Equation for Powder Injection Molding with Slip-velocity Modelâ??See Pressure-governing Equation in 2.5 Dimensions for Powder Injection Molding with Slip-velocity Model. R Radial Crush Strengthâ??See Bearing Strength. Radiant Heating. Raleigh Instability. Random Packing Density. Random Packing Radial-distribution Function. Reaction-controlled Grain Growthâ??See Grain-growth Master Curve, Interfacial Reaction Control, and Interface-controlled Grain Growth. Reaction-rate Equationâ??See Avrami Equation. Reactive Synthesis. Rearrangement Kinetics in Liquid-phase Sintering. Recalescence Temperature. S Saddle-surface Stressâ??See Neck-curvature Stress. Scherrer Formula. Screen Sizesâ??See Sieve Progression. Secondary Dendrite-Arm Spacing. Secondary Recrystallizationâ??See Abnormal Grain Growth. Second-stage Liquid-phase Sintering Modelâ??See Intermediate-stage Liquid-phase Sintering Model. Second-stage Sintering Densificationâ??See Intermediate-stage Sintering-density Model. Second-stage Sintering Pore Eliminationâ??See Intermediate-stage Pore Elimination. Second-stage Sintering Surface-area Reductionâ??See Intermediate-stage Surface-area Reduction. Sedimentation Particle-size Analysisâ??See Stokesâ?? Law Particle-size Analysis. T Tap Densityâ??See Vibration-induced Particle Packing. Temperature Adjustments for Equivalent Sintering. Temperature Dependenceâ??See Arrhenius Relation. Terminal Densityâ??See Final-stage Sintering Limited Density. Terminal Neck Sizeâ??See Neck Growth Limited by Grain Growth. Terminal Neck Size in Sinteringâ??See Limiting Neck Size. Terminal Pore Sizeâ??See Final-stage Pore Size. Terminal Settling Velocityâ??See Stokesâ?? Law. Terminal Sinteringâ??See Trapped-gas Pore Stabilization. Terminal Velocityâ??See Acceleration of Free-settling Particles. U Ultrasonic Velocity. V Vacancy Concentration Dependence on Surface Curvature. Vacancy Diffusion. Vacuum Debindingâ??See Vacuum Thermal Debinding. Vacuum Distillation Rate. Vacuum Flux in Sintering. Vacuum Thermal Debinding. Vapor Mean Free Path. Vapor Pressure. Vibration-induced Particle Packing. Vickers Hardness Number. W Washburn Equation. Water-atomization Particle Size. Water Immersion Densityâ??See Archimedes Density. Weber Number. Weibull Distribution. Wetting Angle. Wicking. Work Hardeningâ??See Strain Hardening. Work of Sinteringâ??See Master Sintering Curve. X X-ray Line Broadeningâ??See Scherrer Formula. Y Yield Strength in Viscous Flowâ??See Bingham Viscous-flow Model. Yield Strength of Particleâ??Polymer Feedstock Youngâ??s Equationâ??See Contact Angle and Wetting Angle. Youngâ??s Modulusâ??See Elastic Modulus. Z Zener Relation. Zeta Potential. Appendix. References.

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Book SynopsisThis text summarizes the core undergraduate physics curriculum together with the mathematics frequently encountered in engineering and physics calculations. The author emphasizes fundamental formulas and derivations and provides simple, coherent explanations of the underlying concepts.Trade ReviewThis book is an excellent study guide for students, and a good reference book for working professionals who may need a convenient source for fundamental equations on various topics (IEEE Electrical Insulation Magazine 2016)Table of Contents1 Introduction 1 2 Problem Solving 3 2.1 Analysis 3 2.2 Test-Taking Techniques 4 2.2.1 Dimensional Analysis 5 3 Scientific Programming 6 3.1 Language Fundamentals 6 3.1.1 Octave Programming 7 4 Elementary Mathematics 12 4.1 Algebra 12 4.1.1 Equation Manipulation 12 4.1.2 Linear Equation Systems 13 4.1.3 Factoring 14 4.1.4 Inequalities 15 4.1.5 Sum Formulas 16 4.1.6 Binomial Theorem 17 4.2 Geometry 17 4.2.1 Angles 18 4.2.2 Triangles 18 4.2.3 Right Triangles 19 4.2.4 Polygons 20 4.2.5 Circles 20 4.3 Exponential, Logarithmic Functions, and Trigonometry 21 4.3.1 Exponential Functions 21 4.3.2 Inverse Functions and Logarithms 21 4.3.3 Hyperbolic Functions 22 4.3.4 Complex Numbers and Harmonic Functions 23 4.3.5 Inverse Harmonic and Hyperbolic Functions 25 4.3.6 Trigonometric Identities 26 4.4 Analytic Geometry 28 4.4.1 Lines and Planes 28 4.4.2 Conic Sections 29 4.4.3 Areas, Volumes, and Solid Angles 31 5 Vectors and Matrices 32 5.1 Matrices and Matrix Products 32 5.2 Equation Systems 34 5.3 Traces and Determinants 35 5.4 Vectors and Inner Products 38 5.5 Cross and Outer Products 40 5.6 Vector Identities 41 5.7 Rotations and Orthogonal Matrices 42 5.8 Groups and Matrix Generators 43 5.9 Eigenvalues and Eigenvectors 45 5.10 Similarity Transformations 48 6 Calculus of a Single Variable 50 6.1 Derivatives 50 6.2 Integrals 54 6.3 Series 60 7 Calculus of Several Variables 62 7.1 Partial Derivatives 62 7.2 Multidimensional Taylor Series and Extrema 66 7.3 Multiple Integration 67 7.4 Volumes and Surfaces of Revolution 69 7.5 Change of Variables and Jacobians 70 8 Calculus of Vector Functions 72 8.1 Generalized Coordinates 72 8.2 Vector Differential Operators 77 8.3 Vector Differential Identities 81 8.4 Gauss’s and Stokes’ Laws and Green’s Identities 82 8.5 Lagrange Multipliers 83 9 Probability Theory and Statistics 85 9.1 Random Variables, Probability Density, and Distributions 85 9.2 Mean, Variance, and Standard Deviation 86 9.3 Variable Transformations 86 9.4 Moments and Moment-Generating Function 86 9.5 Multivariate Probability Distributions, Covariance, and Correlation 87 9.6 Gaussian, Binomial, and Poisson Distributions 87 9.7 Least Squares Regression 91 9.8 Error Propagation 92 9.9 Numerical Models 93 10 Complex Analysis 94 10.1 Functions of a Complex Variable 94 10.2 Derivatives, Analyticity, and the Cauchy–Riemann Relations 95 10.3 Conformal Mapping 96 10.4 Cauchy’s Theorem and Taylor and Laurent Series 97 10.5 Residue Theorem 101 10.6 Dispersion Relations 105 10.7 Method of Steepest Decent 106 11 Differential Equations 108 11.1 Linearity, Superposition, and Initial and Boundary Values 108 11.2 Numerical Solutions 109 11.3 First-Order Differential Equations 112 11.4 Wronskian 114 11.5 Factorization 115 11.6 Method of Undetermined Coefficients 115 11.7 Variation of Parameters 116 11.8 Reduction of Order 118 11.9 Series Solution and Method of Frobenius 118 11.10 Systems of Equations, Eigenvalues, and Eigenvectors 119 12 Transform Theory 122 12.1 Eigenfunctions and Eigenvectors 122 12.2 Sturm–Liouville Theory 123 12.3 Fourier Series 125 12.4 Fourier Transforms 127 12.5 Delta Functions 128 12.6 Green’s Functions 131 12.7 Laplace Transforms 135 12.8 z-Transforms 137 13 Partial Differential Equations and Special Functions 138 13.1 Separation of Variables and Rectangular Coordinates 138 13.2 Legendre Polynomials 145 13.3 Spherical Harmonics 150 13.4 Bessel Functions 156 13.5 Spherical Bessel Functions 162 14 Integral Equations and the Calculus of Variations 166 14.1 Volterra and Fredholm Equations 166 14.2 Calculus of Variations the Euler-Lagrange Equation 168 15 Particle Mechanics 170 15.1 Newton’s Laws 170 15.2 Forces 171 15.3 Numerical Methods 173 15.4 Work and Energy 174 15.5 Lagrange Equations 176 15.6 Three-Dimensional Particle Motion 180 15.7 Impulse 181 15.8 Oscillatory Motion 181 15.9 Rotational Motion About a Fixed Axis 185 15.10 Torque and Angular Momentum 187 15.11 Motion in Accelerating Reference Systems 188 15.12 Gravitational Forces and Fields 189 15.13 Celestial Mechanics 191 15.14 Dynamics of Systems of Particles 193 15.15 Two-Particle Collisions and Scattering 197 15.16 Mechanics of Rigid Bodies 199 15.17 Hamilton’s Equation and Kinematics 206 16 Fluid Mechanics 210 16.1 Continuity Equation 210 16.2 Euler’s Equation 212 16.3 Bernoulli’s Equation 213 17 Special Relativity 215 17.1 Four-Vectors and Lorentz Transformation 215 17.2 Length Contraction, Time Dilation, and Simultaneity 217 17.3 Covariant Notation 219 17.4 Casuality and Minkowski Diagrams 221 17.5 Velocity Addition and Doppler Shift 222 17.6 Energy and Momentum 223 18 Electromagnetism 227 18.1 Maxwell’s Equations 227 18.2 Gauss’s Law 233 18.3 Electric Potential 235 18.4 Current and Resistivity 238 18.5 Dipoles and Polarization 241 18.6 Boundary Conditions and Green’s Functions 244 18.7 Multipole Expansion 248 18.8 Relativistic Formulation of Electromagnetism, Gauge Transformations, and Magnetic Fields 249 18.9 Magnetostatics 256 18.10 Magnetic Dipoles 259 18.11 Magnetization 260 18.12 Induction and Faraday’s Law 262 18.13 Circuit Theory and Kirchoff’s Laws 266 18.14 Conservation Laws and the Stress Tensor 270 18.15 Lienard–Wiechert Potentials 274 18.16 Radiation from Moving Charges 275 19 Wave Motion 282 19.1 Wave Equation 282 19.2 Propagation of Waves 284 19.3 Planar Electromagnetic Waves 286 19.4 Polarization 287 19.5 Superposition and Interference 288 19.6 Multipole Expansion for Radiating Fields 292 19.7 Phase and Group Velocity 295 19.8 Minimum Time Principle and Ray Optics 296 19.9 Refraction and Snell’s Law 297 19.10 Lenses 299 19.11 Mechanical Reflection 301 19.12 Doppler Effect and Shock Waves 302 19.13 Waves in Periodic Media 303 19.14 Conducting Media 304 19.15 Dielectric Media 306 19.16 Reflection and Transmission 307 19.17 Diffraction 311 19.18 Waveguides and Cavities 313 20 Quantum Mechanics 318 20.1 Fundamental Principles 318 20.2 Particle–Wave Duality 319 20.3 Interference of Quantum Waves 320 20.4 Schrödinger Equation 321 20.5 Particle Flux and Reflection 322 20.6 Wave Packet Propagation 324 20.7 Numerical Solutions 326 20.8 Quantum Mechanical Operators 328 20.9 Heisenberg Uncertainty Relation 331 20.10 Hilbert Space Representation 334 20.11 Square Well and Delta Function Potentials 336 20.12 WKB Method 339 20.13 Harmonic Oscillators 342 20.14 Heisenberg Representation 343 20.15 Translation Operators 344 20.16 Perturbation Theory 345 20.17 Adiabatic Theorem 351 21 Atomic Physics 353 21.1 Properties of Fermions 353 21.2 Bohr Model 354 21.3 Atomic Spectra and X-Rays 356 21.4 Atomic Units 356 21.5 Angular Momentum 357 21.6 Spin 358 21.7 Interaction of Spins 359 21.8 Hydrogenic Atoms 360 21.9 Atomic Structure 362 21.10 Spin–Orbit Coupling 362 21.11 Atoms in Static Electric and Magnetic Fields 364 21.12 Helium Atom and the H+2 Molecule 368 21.13 Interaction of Atoms with Radiation 371 21.14 Selection Rules 373 21.15 Scattering Theory 374 22 Nuclear and Particle Physics 379 22.1 Nuclear Properties 379 22.2 Radioactive Decay 381 22.3 Nuclear Reactions 382 22.4 Fission and Fusion 383 22.5 Fundamental Properties of Elementary Particles 383 23 Thermodynamics and Statistical Mechanics 386 23.1 Entropy 386 23.2 Ensembles 388 23.3 Statistics 391 23.4 Partition Functions 393 23.5 Density of States 396 23.6 Temperature and Energy 397 23.7 Phonons and Photons 400 23.8 The Laws of Thermodynamics 401 23.9 The Legendre Transformation and Thermodynamic Quantities 403 23.10 Expansion of Gases 407 23.11 Heat Engines and the Carnot Cycle 409 23.12 Thermodynamic Fluctuations 410 23.13 Phase Transformations 412 23.14 The Chemical Potential and Chemical Reactions 413 23.15 The Fermi Gas 414 23.16 Bose–Einstein Condensation 416 23.17 Physical Kinetics and Transport Theory 417 24 Condensed Matter Physics 422 24.1 Crystal Structure 422 24.2 X-Ray Diffraction 423 24.3 Thermal Properties 424 24.4 Electron Theory of Metals 425 24.5 Superconductors 426 24.6 Semiconductors 427 25 Laboratory Methods 430 25.1 Interaction of Particles with Matter 430 25.2 Radiation Detection and Counting Statistics 431 25.3 Lasers 432 Index 434

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Book SynopsisAn accessible introduction to metaheuristics and optimization, featuring powerful and modern algorithms for application across engineering and the sciences From engineering and computer science to economics and management science, optimization is a core component for problem solving. Highlighting the latest developments that have evolved in recent years, Engineering Optimization: An Introduction with Metaheuristic Applications outlines popular metaheuristic algorithms and equips readers with the skills needed to apply these techniques to their own optimization problems. With insightful examples from various fields of study, the author highlights key concepts and techniques for the successful application of commonly-used metaheuristc algorithms, including simulated annealing, particle swarm optimization, harmony search, and genetic algorithms. The author introduces all major metaheuristic algorithms and their applications in optimization through a presentation that isTable of ContentsList of Figures. Preface. Acknowledgments. Introduction. PART I Foundations of Optimization and Algorithms. 1.1 Before 1900. 1.2 Twentieth Century. 1.3 Heuristics and Metaheuristics. Exercises. 2 Engineering Optimization. 2.1 Optimization. 2.2 Type of Optimization. 2.3 Optimization Algorithms. 2.4 Metaheuristics. 2.5 Order Notation. 2.6 Algorithm Complexity. 2.7 No Free Lunch Theorems. Exercises. 3 Mathematical Foundations. 3.1 Upper and Lower Bounds. 3.2 Basic Calculus. 3.3 Optimality. 3.4 Vector and Matrix Norms. 3.5 Eigenvalues and Definiteness. 3.6 Linear and Affine Functions. 3.7 Gradient and Hessian Matrices. 3.8 Convexity. Exercises. 4 Classic Optimization Methods I. 4.1 Unconstrained Optimization. 4.2 Gradient-Based Methods. 4.3 Constrained Optimization. 4.4 Linear Programming. 4.5 Simplex Method. 4.6 Nonlinear Optimization. 4.7 Penalty Method. 4.8 Lagrange Multipliers. 4.9 Karush-Kuhn-Tucker Conditions. Exercises. 5 Classic Optimization Methods II. 5.1 BFGS Method. 5.2 Nelder-Mead Method. 5.3 Trust-Region Method. 5.4 Sequential Quadratic Programming. Exercises. 6 Convex Optimization. 6.1 KKT Conditions. 6.2 Convex Optimization Examples. 6.3 Equality Constrained Optimization. 6.4 Barrier Functions. 6.5 Interior-Point Methods. 6.6 Stochastic and Robust Optimization. Exercises. 7 Calculus of Variations. 7.1 Euler-Lagrange Equation. 7.2 Variations with Constraints. 7.3 Variations for Multiple Variables. 7.4 Optimal Control. Exercises. 8 Random Number Generators. 8.1 Linear Congruential Algorithms. 8.2 Uniform Distribution. 8.3 Other Distributions. 8.4 Metropolis Algorithms. Exercises. 9 Monte Carlo Methods. 9.1 Estimating p. 9.2 Monte Carlo Integration. 9.3 Importance of Sampling. Exercises. 10 Random Walk and Markov Chain. 10.1 Random Process. 10.2 Random Walk. 10.3 Lévy Flights. 10.4 Markov Chain. 10.5 Markov Chain Monte Carlo. 10.6 Markov Chain and Optimisation. Exercises. PART II Metaheuristic Algorithms. 11 Genetic Algorithms. 11.1 Introduction. 11.2 Genetic Algorithms. 11.3 Implementation. Exercises. 12 Simulated Annealing. 12.1 Annealing and Probability. 12.2 Choice of Parameters. 12.3 SA Algorithm. 12.4 Implementation. Exercises. 13 Ant Algorithms. 13.1 Behaviour of Ants. 13.2 Ant Colony Optimization. 13.3 Double Bridge Problem. 13.4 Virtual Ant Algorithm. Exercises. 14 Bee Algorithms. 14.1 Behavior of Honey Bees. 14.2 Bee Algorithms. 14.3 Applications. Exercises. 15 Particle Swarm Optimization. 15.1 Swarm Intelligence. 15.2 PSO algorithms. 15.3 Accelerated PSO. 15.4 Implementation. 15.5 Constraints. Exercises. 16 Harmony Search. 16.1 Music-Based Algorithms. 16.2 Harmony Search. 16.3 Implementation. Exercises. 17 Firefly Algorithm. 17.1 Behaviour of Fireflies. 17.2 Firefly-Inspired Algorithm. 17.3 Implementation. Exercises. PART III Applications. 18 Multiobjective Optimization. 18.1 Pareto Optimality. 18.2 Weighted Sum Method. 18.3 Utility Method. 18.4 Metaheuristic Search. 18.5 Other Algorithms. Exercises. 19 Engineering Applications. 19.1 Spring Design. 19.2 Pressure Vessel. 19.3 Shape Optimization. 19.4 Optimization of Eigenvalues and Frequencies. 19.5 Inverse Finite Element Analysis. Exercises. Appendices. Appendix A: Test Problems in Optimization. Appendix B: Matlab® Programs. B.1 Genetic Algorithms. B.2 Simulated Annealing. B.3 Particle Swarm Optimization. B.4 Harmony Search. B.5 Firefly Algorithm. B.6 Large Sparse Linear Systems. B.7 Nonlinear Optimization. B.7.1 Spring Design. B.7.2 Pressure Vessel. Appendix C: Glossary. Appendix D: Problem Solutions. References. Index.

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Book SynopsisThe concise yet authoritative presentation of key techniques for basic mixtures experiments Inspired by the author's bestselling advanced book on the topic, A Primer on Experiments with Mixtures provides an introductory presentation of the key principles behind experimenting with mixtures.Table of ContentsPreface ix 1. Introduction 1 1.1 The Original Mixture Problem 2 1.2 A Pesticide Example Involving Two Chemicals 2 1.3 General Remarks About Response Surface Methods 9 1.4 An Historical Perspective 13 References and Recommended Reading 17 Questions 17 Appendix 1A: Testing for Nonlinear Blending of the Two Chemicals Vendex and Kelthane While Measuring the Average Percent Mortality (APM) of Mites 20 2. The Original Mixture Problem: Designs and Models for Exploring the Entire Simplex Factor Space 23 2.1 The Simplex-Lattice Designs 23 2.2 The Canonical Polynomials 26 2.3 The Polynomial Coefficients as Functions of the Responses at the Points of the Lattices 31 2.4 Estimating The Parameters in the {q,m} Polynomials 34 2.5 Properties of the Estimate of the Response, ŷ(x) 37 2.6 A Three-Component Yarn Example Using A {3 2} Simplex-Lattice Design 38 2.7 The Analysis of Variance Table 42 2.8 Analysis of Variance Calculations of the Yarn Elongation Data 45 2.9 The Plotting of Individual Residuals 48 2.10 Testing the Degree of the Fitted Model: A Quadratic Model or Planar Model? 49 2.11 Testing Model Lack of Fit Using Extra Points and Replicated Observations 55 2.12 The Simplex-Centroid Design and Associated Polynomial Model 58 2.13 An Application of a Four-Component Simplex-Centroid Design: Blending Chemical Pesticides for Control of Mites 60 2.14 Axial Designs 62 2.15 Comments on a Comparison Made Between an Augmented Simplex-Centroid Design and a Full Cubic Lattice for Three Components Where Each Design Contains Ten Points 66 2.16 Reparameterizing Scheffé’s Mixture Models to Contain a Constant (β0) Term: A Numerical Example 69 2.17 Questions to Consider at the Planning Stages of a Mixture Experiment 77 2.18 Summary 78 References and Recommended Reading 78 Questions 80 Appendix 2A: Least-Squares Estimation Formula for the Polynomial Coefficients and Their Variances: Matrix Notation 85 Appendix 2B: Cubic and Quartic Polynomials and Formulas for the Estimates of the Coefficients 90 Appendix 2C: The Partitioning of the Sources in the Analysis of Variance Table When Fitting the Scheffé Mixture Models 91 3. Multiple Constraints on the Component Proportions 95 3.1 Lower-Bound Restrictions on Some or All of the Component Proportions 95 3.2 Introducing L-Pseudocomponents 97 3.3 A Numerical Example of Fitting an L-Pseudocomponent Model 99 3.4 Upper-Bound Restrictions on Some or All Component Proportions 101 3.5 An Example of the Placing of an Upper Bound on a Single Component: The Formulation of a Tropical Beverage 103 3.6 Introducing U-Pseudocomponents 107 3.7 The Placing of Both Upper and Lower Bounds on the Component Proportions 112 3.8 Formulas for Enumerating the Number of Extreme Vertices, Edges, and Two-Dimensional Faces of the Constrained Region 119 3.9 McLean and Anderson’s Algorithm for Calculating the Coordinates of the Extreme Vertices of a Constrained Region 123 3.10 Multicomponent Constraints 128 3.11 Some Examples of Designs for Constrained Mixture Regions: CONVRT and CONAEV Programs 131 3.12 Multiple Lattices for Major and Minor Component Classifications 138 Summary 154 References and Recommended Reading 155 Questions 157 4. The Analysis of Mixture Data 159 4.1 Techniques Used in the Analysis of Mixture Data 160 4.2 Test Statistics for Testing the Usefulness of the Terms in the Scheffé Polynomials 163 4.3 Model Reduction 170 4.4 An Example of Reducing the System from Three to Two Components 173 4.5 Screening Components 175 4.6 Other Techniques Used to Measure Component Effects 179 4.7 Leverage and the Hat Matrix 190 4.8 A Three-Component Propellant Example 192 4.9 Summary 195 References and Recommended Reading 196 Questions 197 5. Other Mixture Model Forms 201 5.1 The Inclusion of Inverse Terms in the Scheffé Polynomials 201 5.2 Fitting Gasoline Octane Numbers Using Inverse Terms in the Model 204 5.3 An Alternative Model Form for Modeling the Additive Blending Effect of One Component in a Multicomponent System 205 5.4 A Biological Example on the Linear Effect of a Powder Pesticide in Combination with Two Liquid Pesticides Used for Suppressing Mite Population Numbers 212 5.5 The Use of Ratios of Components 215 5.6 Cox’s Mixture Polynomials: Measuring Component Effects 219 5.7 An Example Illustrating the Fits of Cox’s Model and Scheffé’s Polynomial 224 5.8 Fitting a Slack-Variable Model 229 5.9 A Numerical Example Illustrating the Fits of Different Reduced Slack-Variable Models: Tint Strength of a House Paint 233 5.10 Summary 239 References and Recommended Reading 240 Questions 242 6. The Inclusion of Process Variables in Mixture Experiments 247 6.1 Designs Consisting of Simplex-Lattices and Factorial Arrangements 249 6.2 Measuring the Effects of Cooking Temperature and Cooking Time on the Texture of Patties Made from Two Types of Fish 251 6.3 Mixture-Amount Experiments 256 6.4 Determining the Optimal Fertilizer Blend and Rate for Young Citrus Trees 262 6.5 A Numerical Example of the Fit of a Combined Model to Data Collected on Fractions of the Fish Patty Experimental Design 269 6.6 Questions Raised and Recommendations Made When Fitting a Combined Model Containing Mixture Components and Other Variables 272 6.7 Summary 277 References and Recommended Reading 278 Questions 280 Appendix 6A: Calculating the Estimated Combined Mixture Component–Process Variable Model of Eq. (6.10) Without the Computer 282 7. A Review of Least Squares and the Analysis of Variance 285 7.1 A Review of Least Squares 285 7.2 The Analysis of Variance 288 7.3 A Numerical Example: Modeling the Texture of Fish Patties 289 7.4 The Adjusted Multiple Correlation Coefficient 293 7.5 The Press Statistic and Studentized Residuals 293 7.6 Testing Hypotheses About the Form of the Model: Tests of Significance 295 References and Recommended Reading 298 Bibliography 299 Answers to Selected Questions 317 Appendix 337 Index 347

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Book SynopsisAn understanding of the extended finite element method (XFEM) is critical for users, developers, researchers, and engineers working on industrial products. The first guide to the foundations of XFEM and its implementation, this book demystifies the theory behind this method and makes it accessible to anyone with previous knowledge of FEM.Table of ContentsList of Contributors xi Preface xiii Acknowledgments xv 1 Introduction 1 1.1 The Finite Element Method 2 1.2 Suitability of the Finite Element Method 9 1.3 Some Limitations of the FEM 11 1.4 The Idea of Enrichment 16 1.5 Conclusions 19 2 A Step-by-Step Introduction to Enrichment 23 2.1 History of Enrichment for Singularities and Localized Gradients 25 2.2 Weak Discontinuities for One-dimensional Problems 38 2.3 Strong Discontinuities for One-dimensional Problem 58 2.4 Conclusions 61 3 Partition of Unity Revisited 67 3.1 Completeness, Consistency, and Reproducing Conditions 67 3.2 Partition of Unity 68 3.3 Enrichment 69 3.4 Numerical Examples 86 3.5 Conclusions 95 4 Advanced Topics 99 4.1 Size of the Enrichment Zone 99 4.2 Numerical Integration 100 4.3 Blending Elements and Corrections 108 4.4 Preconditioning Techniques 116 5 Applications 125 5.1 Linear Elastic Fracture in Two Dimensions with XFEM 125 5.2 Numerical Enrichment for Anisotropic Linear Elastic Fracture Mechanics 130 5.3 Creep and Crack Growth in Polycrystals 133 5.4 Fatigue Crack Growth Simulations 138 5.5 Rectangular Plate with an Inclined Crack Subjected to Thermo-Mechanical Loading 140 6 Recovery-Based Error Estimation and Bounding in XFEM 145 6.1 Introduction 145 6.2 Error Estimation in the Energy Norm. The ZZ Error Estimator 147 6.3 Recovery-based Error Estimation in XFEM 151 6.4 Recovery Techniques in Error Bounding. Practical Error Bounds. 174 6.5 Error Estimation in Quantities of Interest 179 7 Φ-FEM: An Efficient Simulation Tool Using Simple Meshes for Problems in Structure Mechanics and Heat Transfer 191 7.1 Introduction 191 7.2 Linear Elasticity 194 7.3 Linear Elasticity with Multiple Materials 204 7.4 Linear Elasticity with Cracks 208 7.5 Heat Equation 212 7.6 Conclusions and Perspectives 214 8 eXtended Boundary Element Method (XBEM) for Fracture Mechanics and Wave Problems 217 8.1 Introduction 217 8.2 Conventional BEM Formulation 218 8.3 Shortcomings of the Conventional Formulations 226 8.4 Partition of Unity BEM Formulation 228 8.5 XBEM for Accurate Fracture Analysis 228 8.6 XBEM for ShortWave Simulation 235 8.7 Conditioning and its Control 243 8.8 Conclusions 245 9 Combined Extended Finite Element and Level Set Method (XFE-LSM) for Free Boundary Problems 249 9.1 Motivation 249 9.2 The Level Set Method 250 9.3 Biofilm Evolution 256 9.4 Conclusion 269 10 XFEM for 3D Fracture Simulation 273 10.1 Introduction 273 10.2 Governing Equations 274 10.3 XFEM Enrichment Approximation 275 10.4 Vector Level Set 280 10.5 Computation of Stress Intensity Factor 282 10.6 Numerical Simulations 288 10.7 Summary 300 11 XFEM Modeling of Cracked Elastic-Plastic Solids 303 11.1 Introduction 303 11.2 Conventional von Mises Plasticity 303 11.3 Strain Gradient Plasticity 312 11.4 Conclusions 323 12 An Introduction to Multiscale analysis with XFEM 329 12.1 Introduction 329 12.2 Molecular Statics 330 12.3 Hierarchical Multiscale Models of Elastic Behavior -- The Cauchy-Born Rule 336 12.4 Current Multiscale Analysis -- The Bridging Domain Method 338 12.5 The eXtended Bridging Domain Method 340 References 344 Index 345

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Book SynopsisThis is a practical book on how to apply statistical methods successfully. The Authors have deliberately kept formulae to a minimum to enable the reader to concentrate on how to use the methods and to understand what the methods are for. Each method is introduced and used in a real situation from industry or research. Each chapter features situations based on the authors' experience and looks at statistical methods for analysing data and, where appropriate, discusses the assumptions of these methods. Key features: Provides a practical hands-on manual for workplace applications. Introduces a broad range of statistical methods from confidence intervals to trend analysis. Combines realistic case studies and examples with a practical approach to statistical analysis. Features examples drawn from a wide range of industries including chemicals, petrochemicals, nuclear power, food and pharmaceuticals. Includes a supportingTrade Review"Overall, the book could be a clear introduction to a set of useful tools either in self study or used as an aid for instruction for those with no previous exposure." (The American Statistician, 1 February 2011) Table of Contents Preface. 1 Samples and populations. Introduction. What a lottery! No can do. Nobody is listening to me. How clean is my river? Discussion. 2 What is the true mean? Introduction. Presenting data. Averages. Measures of variability. Relative standard deviation . Degrees of freedom. Confidence interval for the population mean. Sample sizes. How much moisture is in the raw material? Problems. 3 Exploratory data analysis. Introduction. Histograms: is the process capable of meeting specifications? Box plots: how long before the lights go out? The box plot in practice. Problems. 4 Significance testing. Introduction. The one-sample t -test. The significance testing procedure. Confidence intervals as an alternative to significance testing. Confidence interval for the population standard deviation. F-test for ratio of standard deviations. Problems. 5 The normal distribution. Introduction. Properties of the normal distribution. Example. Setting the process mean. Checking for normality. Uses of the normal distribution. Problems. 6 Tolerance intervals. Introduction. Example. Confidence intervals and tolerance intervals. 7 Outliers. Introduction. Grubbs’ test. Warning. 8 Significance tests for comparing two means. Introduction. Example: watching paint lose its gloss. The two-sample t -test for independent samples. An alternative approach: a confidence intervals for the difference between population means. Sample size to estimate the difference between two means. A production example. Confidence intervals for the difference between the two suppliers. Sample size to estimate the difference between two means. Conclusions. Problems. 9 Significance tests for comparing paired measurements. Introduction. Comparing two fabrics. The wrong way. The paired sample t -test. Presenting the results of significance tests. One-sided significance tests. Problems. 10 Regression and correlation. Introduction. Obtaining the best straight line. Confidence intervals for the regression statistics. Extrapolation of the regression line. Correlation coefficient. Is there a significant relationship between the variables? How good a fit is the line to the data? Assumptions. Problems. 11 The binomial distribution. Introduction. Example. An exact binomial test. A quality assurance example. What is the effect of the batch size? Problems. 12 The Poisson distribution. Introduction. Fitting a Poisson distribution. Are the defects random? The Poisson distribution. Poisson dispersion test. Confidence intervals for a Poisson count. A significance test for two Poisson counts. How many black specks are in the batch? How many pathogens are there in the batch? Problems. 13 The chi-squared test for contingency tables. Introduction. Two-sample test for percentages. Comparing several percentages. Where are the differences? Assumptions. Problems. 14 Non-parametric statistics. Introduction. Descriptive statistics. A test for two independent samples: Wilcoxon–Mann–Whitney test. A test for paired data: Wilcoxon matched-pairs sign test. What type of data can be used? Example: cracking shoes. Problems. 15 Analysis of variance: Components of variability. Introduction. Overall variability. Analysis of variance. A practical example. Terminology. Calculations. Significance test. Variation less than chance? When should the above methods not be used? Between- and within-batch variability. How many batches and how many prawns should be sampled? Problems. 16 Cusum analysis for detecting process changes. Introduction. Analysing past data. Intensity. Localised standard deviation. Significance test. Yield. Conclusions from the analysis. Problem. 17 Rounding of results. Introduction. Choosing the rounding scale. Reporting purposes: deciding the amount of rounding. Reporting purposes: rounding of means and standard deviations. Recording the original data and using means and standard deviations in statistical analysis. References. Solutions to Problems. Statistical Tables. Index.

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Book SynopsisAlong with its companion volume, this book provides a comprehensive presentation of the boundary element method (BEM) from fundamentals to advanced engineering applications. It provides comprehensive formulation of the BEM with application to a wide range of engineering problems.Trade Review"...The text is well written and quite thorough..." (Zentralblatt Math, Vol.994, No. 19, 2002)Table of ContentsPreface Preface to Volume 2 Acknowledgements Introduction Elastostatics Plates and Shells Thermoelasticity Elastodynamics Elastoplasticity Contact Mechanics Fracture Mechanics Sensitivity Analysis and Shape Optimization Assembled Structures Numerical Integration A Complex Stress Functions B Limiting Process for Boundary Stress Equation C Limits Integrals for Shallow Shells D Particular Solutions for Shear Deformable Plates E Fundamental Solutions for Elastodynamics F Shape Functions of Brick Cell elements G Fast Solver for Contact Problems Index

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Book SynopsisMost books discuss the theory and computational procedures of finite elements (FE). In the past this was necessary, but today''s software packages make FE accessible to users who knows nothing to the theory or of how FE works. People are now using FE software packages as black boxes'', without knowing the dangers of poor modeling, the need to verify that results are reasonable, or that worthless results can be convincingly displayed. Therefore, it is important to understand the physics of the problem, how elements behave, the assumptions and restrictions of FE implementations, and the need to assess the correctness of computed results.Table of ContentsBars and Beams: Linear Static Analysis. Plane Problems. Isoparametric Elements and Solution Techniques. Modeling, Errors, and Accuracy in Linear Analysis. Solids and Solids of Revolution. Plates and Shells. Thermal Analysis. Vibration and Dynamics. Nonlinearity in Stress Analysis. References. Index.

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Book SynopsisAdvances in computer technology have conveniently coincided withtrends in numerical analysis toward increased complexity ofcomputational algorithms based on finite difference methods. It isno longer feasible to perform stability investigation of thesemethods manually--and no longer necessary. As this book shows,modern computer algebra tools can be combined with methods fromnumerical analysis to generate programs that will do the jobautomatically. Comprehensive, timely, and accessible--this is the definitivereference on the application of computerized symbolic manipulationsfor analyzing the stability of a wide range of difference schemes.In particular, it deals with those schemes that are used to solvecomplex physical problems in areas such as gas dynamics, heat andmass transfer, catastrophe theory, elasticity, shallow watertheory, and more. Introducing many new applications, methods, and concepts,Computer-Aided Analysis of Difference Schemes for PartialDifferential EqTable of ContentsThe Necessary Basics from the Stability Theory of DifferenceSchemes and Polynomials. Symbolic-Numerical Method for the Stability Investigation ofDifference Schemes on a Computer. Application of Optimization Methods to the Stability Analysis ofDifference Schemes. Stability Analysis of Difference Schemes by Catastrophe TheoryMethods. Construction of Multiply Connected Stability Regions of DifferenceSchemes by Computer Algebra and Pattern Recognition. Maximally Stable Difference Schemes. Stability Analysis of Nonlinear Difference Schemes. Symbolic Computation of Differential Approximations. Appendices. Index.

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Book SynopsisNeural networks and fuzzy systems represent two distinct technologies that deal with uncertainty. Researchers are applying neural networks and fuzzy systems in series, from the use of fuzzy inputs and outputs for neural networks to the employment of individual neural networks to quantify the shape of a fuzzy membership function.Table of ContentsIntroduction to Hybrid Artificial Intelligence Systems. FUZZY SYSTEMS: CONCEPTS AND FUNDAMENTALS. Foundations of Fuzzy Approaches. Fuzzy Relations. Fuzzy Numbers. Linguistic Descriptions and Their Analytical Forms. Fuzzy Control. NEURAL NETWORKS: CONCEPTS AND FUNDAMENTALS. Fundamentals of Neural Networks. Backpropagation and Related Training Algorithms. Competitive, Associative, and Other Special Neural Networks. Dynamic Systems and Neural Control. Practical Aspects of Using Neural Networks. INTEGRATED NEURAL-FUZZY TECHNOLOGY. Fuzzy Methods in Neural Networks. Fuzzy Methods in Fuzzy Systems. Selected Hybrid Neurofuzzy Applications. Dynamic Hybrid Neurofuzzy Systems. OTHER ARTIFICAL INTELLIGENCE SYSTEMS. Expert Systems in Neurofuzzy Systems. Genetic Algorithms. Epilogue. Appendix. Index.

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Book SynopsisCovers a range of limit theorems useful in mathematical statistics, along with methods of proof and techniques of application. This book emphasizes the manipulation of "probability" theorems to obtain "statistical" theorems.Trade Review"...even today it still provides a really good introduction into asymptotic statistics..."(Zentralblatt Math, Vol. 1001, No.01, 2003)Table of Contents1 Preliminary Tools and Foundations 1 1.1 Preliminary Notation and Definitions 1 1.2 Modes of Convergence of a Sequence of Random Variables 6 1.3 Relationships Among the Modes of Convergence 9 1.4 Convergence of Moments; Uniform Integrability 13 1.5 Further Discussion of Convergence in Distribution 16 1.6 Operations on Sequences to Produce Specified Convergence Properties 22 1.7 Convergence Properties of Transformed Sequences 24 1.8 Basic Probability Limit Theorems: The WLLN and SLLN 26 1.9 Basic Probability Limit Theorems: The CLT 28 1.10 Basic Probability Limit Theorems: The LIL 35 1.11 Stochastic Process Formulation of the CLT 37 1.12 Taylor’s Theorem; Differentials 43 1.13 Conditions for Determination of a Distribution by Its Moments 45 1.14 Conditions for Existence of Moments of a Distribution 46 1.15 Asymptotic Aspects of Statistical Inference Procedures 47 1.P Problems 52 2 The Basic Sample Statistics 55 2.1 The Sample Distribution Function 56 2.2 The Sample Moments 66 2.3 The Sample Quantiles 74 2.4 The Order Statistics 87 2.5 Asymptotic Representation Theory for Sample Quantiles Order Statistics and Sample Distribution Functions 91 2.6 Confidence Intervals for Quantiles 102 2.7 Asymptotic Multivariate Normality of Cell Frequency Vectors 107 2.8 Stochastic Processes Associated with a Sample 109 2.P Problems 113 3 Transformations of Given Statistics 117 3.1 Functions of Asymptotically Normal Statistics: Univariate Case 118 3.2 Examples and Applications 120 3.3 Functions of Asymptotically Normal Vectors 122 3.4 Further Examples and Applications 125 3.5 Quadratic Forms in Asymptotically Multivariate Normal Vectors 128 3.6 Functions of Order Statistics 134 3.P Problems 136 4 Asymptotic Theory in Parametric Inference 138 4.1 Asymptotic Optimality in Estimation 138 4.2 Estimation by the Method of Maximum Likelihood 143 4.3 Other Approaches toward Estimation 150 4.4 Hypothesis Testing by Likelihood Methods 151 4.5 Estimation via Product-Multinomial Data 160 4.6 Hypothesis Testing via Product-Multinomial Data 165 4.P Problems 169 5 U-Statistics 171 5.1 Basic Description of U-Statistics 172 5.2 The Variance and Other Moments of a U-Statistic 181 5.3 The Projection of a U-Statistic on the Basie Observations 187 5.4 Almost Sure Behavior of U-Statistics 190 5.5 Asymptotic Distribution Theory of U-Statistics 192 5.6 Probability Inequalities and Deviation Probabilities for U-Statistics 199 5.7 Complements 203 5.P Problems 207 6 Von Mises Differentiable Statistical Functions 210 6.1 Statistics Considered as Functions of the Sample Distribution Function 211 6.2 Reduction to a Differential Approximation 214 6.3 Methodology for Analysis of the Differential Approximation 221 6.4 Asymptotic Properties of Differentiable Statistical Functions 225 6.5 Examples 231 6.6 Complements 238 6.P Problems 241 7 M-Estimates 243 7.1 Basic Formulation and Examples 243 7.2 Asymptotic Properties of M-Estimates 248 7.3 Complements 257 7.P Problems 260 8 L-Estimates 8.1 Basic Formulation and Examples 262 8.2 Asymptotic Properties of L-Estimates 271 8.P Problems 290 9 R-Estimates 9.1 Basic Formulation and Examples 292 9.2 Asymptotic Normality of Simple Linear Rank Statistics 295 9.3 Complements 311 9.P Problems 312 10 Asymptotic Relative Efficiency 10.1 Approaches toward Comparison of Test Procedures 314 10.2 The Pitman Approach 316 10.3 The Chernoff Index 325 10.4 Bahadur’s “Stochastic Comparison,” 332 10.5 The Hodges-Lehmann Asymptotic Relative Efficiency 341 10.6 Hoeffding’s Investigation (Multinomial Distributions) 342 10.7 The Rubin‒Sethuraman “Bayes Risk” Efficiency 347 I0.P Problems 348 Appendix 351 References 553 Author Index 365 Subject Index 369

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Book SynopsisMaster the essential statistical skills used in social and behavioral sciences Essentials of Statistics for the Social and Behavioral Sciences distills the overwhelming amount of material covered in introductory statistics courses into a handy, practical resource for students and professionals.Table of ContentsSeries Preface. One. Descriptive Statistics. Two. Introduction to Null Hypothesis Testing. Three. The Two-Group t II Test. Four. Correlation and Regression. Five. One-Way ANOVA and Multiple Comparisons. Six. Power Analysis. Seven. Factorial ANOVA. Eight. Repeated-Measures ANOVA. Nine. Nonparametric Statistics. Appendix A: Statistical Tables. Appendix B: Answers to Putting it into Practice Exercises. References. Annotated Bibliography. Index. Acknowledgments. About the Authors.

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Book SynopsisA thorough guide to the fundamentals--and how to use them--of finite element analysis for elastic structures For elastic structures, the finite element method is an invaluable tool which is used most effectively only when one understands completely each of its facets.Table of ContentsFinite Element Method Prerequisites. The Finite Element Method. Element Stiffness Equations by Direct Methods. Global Stiffness Equations. Element Stiffness Equations by Displaced State Virtual Work Applications. General Approach to Element Stiffness Equations. Plane Stress and Plane Strain. Plane Stress Structural Triangular Finite Elements. Isoparametric Plane Stress Structural Quadrilateral Finite Elements. Flat Plate Flexural Finite Elements. Axisymmetric Structural Finite Elements. Structural Finite Elements in Perspective. Appendix. Answers to Selected Problems. Index.

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Book SynopsisWith the growing complexity of engineered systems, reliability has increased in importance throughout the twentieth century. Initially developed to meet practical needs, reliability theory has become an applied mathematical discipline that permits a priori evaluations of various reliability indices at the design stages.Table of ContentsFundamentals. Reliability Indexes. Unrepairable Systems. Load-Strength Reliability Models. Distributions with Monotone Intensity Functions. Repairable Systems. Repairable Duplicated Systems. Analysis of Performance Effectiveness. Two-Pole Networks. Optimal Redundancy. Optimal Technical Diagnosis. Additional Optimization Problems in Reliability Theory. Heuristic Methods in Reliability. Index.

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Book SynopsisAuthors Cook, Malkus, Plesha and Witt have revised Concepts and Applications of Finite Element Analysis, a text suited for both introductory and more advanced courses in Finite Element Analysis. The fourth edition of this market leading text provides students with up-to-date coverage and clear explanations of finite element analysis concepts and modeling procedures.Table of ContentsNotation. Introduction. One-Dimensional Elements, Computational Procedures. Basic Elements. Formulation Techniques: Variational Methods. Formulation Techniques: Galerkin and Other Weighted Residual Methods. Isoparametric Elements. Isoparametric Triangles and Tetrahedra. Coordinate Transformation and Selected Analysis Options. Error, Error Estimation, and Convergence. Modeling Considerations and Software Use. Finite Elements in Structural Dynamics and Vibrations. Heat Transfer and Selected Fluid Problems. Constaints: Penalty Forms, Locking, and Constraint Counting. Solid of Revolution. Plate Bending. Shells. Nonlinearity: An Introduction. Stress Stiffness and Buckling. Appendix A: Matrices: Selected Definition and Manipulations. Appendix B: Simultaneous Algebraic Equations. Appendix C: Eigenvalues and Eigenvectors. References. Index.

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Book SynopsisA clear, up-to-date presentation of the principles of flow in open channels A fundamental knowledge of flow in open channels is essential for the planning and design of systems to manage water resources.Trade Review"...a new and fresh exposition of important theoretical and computational treatments that are among the clearest available." (Hydraulic Engineering, September 2001)Table of ContentsBasic Equations. Steady Uniform Flow. Control Sections. Gradually Varied Flow. Computation of Gradually Varied Flow. Spatially Varied Flow. Unsteady Flow I. Unsteady Flow II. Artificial Channel Controls. Special Topics. References. Index.

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Book SynopsisA useful balance of theory, applications, and real-world examples The Finite Element Method for Engineers, Fourth Edition presents a clear, easy-to-understand explanation of finite element fundamentals and enables readers to use the method in research and in solving practical, real-life problems.Table of ContentsPART I. 1. Meet the Finite Element Method. 2. The Direct Approach: A Physical Interpretation. 3. The Mathematical Approach: A Variational Interpretation. 4. The Mathematical Approach: A Generalized Interpretation. 5. Elements and Interpolation Functions. PART II. 6. Elasticity Problems. 7. General Field Problems. 8. Heat Transfer Problems. 9. Fluid Mechanics Problems. 10. Boundary Conditions, Mesh Generation, and Other Practical Considerations 11. Finite Elements in Design.

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Book SynopsisThis book provides an excellent introduction to the subject designed for readers from a variety of mathematical backgrounds. It features introductory properties of metric spaces and Banach spaces, and an appendix contains a summary of the concepts of set theory.Trade Review"...deserves to be on the bookshelf of everyone who wants to know about fixed-point theory in metric and Banach spaces and experts who want to read an insightful survey of some basic ideas..." (Mathematical Reviews, 2002b) "Clear, friendly exposition." (American Mathematical Monthly, August/September 2002)Table of ContentsPreface ix I Metric Spaces 1 Introduction 3 1.1 The real numbers R 3 1.2 Continuous mappings in R 5 1.3 The triangle inequality in R 7 1.4 The triangle inequality in R" 8 1.5 Brouwer's Fixed Point Theorem 10 Exercises 11 2 Metric Spaces 13 2.1 The metric topology 15 2.2 Examples of metric spaces 19 2.3 Completeness 26 2.4 Separability and connectedness 33 2.5 Metric convexity and convexity structures 35 Exercises 38 3 Metric Contraction Principles 41 3.1 Banach's Contraction Principle 41 3.2 Further extensions of Banach's Principle 46 3.3 The Caristi-Ekeland Principle 55 3.4 Equivalents of the Caristi-Ekeland Principle 58 3.5 Set-valued contractions 61 3.6 Generalized contractions 64 Exercises 67 4 Hyperconvex Spaces 71 4.1 Introduction 71 4.2 Hyperconvexity 77 4.3 Properties of hyperconvex spaces 80 4.4 A fixed point theorem 84 4.5 Intersections of hyperconvex spaces 87 4.6 Approximate fixed points 89 4.7 Isbell's hyperconvex hull 91 Exercises 98 5 "Normal" Structures in Metric Spaces 101 5.1 A fixed point theorem 101 5.2 Structure of the fixed point set 103 5.3 Uniform normal structure 106 5.4 Uniform relative normal structure 110 5.5 Quasi-normal structure 112 5.6 Stability and normal structure 115 5.7 Ultrametric spaces 116 5.8 Fixed point set structure—separable case 120 Exercises 123 II Banach Spaces 6 Banach Spaces: Introduction 127 6.1 The definition 127 6.2 Convexity 131 6.3 £2 revisited 132 6.4 The modulus of convexity 136 6.5 Uniform convexity of the tp spaces 138 6.6 The dual space: Hahn-Banach Theorem 142 6.7 The weak and weak* topologies 144 6.8 The spaces c, CQ, t\ and ^ 146 6.9 Some more general facts 148 6.10 The Schur property and £j 150 6.11 More on Schauder bases in Banach spaces 154 6.12 Uniform convexity and reflexivity 163 6.13 Banach lattices 165 Exercises 168 7 Continuous Mappings in Banach Spaces 171 7.1 Introduction 171 7.2 Brouwer's Theorem 173 7.3 Further comments on Brouwer's Theorem 176 7.4 Schauder's Theorem 179 7.5 Stability of Schauder's Theorem 180 7.6 Banach algebras: Stone Weierstrass Theorem 182 7.7 Leray-Schauder degree 183 7.8 Condensing mappings 187 7.9 Continuous mappings in hyperconvex spaces 191 Exercises 195 8 Metric Fixed Point Theory 197 8.1 Contraction mappings 197 8.2 Basic theorems for nonexpansive mappings 199 8.3 A closer look at ßë 205 8.4 Stability results in arbitrary spaces 207 8.5 The Goebel-Karlovitz Lemma 211 8.6 Orthogonal convexity 213 8.7 Structure of the fixed point set 215 8.8 Asymptotically regular mappings 219 8.9 Set-valued mappings 222 8.10 Fixed point theory in Banach lattices 225 Exercises 238 9 Banach Space Ultrapowers 243 9.1 Finite representability 243 9.2 Convergence of ultranets 248 9.3 The Banach space ultrapower X 249 9.4 Some properties of X 252 9.5 Extending mappings to X 255 9.6 Some fixed point theorems 257 9.7 Asymptotically nonexpansive mappings 262 9.8 The demiclosedness principle 263 9.9 Uniformly non-creasy spaces 264 Exercises 270 Appendix: Set Theory 273 A.l Mappings 273 A.2 Order relations and Zermelo's Theorem 274 A.3 Zorn's Lemma and the Axiom Of Choice 275 A.4 Nets and subnets 277 A.5 Tychonoff's Theorem 278 A.6 Cardinal numbers 280 A. 7 Ordinal numbers and transfinite induction 281 A.8 Zermelo's Fixed Point Theorem 284 A.9 A remark about constructive mathematics 286 Exercises 287 Bibliography 289 Index 301

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Book SynopsisGives you what you need to know - basic essential concepts - about calculus. Suitable for those looking for a readable alternative to the usual unwieldy calculus text, this title provides in a condensed format the material covered in the standard two-year calculus course. It also covers vectors, lines, and planes in space; and line integrals.Trade Review"...expands coverage to vectors and calculus of several variables...plenty of worked out problems..." (American Mathematical Monthly, August/September 2003) "...material included is well formulated and approachable...recommended." (Choice, Vol. 41, No. 1, September 2003)Table of ContentsAUTHOR'S MESSAGE TO THE READER vii ANNOTATED TABLE OF CONTENTS ix ACKNOWLEDGMENTS xv CHAPTER 1 Lines 1 CHAPTER 2 Parabolas, Ellipses, Hyperbolas 7 CHAPTER 3 Differentiation 13 CHAPTER 4 Differentiation Formulas 19 CHAPTER 5 The Chain Rule 25 CHAPTER 6 Trigonometric Functions 31 CHAPTER 7 Exponential Functions and Logarithms 39 CHAPTER 8 Inverse Functions 45 CHAPTER 9 Derivatives and Graphs 51 CHAPTER 10 Following the Tangent Line 57 CHAPTER 11 The Indefinite Integral 63 CHAPTER 12 The Definite Integral 69 CHAPTER 13 Work, Volume, and Force 75 CHAPTER 14 Parametric Equations 81 CHAPTER 15 Change of Variable 87 CHAPTER 16 Integrating Rational Functions 91 CHAPTER 17 Integration By Parts 97 CHAPTER 18 Trigonometric Integrals 101 CHAPTER 19 Trigonometric Substitution 107 CHAPTER 20 Numerical Integration 115 CHAPTER 21 Limits At oo; Sequences 119 CHAPTER 22 Improper Integrals 127 CHAPTER 23 Series 133 CHAPTER 24 Power Series 141 CHAPTER 25 Taylor Polynomials 149 CHAPTER 26 Taylor Series 155 CHAPTER 27 Separable Differential Equations 161 CHAPTER 28 First-Order Linear Equations 167 CHAPTER 29 Homogeneous Second-Order Linear Equations 173 CHAPTER 30 Nonhomogeneous Second-Order Equations 179 CHAPTER 31 Vectors 185 CHAPTER 32 The Dot Product 195 CHAPTER 33 Lines and Planes in Space 201 CHAPTER 34 Surfaces 211 CHAPTER 35 Partial Derivatives 217 CHAPTER 36 Tangent Plane and Differential Approximation CHAPTER 37 Chain Rules 227 CHAPTER 38 Gradient and Directional Derivatives 233 CHAPTER 39 Maxima and Minima 239 CHAPTER 40 Double Integrals 245 CHAPTER 41 Line Integrals 255 CHAPTER 42 Green's Theorem 259 CHAPTER 43 Exact Differentials 267 ANSWERS 273 INDEX 299 ABOUT THE AUTHOR 303

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Book SynopsisToday''s need-to-know optimization techniques, at your fingertips The use of optimization methods is familiar territory to academicians and researchers. Yet, in today''s world of deregulated electricity markets, it''s just as important for electric power professionals to have a solid grasp of these increasingly relied upon techniques. Making those techniques readily accessible is the hallmark of Optimization Principles: Practical Applications to the Operation and Markets of the Electric Power Industry. With deregulation, market rules and economic principles dictate that commodities be priced at the marginal value of their production. As a result, it''s necessary to work with ever-more-sophisticated algorithms using optimization techniques-either for the optimal dispatch of the system itself, or for pricing commodities and the settlement of markets. Succeeding in this new environment takes a good understanding of methods that involve linear and nonTrade Review"...an important contribution to the field of power system analysis...should provide the reader with a pleasant learning experience." (IEEE Power & Energy Magazine, November/December 2005)Table of ContentsPreface. 1. Introduction. PART I: MATHEMATICAL BACKGROUND. 2. Fundamentals of Matrix Algebra. PART II: LINEAR OPTIMIZATION. 3. Solution of Equations, Inequalities, and Linear Programs. 4. Solved Linear Program Problems. PART III: NONLINEAR OPTIMIZATION. 5. Mathematical Background to Nonlinear Programs. 6. Unconstrained Nonlinear Optimization. 7. Constrained Nonlinear Optimization. 8. Solved Nonlinear Optimization Problems. Appendix A: Basic Principles of Electricity. Appendix B: Network Equations. Appendix C: Relation Between Pseudo-Inverse and Least-Square Error Fit. Bibliography. Index. About the Author.

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Book SynopsisBayesian statistics uses information from past experience to infer the results of future events. With recent advances in computing power and the development of computer intensive methods for statistical estimation, Bayesian approaches to model estimation have become more feasible and popular.Trade Review"I recommend…highly to statisticians, [and] health researchers...among others to consider keeping on their bookshelf." (Journal of Statistical Computation and Simulation, April 2005) "…a great book…fills a critical gap in existing literature. It is an excellent book for anyone interested in Bayesian modeling…" (Journal of the American Statistical Association, March 2005) "It is certainly a fine choice as a supporting reference in either a first or second Bayesian methods course…” (Technometrics, May 2004) "...has a contemporary feel, with recent developments in financial time series modelling and epidemiology included..." (Short Book Reviews, Vol 23(3), December 2003)Table of ContentsPreface. The Basis for, and Advantages of, Bayesian Model Estimation via Repeated Sampling. Hierarchical Mixture Models. Regression Models. Analysis of Multi-Level Data. Models for Time Series. Analysis of Panel Data. Models for Spatial Outcomes and Geographical Association. Structural Equation and Latent Variable Models. Survival and Event History Models. Modelling and Establishing Causal Relations: Epidemiological Methods and Models. Index.

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Book SynopsisIn modern society, we are ever more aware of the environmentalissues we face, whether these relate to global warming, depletionof rivers and oceans, despoliation of forests, pollution of land,poor air quality, environmental health issues, etc. At the mostfundamental level it is necessary to monitor what is happening inthe environment - collecting data to describe the changingscene. More importantly, it is crucial to formally describe theenvironment with sound and validated models, and to analyse andinterpret the data we obtain in order to take action. Environmental Statistics provides a broad overview of thestatistical methodology used in the study of the environment,written in an accessible style by a leading authority on thesubject. It serves as both a textbook for students of environmentalstatistics, as well as a comprehensive source of reference foranyone working in statistical investigation of environmentalissues. * Provides broad coverage of the methodology used in tTrade Review"Inspired by the Encyclopedia of Statistical Sciences, SecondEdition (ESS2e), this volume presents a concise, well-rounded focuson the statistical concepts and applications that are essential forunderstanding gathered data in the fields of engineering, qualitycontrol, and the physical sciences. The book successfully upholdsthe goals of ESS2e by combining both previously-published and newlydeveloped contributions written by over 100 leading academics,researchers, and practitioner in a comprehensive, approachableformat. The result is a succinct reference that unveils modern,cutting-edge approaches to acquiring and analyzing data acrossdiverse subject areas within these three disciplines, includingoperations research, chemistry, physics, the earth sciences,electrical engineering, and quality assurance." (Finwin, 7September 2011) "In this book, Vic Barnett, a distinguished environmentalstatistician, provides an overview of statistical methods that havebeen used on such problems in the environmental sciences."(Journal of the American Statistical Association, September2006) "...combines sound fundamentals and their applications."(European Journal of Soil Science, No.56, April 2005) "Many tables, graphs and figures illustrate the environmentalapplications of the statistical methods that are described."(Journal of the Royal Statistical Society, Series A,Vol.168, No.2, March 2005) "...well written...methods are illustrated with interestingexamples...a comprehensive reference source for anyone working onenvironmental issues..." (Short Book Reviews, Vol.24, No.3,December 2004) "Statisticians should enjoy the book. The author is an extremelyknowledgeable statistician, and he is writing about an applicationdomain that he clearly knows." (Technometrics, November2004) "An excellent book. Highly recommended." (Choice, July2004) "...this provides an excellent sketch of the current state ofdevelopment for new statistical methodologies...a valuableresource..." (Statistics in Medicine, 15th August 2005)Table of ContentsPreface. Chapter 1: Introduction. 1.1 Tomorrow is too Late! 1.2 Environmental Statistics. 1.3 Some Examples. 1.3.1 ‘Getting it all together’. 1.3.2 ‘In time and space’. 1.3.3 ‘Keep it simple’. 1.3.4 ‘How much can we take?’ 1.3.5 ‘Over the top’. 1.4 Fundamentals. 1.5 Bibliography. PART I: EXTREMAL STRESSES: EXTREMES, OUTLIERS, ROBUSTNESS. Chapter 2: Ordering and Extremes: Applications, models, inference. 2.1 Ordering the Sample. 2.1.1 Order statistics. 2.2 Order-based Inference. 2.3 Extremes and Extremal Processes. 2.3.1 Practical study and empirical models; generalized extreme-value distributions. 2.4 Peaks over Thresholds and the Generalized Pareto Distribution. Chapter 3: Outliers and Robustness. 3.1 What is an Outlier? 3.2 Outlier Aims and Objectives. 3.3 Outlier-Generating Models. 3.3.1 Discordancy and models for outlier generation. 3.3.2 Tests of discordancy for specific distributions. 3.4 Multiple Outliers: Masking and Swamping. 3.5 Accommodation: Outlier-Robust Methods. 3.6 A Possible New Approach to Outliers. 3.7 Multivariate Outliers. 3.8 Detecting Multivariate Outliers. 3.8.1 Principles. 3.8.2 Informal methods. 3.9 Tests of Discordancy. 3.10 Accommodation. 3.11 Outliers in linear models. 3.12 Robustness in General. PART II: COLLECTING ENVIRONMENTAL DATA: SAMPLING AND MONITORING. Chapter 4: Finite-Population Sampling. 4.1 A Probabilistic Sampling Scheme. 4.2 Simple Random Sampling. 4.2.1 Estimating the mean, &Xmacr;. 4.2.2 Estimating the variance, S2. 4.2.3 Choice of sample size, n. 4.2.4 Estimating the population total, XT. 4.2.5 Estimating a proportion, P. 4.3 Ratios and Ratio Estimators. 4.3.1 The estimation of a ratio. 4.3.2 Ratio estimator of a population total or mean. 4.4 Stratified (simple) Random Sampling. 4.4.1 Comparing the simple random sample mean and the stratified sample mean. 4.4.2 Choice of sample sizes. 4.4.3 Comparison of proportional allocation and optimum allocation. 4.4.4 Optimum allocation for estimating proportions. 4.5 Developments of Survey Sampling. Chapter 5: Inaccessible and Sensitive Data. 5.1 Encountered Data. 5.2 Length-Biased or Size-Biased Sampling and Weighted Distributions. 5.2.1 Weighted distribution methods. 5.3 Composite Sampling. 5.3.1 Attribute Sampling. 5.3.2 Continuous variables. 5.3.3 Estimating mean and variance. 5.4 Ranked-Set Sampling. 5.4.1 The ranked-set sample mean. 5.4.2 Optimal estimation. 5.4.3 Ranked-set sampling for normal and exponential distributions. 5.4.4 Imperfect ordering. Chapter 6: Sampling in the Wild. 6.1 Quadrat Sampling. 6.2 Recapture Sampling. 6.2.1 The Petersen and Chapman estimators. 6.2.2 Capture–recapture methods in open populations. 6.3 Transect Sampling. 6.3.1 The simplest case: strip transects. 6.3.2 Using a detectability function. 6.3.3 Estimating f (y). 6.3.4 Modifications of approach. 6.3.5 Point transects or variable circular plots. 6.4 Adaptive Sampling. 6.4.1 Simple models for adaptive sampling. Part III: EXAMINING ENVIRONMENTAL EFFECTS: STIMULUS–RESPONSE RELATIONSHIPS. Chapter 7: Relationship: regression-type models and methods. 7.1 Linear Models. 7.1.1 The linear model. 7.1.2 The extended linear model. 7.1.3 The normal linear model. 7.2 Transformations. 7.2.1 Looking at the data. 7.2.2 Simple transformations. 7.2.3 General transformations. 7.3 The Generalized Linear Model. Chapter 8: Special Relationship Models, Including Quantal Response and Repeated Measures. 8.1 Toxicology Concerns. 8.2 Quantal Response. 8.3 Bioassay. 8.4 Repeated Measures. Part IV: STANDARDS AND REGULATIONS. Chapter 9: Environmental Standards. 9.1 Introduction. 9.2 The Statistically Verifiable Ideal Standard. 9.2.1 Other sampling methods. 9.3 Guard Point Standards. 9.4 Standards Along the Cause–Effect Chain. Part V: A MANY-DIMENSIONAL ENVIRONMENT: SPATIAL AND TEMPORAL PROCESSES. Chapter 10: Time-Series Methods. 10.1 Space and Time Effects. 10.2 Time Series. 10.3 Basic Issues. 10.4 Descriptive Methods. 10.4.1 Estimating or eliminating trend. 10.4.2 Periodicities. 10.4.3 Stationary time series. 10.5 Time-Domain Models and Methods. 10.6 Frequency-Domain Models and Methods. 10.6.1 Properties of the spectral representation. 10.6.2 Outliers in time series. 10.7 Point Processes. 10.7.1 The Poisson process. 10.7.2 Other point processes. Chapter 11: Spatial Methods for Environmental Processes. 11.1 Spatial Point Process Models and Methods. 11.2 The General Spatial Process. 11.2.1 Predication, interpolation and kriging. 11.2.2 Estimation of the variogram. 11.2.3 Other forms of kriging. 11.3 More about Standards Over Space and Time. 11.4 Relationship. 11.5 More about Spatial Models. 11.5.1 Types of spatial model. 11.5.2 Harmonic analysis of spatial processes. 11.6 Spatial Sampling and Spatial Design. 11.6.1 Spatial sampling. 11.6.2 Spatial design. 11.7 Spatial-Temporal Models and Methods. References. Index.

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Book SynopsisFinite Element Methods are used for numerous engineering applications where numerical solutions of partial differential equations are needed. As computers can now deal with the millions of parameters used in these methods, automatic error estimation and automatic adaptation of the utilised method (according to this error estimation), has become a hot research topic. This text offers comprehensive coverage of this new field of automatic adaptation and error estimation, bringing together the work of eight outstanding researchers in this field who have completed a six year national research project within the German Science Foundation. The result is a state-of-the-art work in true reference style. Each chapter is self-contained and covers theoretical, algorithmic and software presentations as well as solved problems. A main feature consists of several carefully elaborated benchmarks of 2D- and 3D- applications. First book to go beyond the Finite Element Method in itTable of ContentsPreface. Introduction (Stein). Error Estimation and Adaptive Mesh Design for FE Models in Elasto-Plasticity Theory (Rannacher and Suttmeier). Adaptive FEM for elasto-plastic Deformations (Stein and Schmidt). Numerical Simulation of Localization Phenomena in Geomechanics by Entended Continuum Formulations (Wunderlich et al). Adaptive Methods for Contact Problems (Rieger et al). An Adaptive Boundary Element Method for Contact Problems (Eck et al). Goal-Oriented Error Estimation in Solid Mechanics (Steeb,Maute and Ramm). The p-version of the Finite Element Method for Structural Problems (Rank et al). Adaptive Analysis of Plate and Shell Structures Under Transient Loading (Schweizerhof, Neumann and Riccius). The Application of Adaptive Parallel Multigrid Methods to Problems in Nonlinear Solid Mechanics (Lang, Wieners and Wittum). Benchmarks (Stein et al).

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Book SynopsisContact mechanics is a specialist area in engineering mechanics. It deals with non standard mechanics which frequently appear in real technical applications. Examples include the simulation of car crashes, human joints, car tyres, rubber seals and metal forming processes.Table of ContentsPreface. Introduction. Introduction to Contact Mechanics. Continuum Solid Mechanics and Weak Forms. Contact Kinematics. Constitutive Equations for Contact Interfaces. Contact Boundary Value Problem and Weak Form. Discretization of the Continuum. Discretization, Small Deformation Contact. Discretization, Large Deformation Contact. Solution Algorithms. Thermo-mechanical Contact. Beam Contact. Adaptive Finite Element Methods for Contact Problems. Computation of Critical Points with Contact Constraints. Appendix A: Gauss Integration Rules. Appendix B: Convective Coordinates. Appendix C: Parameter Identification for Friction Materials. References. Index.

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Book SynopsisPresents applications as well as the basic theory of analytic functions of one or several complex variables. The first volume discusses applications and basic theory of conformal mapping and the solution of algebraic and transcendental equations. Volume Two covers topics broadly connected with ordinary differental equations: special functions, integral transforms, asymptotics and continued fractions. Volume Three details discrete fourier analysis, cauchy integrals, construction of conformal maps, univalent functions, potential theory in the plane and polynomial expansions.Table of ContentsInfinite Products. Ordinary Differential Equations. Integral Transforms. Asymptotic Methods. Continued Fractions. Bibliography. Appendix. Index.

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Book SynopsisPRACTICAL ENGINEERING STATISTICS This lucidly written book offers engineers and advanced students all the essential statistical methods and techniques used in day-to-day engineering work.Table of ContentsStatistical Inference. Probability Models. Descriptive Statistics. Inferential Statistics: Mean Values. Analysis of Proportions and Categorical Data. Variability. Analysis of Variance and Experimental Design I. Outliers. Extreme Value Analysis. Sensitivity Testing. Regression and Correlation. Experimental Design II. Control Charts. Reliability and Lifetime. Appendix. Bibliography. Index.

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Book SynopsisThe classic introduction to engineering optimization theory and practice--now expanded and updated Engineering optimization helps engineers zero in on the most effective, efficient solutions to problems. This text provides a practical, real-world understanding of engineering optimization. Rather than belaboring underlying proofs and mathematical derivations, it emphasizes optimization methodology, focusing on techniques and stratagems relevant to engineering applications in design, operations, and analysis. It surveys diverse optimization methods, ranging from those applicable to the minimization of a single-variable function to those most suitable for large-scale, nonlinear constrained problems. New material covered includes the duality theory, interior point methods for solving LP problems, the generalized Lagrange multiplier method and generalization of convex functions, and goal programming for solving multi-objective optimization problems. A practical, hands-on referTable of ContentsPreface. 1 Introduction to Optimization. 1.1 Requirements for the Application of Optimization Methods. 1.2 Applications of Optimization in Engineering. 1.3 Structure of Optimization Problems. 1.4 Scope of This Book. References. 2 Functions of a Single Variable. 2.1 Properties of Single-Variable Functions. 2.2 Optimality Criteria. 2.3 Region Elimination Methods. 2.4 Polynomial Approximation or Point Estimation Methods. 2.5 Methods Requiring Derivatives. 2.6 Comparison of Methods. 2.7 Summary. References. Problems. 3 Functions of Several Variables. 3.1 Optimality Criteria. 3.2 Direct-Search Methods. 3.3 Gradient-Based Methods. 3.4 Comparison of Methods and Numerical Results. 3.5 Summary. References. Problems. 4 Linear Programming. 4.1 Formulation of Linear Programming Models. 4.2 Graphical Solution of Linear Programs in Two Variables. 4.3 Linear Program in Standard Form. 4.5 Computer Solution of Linear Programs. 4.5.1 Computer Codes. 4.6 Sensitivity Analysis in Linear Programming. 4.7 Applications. 4.8 Additional Topics in Linear Programming. 4.9 Summary. References. Problems. 5 Constrained Optimality Criteria. 5.1 Equality-Constrained Problems. 5.2 Lagrange Multipliers. 5.3 Economic Interpretation of Lagrange Multipliers. 5.4 Kuhn-Tucker Conditions. 5.5 Kuhn-Tucker Theorems. 5.6 Saddlepoint Conditions. 5.7 Second-Order Optimality Conditions. 5.8 Generalized Lagrange Multiplier Method. 5.9 Generalization of Convex Functions. 5.10 Summary. References. Problems. 6 Transformation Methods. 6.1 Penalty Concept. 6.2 Algorithms, Codes, and Other Contributions. 6.3 Method of Multipliers. 6.4 Summary. References. Problems. 7 Constrained Direct Search. 7.1 Problem Preparation. 7.2 Adaptations of Unconstrained Search Methods. 7.3 Random-Search Methods. 7.4 Summary. References. Problems. 8 Linearization Methods for Constrained Problems. 8.1 Direct Use of Successive Linear Programs. 8.2 Separable Programming. 8.3 Summary. References. Problems. 9 Direction Generation Methods Based on Linearization. 9.1 Method of Feasible Directions. 9.2 Simplex Extensions for Linearly Constrained Problems. 9.3 Generalized Reduced Gradient Method. 9.4 Design Application. 9.5 Summary. References. Problems. 10 Quadratic Approximation Methods for Constrained Problems. 10.1 Direct Quadratic Approximation. 10.2 Quadratic Approximation of the Lagrangian Function. 10.3 Variable Metric Methods for Constrained Optimization. 10.4 Discussion. 10.5 Summary. References. Problems. 11 Structured Problems and Algorithms. 11.1 Integer Programming. 11.2 Quadratic Programming. 11.3 Complementary Pivot Problems. 11.4 Goal Programming. 11.5 Summary. References. Problems. 12 Comparison of Constrained Optimization Methods. 12.1 Software Availability. 12.2 A Comparison Philosophy. 12.3 Brief History of Classical Comparative Experiments. 12.4 Summary. References. 13 Strategies for Optimization Studies. 13.1 Model Formulation. 13.2 Problem Implementation. 13.3 Solution Evaluation. 13.4 Summary. References. Problems. 14 Engineering Case Studies. 14.1 Optimal Location of Coal-Blending Plants by Mixed-Integer Programming. 14.2 Optimization of an Ethylene Glycol-Ethylene Oxide Process. 14.3 Optimal Design of a Compressed Air Energy Storage System. 14.4 Summary. References. Appendix A Review of Linear Algebra. A.1 Set Theory. A.2 Vectors. A.3 Matrices. A.3.1 Matrix Operations. A.3.2 Determinant of a Square Matrix. A.3.3 Inverse of a Matrix. A.3.4 Condition of a Matrix. A.3.5 Sparse Matrix. A.4 Quadratic Forms. A.4.1 Principal Minor. A.4.2 Completing the Square. A.5 Convex Sets. Appendix B Convex and Concave Functions. Appendix C Gauss-Jordan Elimination Scheme. Author Index. Subject Index.

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Book SynopsisThis comprehensive reference presents the latest techniques for numerical analysis of forming operations. This is the perfect tool for those who wish to investigate new analytical methods for forming.Table of ContentsThe Tensile Test and Basic Material Behavior. Tensors, Matrices, Notation. Stress. Strain. Standard Mechanical Principles. Elasticity. Plasticity. Crystal-Based Plasticity. Friction. Classical Forming Analysis. Index.

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Book SynopsisAn updated and revised edition of the standard work on the use of critical path methods (CPM) in the construction industry. Describes the mechanics and procedures of CPM in construction planning and works control and demonstrates its application to large and small projects alike.Table of ContentsCritical Path Method Procedures and Terminology. The Network Diagram and Utility Data. Network Calculations I: Critical Paths and Floats. Network Calculations II: Simple Compression. Network Calculations III: Complex Compression andDecompression. Network Calculations IV: Scheduling and Resource Leveling. Practical Planning with Critical Path Methods. Project Control with Critical Path Methods. Financial Planning and Cost Control. Evaluation of Work Changes and Delays. Attitudes, Responsibilities, and Duties. Computer-Aided CPM. Selection of Technique. Integrated Project Development and Management. CPM, a Systems Concept. Appendices. Index.

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Book SynopsisNumerical Computation of Internal and External Flows Volume 2: Computational Methods for Inviscid and Viscous Flows C. Hirsch, Vrije Universiteit Brussel, Brussels, Belgium This second volume deals with the applications of computational methods to the problems of fluid dynamics.Table of ContentsPreface xv Nomenclature xix Part V: The Numerical Computation of Potential Flows 1 Chapter 13 The Mathematical Formulations of the Potential Flow Model 4 13.1 Conservative Form of the Potential Equation 4 13.2 The Non-conservative Form of the Isentropic Potential Flow Model 6 13.2.1 Small-perturbation potential equation 7 13.3 The Mathematical Properties of the Potential Equation 9 13.3.1 Unsteady potential flow 9 13.3.2 Steady potential flow 9 13.4 Boundary Conditions 14 13.4.1 Solid wall boundary condition 14 13.4.2 Far field conditions 15 13.4.3 Cascade and channel flows 17 13.4.4 Circulation and Kutta condition 18 13.5 Integral or Weak Formulation of the Potential Model 18 13.5.1 Bateman variational principle 19 13.5.2 Analysis of some properties of the variational integral 20 Chapter 14 The Discretization of the Subsonic Potential Equation 26 14.1 Finite Difference Formulation 27 14.1.1 Numerical estimation of the density 29 14.1.2 Curvilinear mesh 31 14.1.3 Consistency of the discretization of metric coefficients 34 14.1.4 Boundary conditions—curved solid wall 36 14.2 Finite Volume Formulation 38 14.2.1 Jameson and Caughey’s finite volume method 39 14.3 Finite Element Formulation 42 14.3.1 The finite element—Galerkin method 43 14.3.2 Least squares or optimal control approach 47 14.4 Iteration Scheme for the Density 47 Chapter 15 The Computation of Stationary Transonic Potential Flows 57 15.1 The Treatment of the Supersonic Region: Artificial Viscosity—Density and Flux Upwinding 61 15.1.1 Artificial viscosity—non-conservative potential equation 62 15.1.2 Artificial viscosity—conservative potential equation 66 15.1.3 Artificial compressibility 67 15.1.4 Artificial flux or flux upwinding 70 15.2 Iteration Schemes for Potential Flow Computations 77 15.2.1 Line relaxation schemes 77 15.2.2 Guidelines for resolution of the discretized potential equation 81 15.2.3 The alternating direction implicit method—approximate factorization schemes 88 15.2.4 Other techniques—multigrid methods 98 15.3 Non-uniqueness and Non-isentropic Potential Models 104 15.3.1 Isentropic shocks 105 15.3.2 Non-uniqueness and breakdown of the transonic potential flow model 105 15.3.3 Non-isentropic potential models 112 15.4 Conclusions 117 Part VI: The Numerical Solution of the System of Euler Equations 125 Chapter 16 The Mathematical Formulation of the System of Euler Equations 132 16.1 The Conservative Formulation of the Euler Equations 132 16.1.1 Integral conservative formulation of the Euler equations 133 16.1.2 Differential conservative formulation 134 16.1.3 Cartesian system of coordinates 134 16.1.4 Discontinuities and Rankine-Hugoniot relations—entropy condition 135 16.2 The Quasi-linear Formulation of the Euler Equations 138 16.2.l The Jacobian matrices for conservative variables 138 16.2.2 The Jacobian matrices for primitive variables 145 16.2.3 Transformation matrices between conservative and non-conservative variables 147 16.3 The Characteristic Formulation of the Euler Equations—Eigenvalues and Compatibility Relations 150 16.3.1 General properties of characteristics 151 16.3.2 Diagonalization of the Jacobian matrices 153 16.3.3 Compatibility equations 154 16.4 Characteristic Variables and Eigenvalues for One-dimensional Flows 157 16.4.1 Eigenvalues and eigenvectors of Jacobian matrix 158 16.4.2 Characteristic variables 162 16.4.3 Characteristics in the xt-plane—shocks and contact discontinuities 168 16.4.4 Physical boundary conditions 171 16.4.5 Characteristics and simple wave solutions 173 16.5 Eigenvalues and Compatibility Relations in Multidimensional Flows 176 16.5.1 Jacobian eigenvalues and eigenvectors in primitive variables 177 16.5.2 Diagonalization of the conservative Jacobians 180 16.5.3 Mach cone and compatibility relations 184 16.5.4 Boundary conditions 191 16.6 Some Simple Exact Reference Solutions for One-dimensional Inviscid Flows 196 16.6.1 The linear wave equation 196 16.6.2 The inviscid Burgers equation 196 16.6.3 The shock tube problem or Riemann problem 204 16.6.4 The quasi-one-dimensional nozzle flow 211 Chapter 17 The Lax–Wendroff Family of Space-centred Schemes 224 17.1 The Space-centred Explicit Schemes of First Order 226 17.1.1 The one-dimensional Lax–Friedrichs scheme 226 17.1.2 The two-dimensional Lax–Friedrichs scheme 229 17.1.3 Corrected viscosity scheme 233 17.2 The Space-centred Explicit Schemes of Second Order 234 17.2.1 The basic one-dimensional Lax–Wendroff scheme 234 17.2.2 The two-step Lax–Wendroff schemes in one dimension 238 17.2.3 Lerat and Peyret’s family of non-linear two-step Lax–Wendroff schemes 246 17.2.4 One-step Lax–Wendroff schemes in two dimensions 251 17.2.5 Two-step Lax–Wendroff schemes in two dimensions 258 17.3 The Concept of Artificial Dissipation or Artificial Viscosity 272 17.3.1 General form of artificial dissipation terms 273 17.3.2 Von Neumann–Richtmyer artificial viscosity 274 17.3.3 Higher-order artificial viscosities 279 17.4 Lerat’s Implicit Schemes of Lax–Wendroff Type 283 17.4.1 Analysis for linear systems in one dimension 285 17.4.2 Construction of the family of schemes 288 17.4.3 Extension to non-linear systems in conservation form 292 17.4.4 Extension to multi-dimensional flows 296 17.5 Summary 296 Chapter 18 The Central Schemes with Independent Time Integration 307 18.1 The Central Second-order Implicit Schemes of Beam and Warming in One Dimension 309 18.1.1 The basic Beam and Warming schemes 310 18.1.2 Addition of artificial viscosity 315 18.2 The Multidimensional Implicit Beam and Warming Schemes 326 18.2.1 The diagonal variant of Pulliam and Chaussee 328 18.3 Jameson’s Multistage Method 334 18.3.1 Time integration 334 18.3.2 Convergence acceleration to steady state 335 Chapter 19 The Treatment of Boundary Conditions 344 19.1 One-dimensional Boundary Treatment for Euler Equations 345 19.1.1 Characteristic boundary conditions 346 19.1.2 Compatibility relations 347 19.1.3 Characteristic boundary conditions as a function of conservative and primitive variables 349 19.1.4 Extrapolation methods 353 19.1.5 Practical implementation methods for numerical boundary conditions 357 19.1.6 Nonreflecting boundary conditions 369 19.2 Multidimensional Boundary Treatment 372 19.2.1 Physical and numerical boundary conditions 372 19.2.2 Multidimensional compatibility relations 376 19.2.3 Farfield treatment for steadystate flows 377 19.2.4 Solid wall boundary 379 19.2.5 Nonreflective boundary conditions 384 19.3 The Far-field Boundary Corrections 385 19.4 The Kutta Condition 395 19.5 Summary 401 Chapter 20 Upwind Schemes for the Euler Equations 408 20.1 The Basic Principles of Upwind Schemes 409 20.2 One-dimensional Flux Vector Splitting 415 20.2.1 Steger and Warming flux vector splitting 415 20.2.2 Properties of split flux vectors 417 20.2.3 Van Leer’s flux splitting 420 20.2.4 Non-reflective boundary conditions and split fluxes 425 20.3 One-dimensional Upwind Discretizations Based on Flux Vector Splitting 426 20.3.1 First-order explicit upwind schemes 426 20.3.2 Stability conditions for first-order flux vector splitting schemes 428 20.3.3 Non-conservative firstorder upwind schemes 438 20.4 Multi-dimensional Flux Vector Splitting 438 20.4.1 Steger and Warming flux splitting 440 20.4.2 Van Leer flux splitting 440 20.4.3 Arbitrary meshes 441 20.5 The Godunov-type Schemes 443 20.5.1 The basic Godunov scheme 444 20.5.2 Osher’s approximate Riemann solver 453 20.5.3 Roe’s approximate Riemann solver 460 20.5.4 Other Godunov-type methods 469 20.5.5 Summary 472 20.6 First-order Implicit Upwind Schemes 473 20.7 Multi-dimensional First-order Upwind Schemes 475 Chapter 21 Second-order Upwind and High-resolution Schemes 493 21.1 General Formulation of Higher-order Upwind Schemes 494 21.1.1 Higher-order projection stages-variable extrapolation or MUSCL approach 495 21.1.2 Numerical flux for higher-order upwind schemes 498 21.1.3 Second-order space- and time-accurate upwind schemes based on variable extrapolation 499 21.1.4 Linearized analysis of second-order upwind schemes 502 21.1.5 Numerical flux for higher-order upwind schemes—flux extrapolation 504 21.1.6 Implicit second-order upwind schemes 512 21.1.7 Implicit second-order upwind schemes in two dimensions 514 21.1.8 Summary 516 21.2 The Definition of High-resolution Schemes 517 21.2.1 The generalized entropy condition for inviscid equations 519 21.2.2 Monotonicity condition 525 21.2.3 Total variation diminishing (TVD)schemes 528 21.3 Second-order TVD Semi-discretized Schemes with Limiters 536 21.3.1 Definition of limiters for the linear convection equation 537 21.3.2 General definition of flux limiters 550 21.3.3 Limiters for variable extrapolation—MUSCL—method 552 21.4 Timeintegration Methods for TVD Schemes 556 21.4.1 Explicit TVD schemes of first-order accuracy in time 557 21.4.2 Implicit TVD schemes 558 21.4.3 Explicit second-order TVD schemes 560 21.4.4 TVD schemes and artificial dissipation 564 21.4.5 TVD limiters and the entropy condition 568 21.5 Extension to Non-linear Systems and to Multi-dimensions 570 21.6 Conclusions to Part VI 583 Part VII: The Numerical Solution of the Navier-Stokes Equations 595 Chapter 22 The Properties of the System of Navier–Stokes Equations 597 22.1 Mathematical Formulation of the Navier–Stokes Equations 597 22.1.1 Conservative form of the Navier–Stokes equations 597 22.1.2 Integral form of the Navier–Stokes equations 599 22.1.3 Shock waves and contact layers 600 22.1.4 Mathematical properties and boundary conditions 601 22.2 Reynolds-averaged Navier–Stokes Equations 603 22.2.1 Turbulent-averaged energy equation 604 22.3 Turbulence Models 606 22.3.1 Algebraic models 608 22.3.2 One- and two-equation models—k–ε models 613 22.3.3 Algebraic Reynolds stress models 615 22.4 Some Exact One-dimensional Solutions 618 22.4.1 Solutions to the linear convection-diffusion equation 618 22.4.2 Solutions to Burgers equation 620 22.4.3 Other simple test cases 621 Chapter 23 Discretization Methods for the Navier–Stokes Equations 624 23.1 Discretization of Viscous and Heat Conduction Terms 625 23.2 Time-dependent Methods for Compressible Navier–Stokes Equations 627 23.2.1 First-order explicit central schemes 628 23.2.2 One-step Lax–Wendroff schemes 629 23.2.3 Two-step Lax–Wendroff schemes 630 23.2.4 Central schemes with separate space and time discretization 636 23.2.5 Upwind schemes 648 23.3 Discretization of the Incompressible Navier–Stokes Equations 654 23.3.1 Incompressible Navier–Stokes equations 654 23.3.2 Pseudo-compressibility method 656 23.3.3 Pressure correction methods 661 23.3.4 Selection of the space discretization 666 23.4 Conclusions to Part VII 674 Index 685

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Book SynopsisChange-point problems arise in a variety of experimental andmathematical sciences, as well as in engineering and healthsciences. This rigorously researched text provides a comprehensivereview of recent probabilistic methods for detecting various typesof possible changes in the distribution of chronologically orderedobservations. Further developing the already well-establishedtheory of weighted approximations and weak convergence, the authorsprovide a thorough survey of parametric and non-parametric methods,regression and time series models together with sequential methods.All but the most basic models are carefully developed with detailedproofs, and illustrated by using a number of data sets. Contains athorough survey of: * The Likelihood Approach * Non-Parametric Methods * Linear Models * Dependent Observations This book is undoubtedly of interest to all probabilists andstatisticians, experimental and health scientists, engineers, andessential for those wTrade Review"This book is suitable for Ph.D. students who wish to establish a solid grounding in the field, and researchers who need a reliable reference to precisely formulated results and their proofs. The book contains a very extensive list of references reading into the late 1990's." (Mathematical Reviews, 2011)Table of ContentsThe Likelihood Approach. Nonparametric Methods. Linear Models. Dependent Observations. Appendix. References. Indexes.

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Book SynopsisThe concept of a system as an entity in its own right has emergedwith increasing force in the past few decades in, for example, theareas of electrical and control engineering, economics, ecology,urban structures, automaton theory, operational research andindustry. The more definite concept of a large-scale system isimplicit in these applications, but is particularly evident infields such as the study of communication networks, computernetworks and neural networks. The Wiley-Interscience Series inSystems and Optimization has been established to serve the needs ofresearchers in these rapidly developing fields. It is intended forworks concerned with developments in quantitative systems theory,applications of such theory in areas of interest, or associatedmethodology. This is the first book-length treatment of risk-sensitive control,with many new results. The quadratic cost function of the standardLQG (linear/quadratic/Gaussian) treatment is replaced by theexponential of a quadratTable of ContentsBASICS. Deterministic Models. Stochastic Models. BEYOND. Risk-Sensitive and H infinity Criteria. Time-Integral Methods and Optimal Stationary Policies. Near-Determinism and Large Deviation Theory. Appendices. References. Index.

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Book SynopsisClearly written and free of statistical jargon, this invaluable guide concentrates on the practicalities of statistical analysis for anyone involved with agricultural research. Each section starts with the key points, giving a quick reference to the contents and plenty of examples using a reala data.Table of ContentsAcknowledgements INTRODUCTION Notation A little history Population versus samples PLANNING Formulating the idea Defining objectives Defining the population Formulating hypotheses Hypothesis testing Anticipating treatment differences DESIGN Variables Choosing the treatments Constraints Replication Blocking Randomization Covariants Confounding TRIAL STRUCTURE Considerations Single-treatment factor designs Multi-treatment factor designs Some other designs DATA ENTRY AND EXPLORATION Data entry Data Data checking Data exploration ANALYTICAL TECHNIQUES Parametric techniques Non-parametric techniques Comparison of parametric and non-parametric techniques OTHER STATISTICAL TECHNIQUES Multivariate analysis Time series analysis ASPECTS OF COMPUTING APPENDICES Glossary of Statistical Terms Analysis of Variance Formulae INDEX

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Book SynopsisMatrices are used in many fields such as statistics, econometrics, mathematics, natural sciences and engineering. They provide a concise, simple method for describing long and complicated computations. This is a comprehensive handbook and dictionary of terms for matrix theory.Table of ContentsDefinitions, Notations, Terminology. Rules for Matrix Operations. Matrix Valued Functions of a Matrix. Trace, Determinant and Rank of a Matrix. Eigenvalues and Singular Values. Matrix Decompositions and Canonical Forms. Vectorization Operators. Vector and Matrix Norms. Properties of Special Matrices. Vector and Matrix Derivatives. Polynomials, Power Series and Matrices. Appendix. References. Index.

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Book SynopsisThe finite element method and the boundary element method are two computational methods available for designing structures ranging from aircraft and ships to dams and tunnels. This text presents the mathematical basis of the joint use of both methods and their computer implementation.Table of ContentsBasic principle and domains of application. I. BOUNDARY INTEGRAL EQUATIONS FOR STATIC PROBLEMS : Integral Equations and Representations for the Poisson Equation; Numerical Solution using Boundary Elements; Integral Equations and Representations for Elastostatics; Integral Representations of Gradients and Stresses on the Boundary; Some Classical Mathematical Results II. BOUNDARY INTEGRAL EQUATIONS FOR WAVE AND EVOLUTION PROBLEMS: Waves and Elastodynamics in Time Domain; Waves and Elastodynamics in Frequency Domain; Diffusion, Fluid Flow. III. ADVANCED TOPICS : Variational Boundary Integral Formulations; Exploitation of Geometrical Symmetry; Domain Derivative and Boundary Integral Eequations. IV. ADDITIONAL TOPICS IN SOLID MECHANICS : Boundary Integral Equations for Cracked Solids; Initial Strain or Stress: Inclusions, Elastoplasticity. APPENDICES : Tangential Differential Operators and Integration by Parts; Interpolation Functions and Numerical Integration. Bibliography. Index.

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Book SynopsisThis book presents ordinary differential equations based on Lie group analysis and related invariance principles. The author provides students and teachers with a text for one-semester undergraduate and graduate courses that spans a variety of topics, from the basic theory through to applications.Trade Review"…this is the first self-contained university text on ordinary differential equations…" (Zentralblatt Math, Vol.1047, No.22, 2004)Table of ContentsIntroduction to Differential Equations. Transformation Groups. Lie Group Analysis of Ordinary Differential Equations. Brief on Lie Algebras. First Order Differential Equations. Integration of Second Order Equations. Basic Theory of Linear Equations. Nonlinear Second Order Equations. Integration of Third Order Equations. Nonlinear Superposition Principle. Index.

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Book SynopsisThis text shows how stochastic geometry can be applied to real structural problems in materials science and technology. It pays particular attention to describing spatial sizes and shapes of grains and particles, developments in stochastic geometry, and relevant computer simulation techniques.Trade Review"...provides many examples...comprehensive discussions...an introduction to the analysis of two-dimensional and three-dimensional microscopic images...references are comprehensive..." (Short Book Reviews, Vol. 21, No. 2, August 2001) "There is no book I know in our own field that deals with the subject in anything like the depth and breadth as this one does." (European Journal of Soil Science, No. 52 2001) "It can be expected that this unusually careful work will soon be acknowledged as an authoritative treatment, and certainly it will remain a major reference of applied stereology in the next two decades at least. Scientific and technical libraries should have multiple copies available." (Ceramics, Vol.45 No.3, 2001) "...an ideal textbook for a one-semester course...also an excellent reference book..." (Technometrics, February 2002)Table of ContentsDedication to Günter Bach. Preface. Series Preface. Acknowledgements. List of Notation. List of Source Codes. Introduction. Methodological Tools. Statistical Estimation of Basic Characteristics. Basic Characteristics and Digitalization. Covariance and Spectral Density. Size Distribution of Spherical Particles. Nonspherical Particles of Constant Shape. Size-Shape Distribution of Particles. Arrangement of Objects. Single-Phase Polyhedral Microstructures. Appendix A: Characteristics of Geometric Objects. Appendix B: Software Utilities. References. Index.

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Book SynopsisThis volume presents a unified framework for systems engineering and a systematic and rigorous source for a comprehensive description of the utilization of Monte Carlo methods in practical engineering problems. The author suggests that efficiency can be improved through such an integrated approach.Table of Contents1. Introduction - Probability and statistics 2. Basic concepts in system engineering 3. Basic concepts in Monte Carlo methods 4. Additional applications 5. Elements of uncertainty and uncertainty analysis 6. System transport 7. Realization of system transport Appendix

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