Maths for engineers Books

Book SynopsisAt the official dinner of a· meeting in May 1939, I was seated next to Max Hansen. When I congratulated him on the well deserved success of his "Aufbau der Zweistoff-Legierungen", he smiled: "yes, it was a struggle with the hydra, and so it has taken me seven years", meaning that whenever he had thought to have finished the phase diagram of a particular system, new evidence would turn up like the new heads of the Greek monster. There is no need to point out the importance of assessed phase diagrams to metallurgists or even anyone concerned with the technology and applica­ tion of metals and alloys. The information contained therein is fundamental to considerations concerning the chemical, physical and mechanical properties of alloys. Hansen's German monograph was followed by a revised English edition in 1958 with K. Anderko and the supplements by R.P. Elliott (1965) and F.A. Shunk (1969). All those who have made use of these volumes will admit that much diligent labour has gone into this work, necessary to cope with the ever increasing number of publications and the consequent improvements.Table of ContentsFe-Ag Iron-Silver.- Fe-Li (Na, K) Iron-Alkaline Metals.- Fe-Al Iron-Aluminium (Figs. 1–3).- Fe-Am Iron-Americium.- Fe-As Iron-Arsenic (Fig. 4).- Fe-Au Iron-Gold (Fig. 5).- Fe-B Iron-Boron (Fig. 6).- Fe-Ba Iron-Barium.- Fe-Be Iron-Beryllium (Figs. 7, 8).- Fe-Bi Iron-Bismuth.- Fe-C Iron-Carbon (Figs. 9–12).- Fe-Ca Iron-Calcium.- Fe-Cd Iron-Cadmium.- Fe-Co Iron-Cobalt (Figs. 13, 14).- Fe-Cr Iron-Chromium (Figs. 15, 16).- Fe-Cu Iron-Copper (Figs. 17–20).- Fe-Eu Iron-Europium.- Fe-Ga Iron-Gallium (Figs. 21–24).- Fe-Ge Iron-Germanium (Fig. 25).- Fe-H Iron-Hydrogen (Figs. 26, 27).- Fe-D Iron-Deuterium (Fig. 28).- Fe-T Iron-Tritium (Fig.28).- Fe-Hf Iron-Hafnium (Fig. 29).- Fe-Hg Iron-Mercury (Fig. 30).- Fe-In Iron-Indium (Fig.31).- Fe-Ir Iron-Iridium (Fig. 32).- Fe-La Iron-Lanthanum (Fig. 33).- Fe-Mg Iron-Magnesium (Fig. 34).- Fe-Mn Iron-Manganese (Fig. 35).- Fe-Mo Iron-Molybdenum (Figs. 36–38).- Fe-N Iron-Nitrogen (Figs. 39, 40).- Fe-Nb Iron-Niobium (Fig. 41).- Fe-Ni Iron-Nickel (Figs. 42–44).- Fe-O Iron-Oxygen (Fig. 45).- Fe-Os Iron-Osmium (Figs. 46, 47).- Fe-P Iron-Phosphorus (Figs. 48, 49).- Fe-Pb Iron-Lead (Figs. 50, 51).- Fe-Pd Iron-Palladium (Fig. 52).- Fe-Pt Iron-Platinum (Fig. 53).- Fe-Pu Iron-Plutonium (Figs. 54, 55).- Fe-R Iron-Rare Earth Metals (Figs. 56–68).- Fe-Re Iron-Rhenium (Fig. 69).- Fe-Rh Iron-Rhodium (Fig. 70).- Fe-Ru Iron-Ruthenium (Fig. 71).- Fe-S Iron-Sulphur (Figs. 72, 73).- Fe-Sb Iron-Antimony (Figs. 74, 75).- Fe-Sc Iron-Scandium (Fig. 76).- Fe-Se Iron-Selenium (Fig. 77).- Fe-Si Iron-Silicon (Figs. 78, 79).- Fe-Sn Iron-Tin (Figs. 80, 81).- Fe-Sr Iron-Strontium.- Fe-Ta Iron-Tantalum (Figs. 82, 83).- Fe-Tc Iron-Technetium (Figs. 84, 85).- Fe-Te Iron-Tellurium (Fig. 86).- Fe-Th Iron-Thorium (Fig. 87).- Fe-Ti Iron-Titanium (Figs. 88–90).- Fe-Tl Iron-Thallium.- Fe-U Iron-Uranium (Figs.91, 92).- Fe-V Iron-Vanadium (Figs. 93–95).- Fe-W Iron-Tungsten (Figs. 96, 97).- Fe-Y Iron-Yttrium (Fig. 98).- Fe-Yb Iron-Ytterbium (Fig. 99).- Fe-Zn Iron-Zinc (Figs. 100, 101).- Fe-Zr Iron-Zirconium (Figs. 102, 103).- Appendix Table 1. Physico-chemical properties of the elements.- Table 2. Structural types of elements and compounds.- Table 3. Numerical differences between the International Practical Temperature Scale of 1968 and that of 1948.

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Book SynopsisThis book is conceived as a comprehensive and detailed text-book on non-linear dynamical systems with particular emphasis on the exploration of chaotic phenomena. The self-contained introductory presentation is addressed both to those who wish to study the physics of chaotic systems and non-linear dynamics intensively as well as those who are curious to learn more about the fascinating world of chaotic phenomena. Basic concepts like Poincaré section, iterated mappings, Hamiltonian chaos and KAM theory, strange attractors, fractal dimensions, Lyapunov exponents, bifurcation theory, self-similarity and renormalisation and transitions to chaos are thoroughly explained. To facilitate comprehension, mathematical concepts and tools are introduced in short sub-sections. The text is supported by numerous computer experiments and a multitude of graphical illustrations and colour plates emphasising the geometrical and topological characteristics of the underlying dynamics.This volume is a completely revised and enlarged second edition which comprises recently obtained research results of topical interest, and has been extended to include a new section on the basic concepts of probability theory. A completely new chapter on fully developed turbulence presents the successes of chaos theory, its limitations as well as future trends in the development of complex spatio-temporal structures."This book will be of valuable help for my lectures" Hermann Haken, Stuttgart"This text-book should not be missing in any introductory lecture on non-linear systems and deterministic chaos" Wolfgang Kinzel, Würzburg“This well written book represents a comprehensive treatise on dynamical systems. It may serve as reference book for the whole field of nonlinear and chaotic systems and reports in a unique way on scientific developments of recent decades as well as important applications.” Joachim Peinke, Institute of Physics, Carl-von-Ossietzky University Oldenburg, GermanyTrade Review“Familiarity with ideas and tools presented here is of doubtless use for all those who apply methods of the theory of dynamical systems to various problems in science and technology. I expect the book to find its readership basically as an introduction to nonlinear dynamics for undergraduate students of natural sciences, but also as a general reference work for researchers confronted with the need to understand dynamical mechanisms behind the phenomena which they encounter in their experiments and numerical simulations.” (Mikhail Zaks, Mathematical Reviews, May, 2016)Table of ContentsDescriptive synopsis of the text.- Mathematical introduction to dynamical systems.- Dynamical systems without dissipation.- Dynamical systems with dissipation.- Local bifurcation theory.- Convective flow: Benard problem.- Routes to chaos.- Turbulence.- Computer experiments.

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Book SynopsisDesigned to provide tools for independent study, this book contains student-tested mathematical exercises joined with MATLAB programming exercises.Most chapters open with a review followed by theoretical and programming exercises, with detailed solutions provided for all problems including programs. Many of the MATLAB exercises are presented as Russian dolls: each question improves and completes the previous program and results are provided to validate the intermediate programs.The book offers useful MATLAB commands, advice on tables, vectors, matrices and basic commands for plotting. It contains material on eigenvalues and eigenvectors and important norms of vectors and matrices including perturbation theory; iterative methods for solving nonlinear and linear equations; polynomial and piecewise polynomial interpolation; Bézier curves; approximations of functions and integrals and more. The last two chapters considers ordinary differential equations including two point boundary value problems, and deal with finite difference methods for some partial differential equations.The format is designed to assist students working alone, with concise Review paragraphs, Math Hint footnotes on the mathematical aspects of a problem and MATLAB Hint footnotes with tips on programming.Trade ReviewFrom the book reviews:“This is a very interesting and useful book for any advanced undergraduate and beginning graduate student on mathematics, statistics, computational physics, chemistry, and engineering, with a focus on numerical analysis and computational science. The main scope of this book is to provide students with the opportunity to apply numerical analysis and the well-known MATLAB to solve problems in their own specialties.” (T. E. Simos, Computing Reviews, January, 2015)“This is an interesting new kind of book in the area of numerical analysis. … It is widely accepted that solving exercises is essential to achieve a deeper understanding of a mathematical topic. Under this point of view the present book can be seen as an adequate vehicle to really get into the field of numerical analysis. … the book can also serve as a rich source of exercises for university courses.” (Rolf Dieter Grigorieff, zbMATH, Vol. 1304, 2015)Table of Contents1 An Introduction to MATLAB commands.- 2 Matrices and Linear Systems.- 3 Matrices, Eigenvalues and Eigenvectors.- 4 Matrices, Norms and Conditioning.- 5 Iterative Methods.- 6 Polynomial Interpolation.- 7 Bézier Curves and Bernstein Polynomials.- 8 Piecewise Polynomials, Interpolation and Applications.- 9 Approximation of Integrals.- 10 Linear Least Squares Methods.- 11 Continuous and Discrete Approximations.- 12 Ordinary Differential Equations, One Step Methods.- 13 Finite Differences for differential and partial differential equations.- References.- Index of Names.- Subject Index.- MATLAB Index.

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Book SynopsisWie kann man Ressourcen optimal nutzen? Wie finde ich die richtige Lösung für ein kompliziertes Problem? Wie erreiche ich mit geringstem Aufwand mein Ziel?Ohne mathematische Formeln zu bemühen, geht der Autor diesen und anderen Fragen der Optimierung komplexer Systeme auf den Grund. Die betrachteten Anwendungsfälle reichen von Ablaufplanungen über den Aufbau eines Energienetzes und anderer technischer Strukturen bis hin zu Fragen des täglichen Lebens – wie dem leidigen Kofferpacken oder frustrierten Beziehungen.Leicht verständlich und gut illustriert werden effiziente Herangehensweisen an die verschiedensten Optimierungsprobleme beschrieben und zahlreiche Algorithmen zu ihrer Lösung vorgestellt. Auf fast spielerische Weise betrachtet der Autor von einem einheitlichen Standpunkt aus kombinatorische wie kontinuierliche Optimierungsfragen und schlägt zum Schluss einen Bogen zur philosophischen Betrachtung über die Schönheit unserer Welt.Table of ContentsOptimierung und Technik.- Stell Dir ein Ziel: Zielfunktionen und ihre Landschaften.- Man kann's nicht allen recht machen: Die Optimierung frustrierter Systeme.- Gott würfelt nicht, oder?: Monte-Carlo-Verfahren der globalen Optimierung.- Geht’s nicht auch besser?: Klassische Optimierungsaufgaben.- Das macht es nicht leichter: Probleme mit Einschränkungen.- Optimalität im Kleinen wie im Großen.- Anstelle eines Schlussworts: Die Schönheit des Optimums.

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Book SynopsisKünstliche Intelligenz ist eine Schlüsseltechnologie, mit der sowohl in der Wissenschaft als auch in der Industrie große Erwartungen verbunden sind. In diesem Buch werden sowohl die Perspektiven als auch die Grenzen dieser Technologie diskutiert. Das betrifft die praktischen, theoretischen und konzeptionellen Herausforderungen, denen sich die KI stellen muss. In einer Frühphase standen in der KI Expertensysteme im Vordergrund, bei denen mit Hilfe symbolischer Datenverarbeitung regelbasiertes Wissen verarbeitet wurde. Heute wird die KI von statistik-basierten Methoden im Bereich des maschinellen Lernens beherrscht. Diese subsymbolische KI wird an den Lehren, die aus der Frühphase der KI gezogen werden können, gemessen. Als Ergebnis wird vor allem für eine hybride KI argumentiert, die die Potentiale beider Ansätze zur Entfaltung bringen kann.Table of ContentsZum Begriff der K¨unstlichen Intelligenz.- Praktische Grenzen.- Theoretische Grenzen.- Konzeptionelle Grenzen.- Ausblicke auf Hybride KI.

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Book SynopsisReal world investors differ in their tastes and attitudes and they do not have, in general, perfect information about the future prospects of the economy. Most theoretical models, however, assume to the contrary that investors are homogeneous and perfectly informed about the market. In this book, an attempt is made to overcome these shortcomings. In three different case studies, the effect of heterogeneous time preferences, heterogeneous beliefs and imperfect information about the economy's growth on the term structure of interest rates are studied. The initial chapter gives an introduction to the theory of financial markets in continuous time under imperfect information and establishes the existence of an equilibrium with complete markets.Table of ContentsInformation.- Equilibrium with Imperfect Information and Complete Asset Markets in Continuous Time: Introduction; A Competitive Financial Market with Imperfect Information; Martingale Representation Theorem for the Innovation Process; The Existence of an Arrow-Debreu Equilibrium, Pareter Efficiency and the Representation Agent; Completeness of the Market and Existence of a Financial Equilibrium; Pricing Redundant Securities and the Term Structure of Interest Rates.- Heterogeneous Time Preferences - Preferred Habitat Theory Revisited: Modeling Preferred Habitat Time Preferences; A Model with Heterogeneous Time Preferences; Equilibrium; Analysis of the Term Structure; The Demand for Long-Term Bonds.- Imperfect Information: The Term Structure when the Growth Rate is Unknown: The Model; Estimating the Drift; Equilibrium with Perfect and Imperfect Information; The Yield Curve with Normal and Bernoulli Prior Beliefs; General Prior Beliefs.- Bulls and Bears: Heterogeneous Expectations: Setup; Equilibrium; Two Examples.

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Book SynopsisAddressing students and researchers as well as Computational Fluid Dynamics practitioners, this book is the most comprehensive review of high-resolution schemes based on the principle of Flux-Corrected Transport (FCT). The foreword by J.P. Boris and historical note by D.L. Book describe the development of the classical FCT methodology for convection-dominated transport problems, while the design philosophy behind modern FCT schemes is explained by S.T. Zalesak. The subsequent chapters present various improvements and generalizations proposed over the past three decades. In this new edition, recent results are integrated into existing chapters in order to describe significant advances since the publication of the first edition. Also, 3 new chapters were added in order to cover the following topics: algebraic flux correction for finite elements, iterative and linearized FCT schemes, TVD-like flux limiters, acceleration of explicit and implicit solvers, mesh adaptation, failsafe limiting for systems of conservation laws, flux-corrected interpolation (remapping), positivity preservation in RANS turbulence models, and the use of FCT as an implicit subgrid scale model for large eddy simulations.Table of ContentsThe conception, gestation, birth and infancy of FCT.- The design of flux-corrected transport (FCT) algorithms for structured grids.- On monotonically integrated large eddy simulation of tubulent flows based on FCT algorithms.- Large scale urban simulations with FCT.- 30 years of FCT.- Algebraic flux corretion I.- Algebraic flux correction II.- Algebraic flux correction III.- Algebraic flux correction IV.- An evaluation of the FCT method for high-speed flows.- Flux-corrected and optimization-based remap.

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Book SynopsisChapter 1. Introduction to the bio-inspired X-structure/mechanism approach.- Chapter 2 The symmetric X-shaped structure.- Chapter 3 The horizontally-asymmetric X-shaped structure.- Chapter 4 The vertically-asymmetric X-shaped structure.- Chapter 5 Nonlinear dynamics in X-shaped structure.- Chapter 6 Multi-DoF-Multi-Joint leg-like structure.- Chapter 7 Nonlinear manipulation with X-mechanism.- Chapter 8 The adjustable X-mount.- Chapter 9 The nonlinear damping characteristics of the X-shaped structure.- Chapter 10 The adjustable and robust X-absorber.- Chapter 11 The X-shaped structure coupled with leverage I.- Chapter 12 The X-shaped structure coupled with leverage II.- Chapter 13 The human body inspired nonlinear inertia I.- Chapter 14 The human body inspired nonlinear inertia II.- Chapter 15 Nonlinear inertia coupling with X-mechanism: Modelling & Analysis.- Chapter 16 Nonlinear inertia coupling with X-mechanism: Prototyping & Testing.- Chapter 17 Stewart structure based 6-DoF vibration isolation.- Chapter 18 Compact 3-DoF anti-vibration -I: 10-bar mechanism.- Chapter 19 Compact 3-DoF anti-vibration -II: 4-bar mechanism.- Chapter 20 Compact 3-DoF anti-vibration -III: Adjustable mechanism.- Chapter 21 Vibration energy harvesting by employing nonlinear characteristics and structural benefits I.- Chapter 22 Vibration energy harvesting by employing nonlinear characteristics and structural benefits II.- Chapter 23 Vibration energy harvesting by employing nonlinear characteristics and structural benefits III.- Chapter 24 Structure optimization method for improving energy harvesting.- Chapter 25 Design of Quasi-Zero-Stiffness Sensor -I: without X-structures.- Chapter 26 Design of Quasi-Zero-Stiffness Sensor -I: with X-structures.- Chapter 27 X-structure based sensor systems in noisy environments.- Chapter 28 Fault detection based on X-sensor.- Chapter 28 X-Dynamics-Based Adaptive Tracking Control for Nonlinear Suspension Systems.- Chapter 29 Fuzzy Adaptive Control for Nonlinear Suspension Systems Based on A Bio-inspired Reference Model.- Chapter 30 Switching Logic-Based Saturated Tracking Control based on X-dynamics.- Chapter 31 Fixed-Time Safe-by-Design Control for Uncertain Active Vehicle Suspension Systems with Nonlinear Reference Dynamics.- Chapter 32 Anti-vibration exoskeleton for manipulating demolition tools.- Chapter 33 Design of novel bio-inspired “legs” for tracked robots.- Chapter 34 Design of novel vehicle seat suspension.- Chapter 35 Control of a tracked robot with X-suspension.- .

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Book SynopsisTrade Review"Overall, the reviewer considers this text to offer a good and useful coverage of advanced mathematics for engineers. It gives useful and succinct coverage of the topics included." --IEEE PulseTable of Contents1. Prologue 2. Ordinary Differential Equations 3. Laplace and Fourier Transform Methods 4. Matrices and Linear Systems of Equations 5. Analytical Methods for Solving Partial Differential Equations 6.Difference Numerical Methods for Differential Equations 7. Finite Element Technique 8. Treatment of Experimental Results 9. Numerical Analysis 10. Introduction to Complex Analysis 11. Nondimensionalisation 12. Nonlinear Differential Equations 13. Integral Equations 14. Calculus of Variations

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Book SynopsisGlyn James was most recently Emeritus Professor in Mathematics at Coventry University and was previously Dean of the School of Mathematical and Information Sciences at Coventry University. He had an active interest in mathematics education and was a past chairman of the Education Committee of the Institute of Mathematics and its Applications, and a member of the Royal Society Mathematics Education Subcommittee. In 1995 he was chairman of the Working Group that produced the report Mathematics Matters in Engineering on behalf of UK professional bodies in engineering and mathematics. He also co-edited five mathematics books and was a member of the advisory boards for three international journals. Sadly, Glyn James passed away in October 2019 during the production of this edition; his enthusiastic input was sorely missed, but this and its companion text Advanced Modern Engineering Mathematics remain a fitting legacy.     Phil Dyke

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Book SynopsisThis contributed volume focuses on aspects of dynamic game theory including differential games, evolutionary games, and stochastic games. It covers theoretical developments, algorithmic methods, and applications to fields as varied as mathematical biology, environmental management, economics, engineering, guidance and control, and social interaction. It will be of interest to an interdisciplinary audience of researchers, practitioners, and advanced graduate students.Advances in Dynamic Games presents state-of-the-art research that serves as a testament to the vitality and growth of the field of dynamic games and their applications. Its contributions, written by experts in their respective disciplines, are outgrowths of presentations originally given at the 15th International Symposium of Dynamic Games and Applications held July 19–22, 2012, in Byšice, Czech Republic.Table of ContentsPart I Dynamic Games: Theory and Computation.- 1 Relative Value Iteration for Stochastic Differential Games.- 2 OPTGAME3: A Dynamic Game Solver and an Economic Example.- 3 Dynamic Programming Approach to Aircraft Control in a Windshear.- 4 Existence of Optimal Controls for a Bi-Level Optimal Control Problem.- 5 Static Linear-Quadratic Gaussian Games.- 6 Interior Convergence Under Payoff Monotone Selections and Proper Equilibrium: Application to Equilibrium Selection.- Part II Dynamic Games: Applications.- 7 Should a Retailer Support a Quality Improvements Strategy?.- 8 A Large Population Parental Care Game with Asynchronous Moves.- 9 Conditions for Cooperation and Trading in Value-Cost Dynamic Games.- 10 Intra-seasonal Strategies Based on Energy Budgets in a Dynamic Predator-Prey Game.- 11 On a Game-Theoretic Model of Environmental Pollution Problem.- Part III Pursuit-Evasion Games 12 Open-Loop Solvability Operator in Differential Games with Simple Motions in the Plane.- 13 Game with Two Pursuers and One Evader: Case of Weak Pursuers.- 14 Collaborative Interception of Moving Re-Locatable Target .- 15 The Effect of Pursuer Dynamics on the Value of Linear.- Pursuit-Evasion Games with Bounded Controls.

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Book SynopsisThe development and use of models of various objects is becoming a more common practice in recent days. This is due to the ease with which models can be developed and examined through the use of computers and appropriate software. Of those two, the former - high-speed computers - are easily accessible nowadays, and the latter - existing programs - are being updated almost continuously, and at the same time new powerful software is being developed. Usually a model represents correlations between some processes and their interactions, with better or worse quality of representation. It details and characterizes a part of the real world taking into account a structure of phenomena, as well as quantitative and qualitative relations. There are a great variety of models. Modelling is carried out in many diverse fields. All types of natural phenomena in the area of biology, ecology and medicine are possible subjects for modelling. Models stand for and represent technical objects in physics, chemistry, engineering, social events and behaviours in sociology, financial matters, investments and stock markets in economy, strategy and tactics, defence, security and safety in military fields. There is one common point for all models. We expect them to fulfil the validity of prediction. It means that through the analysis of models it is possible to predict phenomena, which may occur in a fragment of the real world represented by a given model. We also expect to be able to predict future reactions to signals from the outside world.Trade ReviewFrom the reviews:“This textbook gives a short introduction to measurements, mathematical modeling, and computer simulation of dynamic systems. The mathematical modeling of dynamic systems is mainly based on systems of linear ordinary differential equations. … This book is divided into 5 chapters. … mainly written for students and researchers in engineering disciplines, who are interested in measurements, mathematical modeling, and computer simulation of dynamic systems.” (Manfred Tasche, Zentralblatt MATH, Vol. 1185, 2010)Table of Contentsto Measuring Systems.- Sensors.- Methods of Noise Reduction.- Model Development.- Mapping Error.

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Book SynopsisFrom the reviews: "All in all, Graham Borradaile has written and interesting and idiosyncratic book on statistics for geoscientists that will be welcome among students, researchers, and practitioners dealing with orientation data. That should include engineering geologists who work with things like rock fracture orientation measurements or clast alignment in paleoseismic trenches. It won’t replace the collection of statistics and geostatistics texts in my library, but it will have a place among them and will likely be one of several references to which I turn when working with orientation data.... The text is easy to follow and illustrations are generally clear and easy to read..."(William C. Haneberg, Haneberg Geoscience)Trade ReviewFrom the reviews: "All in all, Graham Borradaile has written and interesting and idiosyncratic book on statistics for geoscientists that will be welcome among students, researchers, and practitioners dealing with orientation data. That should include engineering geologists who work with things like rock fracture orientation measurements or clast alignment in paleoseismic trenches. It won’t replace the collection of statistics and geostatistics texts in my library, but it will have a place among them and will likely be one of several references to which I turn when working with orientation data.... The text is easy to follow and illustrations are generally clear and easy to read..."(William C. Haneberg, Haneberg Geoscience) "This monograph is an introductory course in statistically processed data types in earth sciences, where large sample contemporary methods of data gathering are required. … The book is intended for higher course students and aspirants in all earth sciences. It will be helpful for professional researchers in data processing in electronic tables. In contrast to usual textbooks on statistics, this book includes material on sample formation, time series and oriented data up to three dimensions, and is illustrated by substantive examples." (Sultan G. Valeev, Zentralblatt MATH, Vol. 1041 (16), 2004) "The statistical analysis of geological data requires, more often than not, techniques that are only covered by advanced courses in statistics. … G. Borradaile recognises this, and uses it as the starting point for his book … . he succeeds in demonstrating how treatment of Earth Science data can be greatly enhanced and quantified without great pain. … Statistics of Earth Science Data is a very convenient and complete introduction in statistics, with an approach that will be appreciated by geologists and other Earth scientists." (Kris Piessens, Geologica Belgica, Issue 7, 2004)Table of ContentsIntroduction.- Sampling Schemes.- Central Tendency and Dispersion.- Theoretical Distributions: Binomial, Poisson and Normal Distributions.- Statistical Interference: Estimation and Hypothesis Tests.- Comparing Frequency.- Distribution Curves.- Regression: Linear, Curvilinear and Multilinear.- Correlation and Comparison of Variables.- Sequences, Cycles and Time-series.- Circular Orientation Data.- Spherical Orientation Data.- Spherical Orientation Data: Tensors.- Errors in Compound Quantities.- Notes on the Manual Use of Stereograms.

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Book SynopsisMathematische Begriffe und Schreibweisen.- Elementare Rechenoperationen.- Potenzen.- Wurzeln.- Logarithmen.-Gleichungen.- Ungleichungen.- Systeme linearer Gleichungen.- Funktionen.- Analytische Geometrie.- Trigonometrie.- Winkelfunktionen.- Geometrie.- Differentialrechnung.- Integralrechnung.- Vektorrechnung.- Analytische Geometrie auf Vektorbasis.- Komplexe Zahlen und Funktionen.

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Book SynopsisThis guide book to mathematics contains in handbook form the fundamental working knowledge of mathematics which is needed as an everyday guide for working scientists and engineers, as well as for students. Easy to understand, and convenient to use, this guide book gives concisely the information necessary to evaluate most problems which occur in concrete applications. In the newer editions emphasis was laid on those fields of mathematics that became more important for the formulation and modeling of technical and natural processes, namely Numerical Mathematics, Probability Theory and Statistics, as well as Information Processing. Besides many enhancements and new paragraphs, new sections on Geometric and Coordinate Transformations, Quaternions and Applications, and Lie Groups and Lie Algebras were added for the sixth edition.Trade Review“Russian scholars Bronshtein and Semendyayev created a math classic over seven decades ago. … This new Springer edition details over 1,500 entries in its table of contents, including new entries for analytical geometry, Lie groups and Lie algebra, nonlinear optimization, and computer algebra systems. … Summing Up: Recommended. All mathematics library collections.” (K. L. Swetland, Choice, Vol. 53 (11), July, 2016)Table of ContentsArithmetics.- Functions.- Geometry.- Linear Algebra.- Algebra and Discrete Mathematics.- Differentiation.- Infinite Series.- Integral Calculus.- Differential Equations.- Calculus of Variations.- Linear Integral Equations.- Functional Analysis.- Vector Analysis and Vector Fields.- Function Theory.- Integral Transformations.- Probability Theory and Mathematical Statistics.- Dynamical Systems and Chaos.- Optimization.- Numerical Analysis.- Computer Algebra Systems-Example Mathematica.

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Book Synopsis„Was ist Mathematik?” – auf diese Frage gibt dieses dicke Buch zahllose Antworten. Mathematik ist eben viel mehr als ein Schul- und Studienfach oder Rechnen: Es ist Teil der menschlichen Kultur, ein riesiges aktives Forschungsgebiet und ein nützlicher Werkzeugkasten. „Was ist Mathematik?” – statt einer einzelnen Antwort zeichnen die Autoren ein Panorama, bunt und vielfältig. Da geht es um Philosophie, Beweise, große und kleine Probleme, fundamentale Konzepte, Teilgebiete, Forschungspraxis, Anwendungen der Mathematik. Und um Geschichten aus der Geschichte. Das Buch richtet sich an alle, die wissen und darüber nachdenken wollen, was Mathematik ist, insbesondere auch an Studierende der Mathematik. Es begleitet eine Vorlesung, die an der Freien Universität Berlin jährlich vor allem für Lehramtsstudierende angeboten wird.Table of ContentsWas ist Mathematik?- Mathematische Forschung.- Beweise.- Formeln, Zeichnungen und Bilder.- Philosophie der Mathematik.- Primzahlen.- Zahlenbereiche.- Unendlichkeit.- Dimensionen.- Zufall – Wahrscheinlichkeiten – Statistik.- Funktionen.- Anwendungen.- Rechnen.- Algorithmen und Komplexität.- Mathematik in der Öffentlichkeit.

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Book SynopsisComputer Simulation.- Basic Probability.- Conditional Probability.- Discrete Random Variables.- Expected Values for Discrete Random Variables.- Multiple Discrete Random Variables.- Conditional Probability Mass Functions.- Discrete N-Dimensional Random Variables.- Continuous Random Variables.- Expected Values for Continuous Random Variables.- Multiple Continuous Random Variables.- Conditional Probability Density Functions.- Continuous N-Dimensional Random Variables.- Probability and Moment Approximations Using Limit Theorems.- Basic Random Processes.- Wide Sense Stationary Random Processes.- Linear Systems and Wide Sense Stationary Random Processes.- Multiple Wide Sense Stationary Random Processes.- Gaussian Random Processes.- Poisson Random Processes.- Markov Chains.Trade ReviewFrom the reviews:"The book is composed of 22 chapters. … This is a very readable book. … Kay’s book undoubtedly will see its greatest use in engineering schools, but I think it would work nicely in other settings as well. … It is written in a clear and informal style that students will appreciate, its coverage is excellent, and the author’s stated objective (to lessen the difficulty that students usually experience assimilating and applying probability and random processes) will, I predict, be met." (Ralph P. Russo, The American Statistician, Vol. 62 (2), May, 2008)“Kay’s book occupies a unique place in the overcrowded market of textbooks on probability and random processes. … This new textbook is a breath of fresh air in the market of books devoted to probability and random processes. The book lives up to its ambition of setting a new standard for a modern, computer-based treatment of the subject. … I fully recommend its use in undergraduate and first-year graduate courses.” (Osvaldo Simeone, IEEE Control Systems Magazine, Vol. 27, June, 2007)Table of ContentsComputer Simulation.- Basic Probability.- Conditional Probability.- Discrete Random Variables.- Expected Values for Discrete Random Variables.- Multiple Discrete Random Variables.- Conditional Probability Mass Functions.- Discrete N-Dimensional Random Variables.- Continuous Random Variables.- Expected Values for Continuous Random Variables.- Multiple Continuous Random Variables.- Conditional Probability Density Functions.- Continuous N-Dimensional Random Variables.- Probability and Moment Approximations Using Limit Theorems.- Basic Random Processes.- Wide Sense Stationary Random Processes.- Linear Systems and Wide Sense Stationary Random Processes.- Multiple Wide Sense Stationary Random Processes.- Gaussian Random Processes.- Poisson Random Processes.- Markov Chains.

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Book SynopsisDiscover the benefits of applying algorithms to solve scientific, engineering, and practical problems Providing a combination of theory, algorithms, and simulations, Handbook of Applied Algorithms presents an all-encompassing treatment of applying algorithms and discrete mathematics to practical problems in hot application areas, such as computational biology, computational chemistry, wireless networks, and computer vision. In eighteen self-contained chapters, this timely book explores: * Localized algorithms that can be used in topology control for wireless ad-hoc or sensor networks * Bioinformatics algorithms for analyzing data * Clustering algorithms and identification of association rules in data mining * Applications of combinatorial algorithms and graph theory in chemistry and molecular biology * Optimizing the frequency planning of a GSM network using evolutioTable of ContentsPreface. Abstracts. Contributors. 1. Generating All and Random Instances of A combinatorial Object (Ivan Stojmenovic) 2. Backtracking and Isomorph-Free Generation of Polyhexes (Lucia Moura and Ivan Stojmenovic) 3. Graph Theoretic Models in Chemistry and Molecular Biology (Debra Knisley and Jeff Knisley) 4. Algorithmic Methods for the Analysis of Gene Expression Data (Hongbo Xie, Uros Midic, Slobodan Vucetic, and Zoran Obradovic) 5. Algorithms of Reaction-Diffusion Computing (Andrew Adamatzky) 6. Data Mining Algorithms I: Clustering (Dan A. Simovici) 7. Data Mining Algorithms II: Frequent Item Sets (Dan A. Simovici) 8. Algorithms for Data Streams (Camil Demetrescu and Irene Finocchi) 9. Applying Evolutionary Algorithms to Solve the Automatic Frequency Planning Problem (Francisco Luna, Enrique Alba, Antonio J. Nero, Patrick Nauru, and Salvador Pedraza) 10. Algorithmic Game Theory and Application s(Marios Mavronicolas, Vicky Papdopoulou, and Paul Spirakis) 11. Algorithms for Real-Time Object Detection in Images (Milos Stojmenovic) 12. 2D Shape Measures for Computer Vision (Paul L. Rosin and Jovisa Zunic) 13. Cryptographic Algorithms (Binal Roy and Amiya Nayak) 14. Secure Communication in Distributed Sensor Networks (DSN) (Subhamoy Maitra and Bimal Roy) 15. Localized Topology Control Algorithms for Ad Hoc and Sensor Networks (Hannes Frey and David Simplot-Ryl) 16. A Novel Admission Control for Multimedia LEO Satellite Networks (Syed R. Rizvi, Stephan Olariu, and Mona E. Rizvi) 17. Resilient Recursive Routing in Communication Networks (Costas C. Constantinou, Alexander S. Stepanenko, Theodoros N. Arvanitis, Kevin J. Baughan, and Bin Liu) 18. Routing Algorithms on WDM Optical Networks (Qian-Ping Gu) Index.

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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 increasing sophistication of buildings and bridges demands new analytical techniques. Reliability-based design is a well established technique in the structural and mechanical engineering communities that is now gaining momentum among geotechnical engineers.Trade Review"The publication presents an examination of the theories and methodologies available for risk assessment in geotechnical engineering, spanning the full range from established single-variable and “first order” methods to the most recent, advanced numerical developments. In response to the growing application of LRFD methodologies in geotechnical design, coupled with increased demand for risk assessments by clients ranging from regulatory agencies to insurance companies, the authors have introduced an innovative reliability-based risk assessment method, the Random Finite Element Method (RFEM). The authors have spent more than fifteen years developing this statistically based method for modeling the real spatial variability of soils and rocks." (MCEER, Information Service, January 5, 2009)Table of ContentsPreface. Acknowledgements. PART 1: THEORY. Chapter 1: Review of Probability Theory. 1.1 Introduction. 1.2 Basic Set Theory. 1.3 Probability. 1.4 Conditional Probability. 1.5 Random Variables and Probability Distributions. 1.6 Measures of Central Tendency, Variability, and Association. 1.7 Linear Combinations of Random Variables. 1.8 Functions of Random Variables. 1.9 Common Discrete Probability Distributions. 1.10 Common Continuous Probability Distributions. 1.11 Extreme-Value Distributions. Chapter2: Discrete random Processes. 2.1 Introduction. 2.2 Discrete-Time, Discrete-State Markov Chains. 2.3 Continuous-Time Markov Chains. 2.4 Queueing Models. Chapter 3: Random Fields. 3.1 Introduction. 3.2 Covariance Function. 3.3 Spectral Density Function. 3.4 Variance Function. 3.5 Correlation Length. 3.6 Some Common Models. 3.7 Random Fields in Higher Dimensions. Chapter 4: Best Estimates, Excursions, and Averages. 4.1 Best Linear Unbiased Estimation. 4.2 Threshold Excursions in One Dimension. 4.3 Threshold Excursions in Two Dimensions. 4.4 Averages. Chapter 5: Estimation. 5.1 Introduction. 5.2 Choosing a Distribution. 5.3 Estimation in Presence of Correlation. 5.4 Advanced Estimation Techniques. Chapter 6: Simulation. 6.1 Introduction. 6.2 Random-Number Generators. 6.3 Generating Nonuniform Random Variables. 6.4 Generating Random Fields. 6.5 Conditional Simulation of Random Fields. 6.6 Monte carlo Simulation. Chapter 7: Reliability-Based Design. 7.1 Acceptable Risk. 7.2 Assessing Risk. 7.3 Background to Design Methodologies. 7.4 Load and Resistance Factor Design. 7.5 Going Beyond Calibration. 7.6 Risk-Based Decision making. PART 2: PRACTICE. Chapter 8: Groundwater Modeling. 8.1 Introduction. 8.2 Finite-Element Model. 8.3 One-Dimensional Flow. 8.4 Simple Two-Dimensional Flow. 8.5 Two-Dimensional Flow Beneath Water-Retaining Structures. 8.6 Three-Dimensional Flow. 8.7 Three Dimensional Exit Gradient Analysis. Chapter 9: Flow Through Earth Dams. 9.1 Statistics of Flow Through Earth Dams. 9.2 Extreme Hydraulic Gradient Statistics. Chapter 10: Settlement of Shallow Foundations. 10.1 Introduction. 10.2 Two-Dimensional Probabilistic Foundation Settlement. 10.3 Three-Dimensional Probabilistic Foundation Settlement. 10.4 Strip Footing Risk Assessment. 10.5 Resistance Factors for Shallow-Foundation Settlement Design. Chapter 11: Bearing Capacity. 11.1 Strip Footings on c-ø Soils. 11.2 Load and Resistance Factor Design of Shallow Foundations. 11.3 Summary. Chapter 12: Deep Foundations. 12.1 Introduction. 12.2 Random Finite-Element Method. 12.3 Monte Carlo Estimation of Pile Capacity. 12.4 Summary. Chapter 13: Slope Stability. 13.1 Introduction. 13.2 Probabilistic Slope Stability Analysis. 13.3 Slope Stability Reliability Model. Chapter 14: Earth Pressure. 14.1 Introduction. 14.2 Passive Earth Pressures. 14.3 Active Earth Pressures: Retaining Wall Reliability. Chapter 15: Mine Pillar Capacity. 15.1 Introduction. 15.2 Literature. 15.3 Parametric Studies. 15.4 Probabilistic Interpretation. 15.5 Summary. Chapter 16: Liquefaction. 16.1 Introduction. 16.2 Model Size: Soil Liquefaction. 16.3 Monte Carlo Analysis and Results. 16.4 Summary PART 3: APPENDIXES. APPENDIX A: PROBABILITY TABLES. A.1 Normal Distribution. A.2 Inverse Student t-Distribution. A.3 Inverse Chi-Square Distribution APPENDIX B: NUMERICAL INTEGRATION. B.1 Gaussian Quadrature. APPENDIX C. COMPUTING VARIANCES AND CONVARIANCES OF LOCAL AVERAGES. C.1 One-Dimensional Case. C.2 Two-Dimensional Case C.3 Three-Dimensional Case. Index.

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Book Synopsis* This textbook has been in constant use since 1980, and this edition has been rewritten to be even cleaner and clearer and new features have been introduced. * The authors continue to provide real-world, technical applications that promote intuitive reader learning.Table of Contents1 Review of Numerical Computation 1 1–1 The Real Numbers 2 1–2 Addition and Subtraction 9 1–3 Multiplication 15 1–4 Division 19 1–5 Powers and Roots 23 1–6 Combined Operations 29 1–7 Scientific Notation and Engineering Notation 32 1–8 Units of Measurement 41 1–9 Percentage 51 Chapter 1 Review Problems 59 2 Introduction to Algebra 62 2–1 Algebraic Expressions 63 2–2 Adding and Subtracting Polynomials 67 2–3 Laws of Exponents 72 2–4 Multiplying a Monomial by a Monomial 80 2–5 Multiplying a Monomial and a Multinomial 83 2–6 Multiplying a Binomial by a Binomial 86 2–7 Multiplying a Multinomial by a Multinomial 88 2–8 Raising a Multinomial to a Power 90 2–9 Dividing a Monomial by a Monomial 92 2–10 Dividing a Polynomial by a Monomial 95 2–11 Dividing a Polynomial by a Polynomial 98 Chapter 2 Review Problems 101 3 Simple Equations and Word Problems 103 3–1 Solving a Simple Equation 104 3–2 Solving Word Problems 113 3–3 Uniform Motion Applications 118 3–4 Money Problems 121 3–5 Applications Involving Mixtures 123 3–6 Statics Applications 127 3–7 Applications to Work, Fluid Flow, and Energy Flow 129 Chapter 3 Review Problems 133 4 Functions 136 4–1 Functions and Relations 137 4–2 More on Functions 144 Chapter 4 Review Problems 154 5 Graphs 156 5–1 Rectangular Coordinates 157 5–2 Graphing an Equation 161 5–3 Graphing a Function by Calculator 164 5–4 The Straight Line 167 5–5 Solving an Equation Graphically 172 Chapter 5 Review Problems 173 6 Geometry 175 6–1 Straight Lines and Angles 176 6–2 Triangles 180 6–3 Quadrilaterals 187 6–4 The Circle 190 6–5 Polyhedra 196 6–6 Cylinder, Cone, and Sphere 201 Chapter 6 Review Problems 205 7 Right Triangles and Vectors 207 7–1 The Trigonometric Functions 208 7–2 Solution of Right Triangles 212 7–3 Applications of the Right Triangle 216 7–4 Angles in Standard Position 221 7–5 Introduction to Vectors 222 7–6 Applications of Vectors 226 Chapter 7 Review Problems 229 8 Oblique Triangles and Vectors 231 8–1 Trigonometric Functions of Any Angle 232 8–2 Finding the Angle When the Trigonometric Function Is Known 236 8–3 Law of Sines 240 8–4 Law of Cosines 246 8–5 Applications 251 8–6 Non-Perpendicular Vectors 255 Chapter 8 Review Problems 260 9 Systems of Linear Equations 263 9–1 Systems of Two Linear Equations 264 9–2 Applications 270 9–3 Other Systems of Equations 279 9–4 Systems of Three Equations 284 Chapter 9 Review Problems 290 10 Matrices and Determinants 292 10–1 Introduction to Matrices 293 10–2 Solving Systems of Equations by the Unit Matrix Method 297 10–3 Second-Order Determinants 302 10–4 Higher-Order Determinants 308 Chapter 10 Review Problems 316 11 Factoring and Fractions 319 11–1 Common Factors 320 11–2 Difference of Two Squares 323 11–3 Factoring Trinomials 326 11–4 Other Factorable Expressions 333 11–5 Simplifying Fractions 335 11–6 Multiplying and Dividing Fractions 340 11–7 Adding and Subtracting Fractions 344 11–8 Complex Fractions 349 11–9 Fractional Equations 352 11–10 Literal Equations and Formulas 355 Chapter 11 Review Problems 360 12 Quadratic Equations 363 12–1 Solving a Quadratic Equation Graphically and by Calculator 364 12–2 Solving a Quadratic by Formula 368 12–3 Applications 372 Chapter 12 Review Problems 377 13 Exponents and Radicals 379 13–1 Integral Exponents 380 13–2 Simplification of Radicals 385 13–3 Operations with Radicals 392 13–4 Radical Equations 398 Chapter 13 Review Problems 403 14 Radian Measure, Arc Length, and Rotation 405 14–1 Radian Measure 406 14–2 Arc Length 413 14–3 Uniform Circular Motion 416 Chapter 14 Review Problems 420 15 Trigonometric, Parametric, and Polar Graphs 422 15–1 Graphing the Sine Wave by Calculator 423 15–2 Manual Graphing of the Sine Wave 430 15–3 The Sine Wave as a Function of Time 435 15–4 Graphs of the Other Trigonometric Functions 441 15–5 Graphing a Parametric Equation 448 15–6 Graphing in Polar Coordinates 452 Chapter 15 Review Problems 459 16 Trigonometric Identities and Equations 461 16–1 Fundamental Identities 462 16–2 Sum or Difference of Two Angles 469 16–3 Functions of Double Angles and Half-Angles 474 16–4 Evaluating a Trigonometric Expression 481 16–5 Solving a Trigonometric Equation 484 Chapter 16 Review Problems 489 17 Ratio, Proportion, and Variation 491 17–1 Ratio and Proportion 492 17–2 Similar Figures 497 17–3 Direct Variation 501 17–4 The Power Function 505 17–5 Inverse Variation 509 17–6 Functions of More Than One Variable 513 Chapter 17 Review Problems 518 18 Exponential and Logarithmic Functions 521 18–1 The Exponential Function 522 18–2 Logarithms 532 18–3 Properties of Logarithms 539 18–4 Solving an Exponential Equation 547 18–5 Solving a Logarithmic Equation 554 Chapter 18 Review Problems 560 19 Complex Numbers 562 19–1 Complex Numbers in Rectangular Form 563 19–2 Complex Numbers in Polar Form 568 19–3 Complex Numbers on the Calculator 572 19–4 Vector Operations Using Complex Numbers 575 19–5 Alternating Current Applications 578 Chapter 19 Review Problems 584 20 Sequences, Series, and the Binomial Theorem 586 20–1 Sequences and Series 587 20–2 Arithmetic and Harmonic Progressions 593 20–3 Geometric Progressions 600 20–4 Infinite Geometric Progressions 604 20–5 The Binomial Theorem 607 Chapter 20 Review Problems 614 21 Introduction to Statistics and Probability 617 21–1 Definitions and Terminology 618 21–2 Frequency Distributions 622 21–3 Numerical Description of Data 628 21–4 Introduction to Probability 638 21–5 The Normal Curve 648 21–6 Standard Errors 654 21–7 Process Control 661 21–8 Regression 669 Chapter 21 Review Problems 674 22 Analytic Geometry 679 22–1 The Straight Line 680 22–2 Equation of a Straight Line 687 22–3 The Circle 694 22–4 The Parabola 702 22–5 The Ellipse 713 22–6 The Hyperbola 725 Chapter 22 Review Problems 733 Appendices A Summary of Facts and Formulas A-0 B Conversion Factors A-0 C Table of Integrals A-0 Indexes Applications Index I-0 Index to Writing Questions I-0 Index to Projects I-0 General Index I-0

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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 supporting Trade 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 ContentsPreface. 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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a huge range and FREE tracked UK delivery on ALL orders.

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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 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 SynopsisFirst published in 1986, this unique reference to clinical experimentation remains just as relevant today. Focusing on the principles of design and analysis of studies on human subjects, this book utilizes and integrates both modern and classical designs.Table of ContentsReliability of Measurement. Simple Linear Regression Analysis. The Parallel Groups Design. Special Cases of the Parallel Groups Study. Blocking to Control for Prognostic Variables. Stratification to Control for Prognostic Variables. Analysis of Covariance and the Study of Change. Repeated Measurements Studies. Latin and Greco-Latin Squares. The Crossover Study. Balanced Incomplete Block Designs. Factorial Experiments. Split-Plot Designs and Confounding. Appendix. Indexes.

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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 SynopsisFrom the reviews of Numerical Solution of Partial Differential Equations in Science and Engineering: The book by Lapidus and Pinder is a very comprehensive, even exhaustive, survey of the subject . . . [It] is unique in that it covers equally finite difference and finite element methods. Burrelle''s The authors have selected an elementary (but not simplistic) mode of presentation. Many different computational schemes are described in great detail . . . Numerous practical examples and applications are described from beginning to the end, often with calculated results given. Mathematics of Computing This volume . . . devotes its considerable number of pages to lucid developments of the methods [for solving partial differential equations] . . . the writing is very polished and I found it a pleasure to read! Mathematics of Computation Of related interest . . . NUMERICAL ANALYSTable of ContentsFundamental Concepts. Basic Concepts in the Finite Difference and Finite Element Methods. Finite Elements on Irregular Subspaces. Parabolic Partial Differential Equations. Elliptic Partial Differential Equations. Hyperbolic Partial Differential Equations. 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 SynopsisExpert coverage of the design and implementation of state estimation algorithms for tracking and navigation Estimation with Applications to Tracking and Navigation treats the estimation of various quantities from inherently inaccurate remote observations.Table of ContentsPreface. Acronyms. Mathematical Notations. Introduction. Basic Concepts in Estimation. Linear Estimation in Static Systems. Linear Dynamic Systems with Random Inputs. State Estimation in Discrete-Time Linear Dynamic Systems. Estimation for Kinematic Models. Computational Aspects of Estimation. Extensions of Discrete-Time Linear Estimation. Continuous-Time Linear State Estimation. State Estimation for Nonlinear Dynamic Systems. Adaptive Estimation and Maneuvering Targets. Introduction to Navigation Applications. Bibliography. Index.

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