Maths for engineers Books

Book SynopsisThe emphasis of the book is given in how to construct different types of solutions (exact, approximate analytical, numerical, graphical) of numerous nonlinear PDEs correctly, easily, and quickly. The reader can learn a wide variety of techniques and solve numerous nonlinear PDEs included and many other differential equations, simplifying and transforming the equations and solutions, arbitrary functions and parameters, presented in the book). Numerous comparisons and relationships between various types of solutions, different methods and approaches are provided, the results obtained in Maple and Mathematica, facilitates a deeper understanding of the subject. Among a big number of CAS, we choose the two systems, Maple and Mathematica, that are used worldwide by students, research mathematicians, scientists, and engineers. As in the our previous books, we propose the idea to use in parallel both systems, Maple and Mathematica, since in many research problems frequently it is required to compare independent results obtained by using different computer algebra systems, Maple and/or Mathematica, at all stages of the solution process. One of the main points (related to CAS) is based on the implementation of a whole solution method (e.g. starting from an analytical derivation of exact governing equations, constructing discretizations and analytical formulas of a numerical method, performing numerical procedure, obtaining various visualizations, and comparing the numerical solution obtained with other types of solutions considered in the book, e.g. with asymptotic solution).Trade ReviewFrom the reviews:“The authors consider the problem of constructing closed-form and approximate solutions to nonlinear partial differential equations with the help of computer algebra systems. … The book will be useful for readers who want to try modern methods for solving nonlinear partial differential equations on concrete examples without bothering too much about the mathematics behind the methods. Thus it is mainly of interest for applied scientists. Mathematicians may use it in connection with more theoretical works; some references are given throughout the book.” (Werner M. Seiler, Zentralblatt MATH, Vol. 1233, 2012)Table of Contents1 Introduction 1.1 Basic Concepts 2 Algebraic Approach 2.1 Point Transformations 2.2 Contact Transformations 2.3 Transformations Relating Differential Equations 2.4 Linearizing and Bilinearizing Transformations 2.5 Reductions of Nonlinear PDEs 2.6 Separation of Variables 2.7 Transformation Groups 2.8 Nonlinear Systems 3 Geometric-Qualitative Approach 3.1 Method of Characteristics 3.2 Generalized Method of Characteristics 3.3 Qualitative Analysis 4 General Analytical Approach. Integrability 4.1 Painlevé Test and Integrability 4.2 Complete Integrability. Evolution Equations 4.3 Nonlinear Systems. Integrability Conditions 5 Approximate Analytical Approach 5.1 Adomian Decomposition Method 5.2 Asymptotic Expansions. Perturbation Methods 6 Numerical Approach 6.1 Embedded Numerical Methods 6.2 Finite DifferenceMethods 7 Analytical-Numerical Approach 7.1 Method of Lines 7.2 Spectral Collocation Method; A Brief Description of Maple A.1 Introduction A.2 Basic Concepts A.3 Maple Language B Brief Description of Mathematica B.1 Introduction B.2 Basic Concepts B.3 Mathematica Language; References, Index

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Book SynopsisThe best-selling introductory mathematics textbook for students on engineering and science degree and pre-degree courses. Sales stand at more than half a million copies world-wide. Its unique programmed approach really works! Many thousands of students have found that they understand and excel through using this book. It takes you through the mathematics in a step-by-step fashion with a wealth of examples and exercises. The text demands that you engage with it by asking you to complete steps that you should be able to manage from previous examples or knowledge you have acquired, while carefully introducing new steps. By working with the authors through the examples, you become proficient as you go. By the time you come to trying examples on your own, confidence is high. Aimed at undergraduates on Foundation and First Year degree programmes in all Engineering disciplines and Science. The Foundation section covers mathematics from GCSE onwards to allow for revision and gap-filling, aTrade ReviewYour book is the best textbook I have ever bought, read or borrowed on any topic ... Well written, well laid out and easy to follow, it is an absolute must ... All I have achieved in the field of mathematics starts with Engineering Mathematics ... The ONLY mathematics book you’ll ever need. * What students say *Table of ContentsPART I: FOUNDATION TOPICS Arithmetic Introduction to Algebra Expressions and Equations Graphs Linear Equations Polynomial Equations Binomials Partial Fractions Trigonometry Functions Trigonometric and Exponential Functions Differentiation Integration PART II Complex Numbers 1 Complex Numbers 2 Hyperbolic Functions Determinants Matrices Vectors Differentiation Differentiation Applications Tangents, Normals and Curvature Sequences Series 1 Series 2 Curves and Curve Fitting Partial Differentiation 1 Partial Differentiation 2 Integration 1 Integration 2 Reduction Formulas Integration Applications 1 Integration Applications 2 Integration Applications 3 Approximate Integration Polar Coordinate Systems Multiple Integrals First-Order Differential Equations Second-Order Differential Equations Introduction to Laplace Transforms Statistics Probability Answers.

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Book SynopsisEnsure students are fully prepared for A-Level Maths with this revised second edition, fully updated to bridge the GCSE Maths 9-1 and A-level 2017 specifications.Written by an experienced A-level author who is a practising A-level teacher, this fully updated edition is an ideal resource to be used in the classroom or for independent study.Similar in structure to Collins Maths revision guides, the Bridging GCSE and A-level Maths Student Book is split into an explanation section and a practice section. Identify and understand the transition from GCSE to AS and A-level Maths with What you should already know' objectives and What you will learn' objectives at the start of each topic Get a head start on your AS/A-level Maths with introductions to key pure maths topics for all exam boards (AQA, OCR, MEI and Edexcel) Boost your understanding with worked examples which include extra guidance in the form of Handy hint', Checkpoint', A-level Alert!' and Common error' boxes Reinforce and build onTrade ReviewThe transition between GCSE and AS/A-level mathematics is considerable. This essential textbook will help students navigate their way through all the key concepts and applications to enable students to achieve real success in post-16 mathematics. Chris CurtisHead of MathematicsFrome Community College

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Book SynopsisThis self-contained textbook introduces all the relevant mathematical concepts needed to understand and use machine learning methods, with a minimum of prerequisites. Topics include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics.Trade Review'This book provides great coverage of all the basic mathematical concepts for machine learning. I'm looking forward to sharing it with students, colleagues, and anyone interested in building a solid understanding of the fundamentals.' Joelle Pineau, McGill University, Montreal'The field of machine learning has grown dramatically in recent years, with an increasingly impressive spectrum of successful applications. This comprehensive text covers the key mathematical concepts that underpin modern machine learning, with a focus on linear algebra, calculus, and probability theory. It will prove valuable both as a tutorial for newcomers to the field, and as a reference text for machine learning researchers and engineers.' Christopher Bishop, Microsoft Research Cambridge'This book provides a beautiful exposition of the mathematics underpinning modern machine learning. Highly recommended for anyone wanting a one-stop-shop to acquire a deep understanding of machine learning foundations.' Pieter Abbeel, University of California, Berkeley'Really successful are the numerous explanatory illustrations, which help to explain even difficult concepts in a catchy way. Each chapter concludes with many instructive exercises. An outstanding feature of this book is the additional material presented on the website …' Volker H. Schulz, SIAM ReviewTable of Contents1. Introduction and motivation; 2. Linear algebra; 3. Analytic geometry; 4. Matrix decompositions; 5. Vector calculus; 6. Probability and distribution; 7. Optimization; 8. When models meet data; 9. Linear regression; 10. Dimensionality reduction with principal component analysis; 11. Density estimation with Gaussian mixture models; 12. Classification with support vector machines.

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Book SynopsisA long-standing, best-selling, comprehensive textbook covering all the mathematics required on upper level engineering mathematics undergraduate courses. Its unique approach takes you through all the mathematics you need in a step-by-step fashion with a wealth of examples and exercises. The text demands that you engage with it by asking you to complete steps that you should be able to manage from previous examples or knowledge you have acquired, while carefully introducing new steps. By working with the authors through the examples, you become proficient as you go. By the time you come to trying examples on their own, confidence is high. Suitable for undergraduates in second and third year courses on engineering and science degrees.Trade ReviewQuite simply absolutely excellent! All you could want in a maths textbook. Stroud does not “assume”, he teaches. * What students say *Table of ContentsHints on Using the Book Useful Background Information Numerical Solutions of Equations and Interpolation Laplace Transforms Part 1 Laplace Transforms Part 2 Laplace Transforms Part 3 Difference Equations and the Z Transform Introduction to Invariant Linear Systems Fourier Series 1 Fourier Series 2 Introduction to the Fourier Transform Power Series Solutions of Ordinary Differential Equations 1 Power Series Solutions of Ordinary Differential Equations 2 Power Series Solutions of Ordinary Differential Equations 3 Numerical Solutions of Ordinary Differential Equations Matrix Algebra Systems of Ordinary Differential Equations Direction Fields Phase Plane Analysis Non-linear Systems Dynamical Systems Partial Differentiation Partial Differential Equations Numerical Solutions of Partial Differential Equations Multiple Integration Part 1 Multiple Integration Part 2 Integral Functions Vector Analysis Part 1 Vector Analysis Part 2 Vector Analysis Part 3 Complex Analysis Part 1 Complex Analysis Part 2 Complex Analysis Part 3 Optimization and Linear Programming.

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Anthony Croft is Professor of Mathematics Education at Loughborough University. Robert Davison was formerly Head of Quality at the Faculty of Technology, De Montfort University. Martin Hargreaves is a Chartered Physicist James Flint is Senior Lecturer in Wireless Systems Engineering at Loughborough University.

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Book SynopsisTable of ContentsCHAPTER 1 Introduction to statistics CHAPTER 2 Descriptive statistics CHAPTER 3 Elements of probability CHAPTER 4 Random variables and expectation CHAPTER 5 Special random variables CHAPTER 6 Distributions of sampling statistics CHAPTER 7 Parameter estimation CHAPTER 8 Hypothesis testing CHAPTER 9 Regression CHAPTER 10 Analysis of variance CHAPTER 11 Goodness of fit tests and categorical data analysis CHAPTER 12 Nonparametric hypothesis tests CHAPTER 13 Quality control CHAPTER 14 Life testing CHAPTER 15 Simulation, bootstrap statistical methods, and permutation tests CHAPTER 16 Machine learning and big data

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Book SynopsisEncompasses the full range of computational science and engineering from modelling to solution, both analytical and numerical. It develops a framework for the equations and numerical methods of applied mathematics. Gilbert Strang has taught this material to thousands of engineers and scientists (and many more on MIT's OpenCourseWare 18.085-6). His experience is seen in his clear explanations, wide range of examples, and teaching method. The book is solution-based and not formula-based: it integrates analysis and algorithms and MATLAB codes to explain each topic as effectively as possible. The topics include applied linear algebra and fast solvers, differential equations with finite differences and finite elements, Fourier analysis and optimization. This book also serves as a reference for the whole community of computational scientists and engineers. Supporting resources, including MATLAB codes, problem solutions and video lectures from Gilbert Strang's 18.085 courses at MIT, are provi

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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 SynopsisThe Chemistry Maths Book provides a complete course companion suitable for students at all levels. All the most useful and important topics are covered, with numerous examples of applications in chemistry and the physical sciences. Taking a clear, straightforward approach, the book develops ideas in a logical, coherent way, allowing students progressively to build a thorough working understanding of the subject.Topics are organized into three parts: algebra, calculus, differential equations, and expansions in series; vectors, determinants and matrices; and numerical analysis and statistics. The extensive use of examples illustrates every important concept and method in the text, and are used to demonstrate applications of the mathematics in chemistry and several basic concepts in physics. The exercises at the end of each chapter, are an essential element of the development of the subject, and have been designed to give students a working understanding of the material in the text.Online Resources:The online resources feature the following: - Figures from the book in electronic format, ready to download- Full worked solutions to all end of chapter exercisesTrade ReviewReview from previous edition It seems well suited both for its stated purpose and as a "brush-up" book for undergraduates, graduate students, and others. The mathematics are carried out briskly and with very little dressing ... there is much material to cover here and it works well through Steiner's particularly lucid presentation. The notation is standard and clear ... I am impressed with this book, I am sure that it will remain open on my desk and will become well worn in short order. * C. Michael McCallum, University of the Pacific, Journal of Chemical Education, Vol. 74 No. 12 December 1997 *Table of Contents1. Numbers, variables and units ; 2. Algebraic functions ; 3. Transcendental functions ; 4. Differentiation ; 5. Integration ; 6. Methods of integration ; 7. Sequences and series ; 8. Complex numbers ; 9. Functions of several variables ; 10. Functions in 3 dimensions ; 11. First-order differential equations ; 12. Second-order differential equations. Constant coefficients ; 13. Second-order differential equations. Some special functions ; 14. Partial differential equations ; 15. Orthogonal expansions. Fourier analysis ; 16. Vectors ; 17. Determinants ; 18. Matrices and linear transformations ; 19. The matrix eigenvalue problem ; 20. Numerical methods ; 21. Probability and statistics

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Book SynopsisMathematical Techniques provides a complete course in mathematics, covering all the essential topics with which a physical sciences or engineering student should be familiar. It introduces and builds on concepts in a progressive, carefully-layered way, and features over 2000 end of chapter problems, plus additional self-check questions.Trade ReviewReview from previous edition This textbook offers an accessible and comprehensive grounding in many of the mathematical techniques required in the early stages of an engineering or science degree and also for the routine methods needed by first and second year mathematics students. * Engineering Designer March/April 2003 *There are also significant changes in content in the opening chapter, where the foundation material has been expanded usefully. The authors do not attempt to dodge theoretical hurdles. They are careful to explain many of the less intuitive properties of functions and to highlight generalisations without becoming over abstract. * Times Higher Education Supplement, November 2002 *Thoroughly recommended. * Zentralblatt MATH, 993:2002 *Table of ContentsPART 1. ELEMENTARY METHODS, DIFFERENTIATION, COMPLEX NUMBERS; PART 2. MATRIX AND VECTOR ALGEBRA; PART 3. INTEGRATION AND DIFFERENTIAL EQUATIONS; PART 4. TRANSFORMS AND FOURIER SERIES; PART 5. MULTIVARIABLE CALCULUS; PART 6. DISCRETE MATHEMATICS; PART 7. PROBABILITY AND STATISTICS; PART 8. PROJECTS; SELF-TESTS: SELECTED ANSWERS; ANSWERS TO SELECTED PROBLEMS; APPENDICES; FURTHER READING; INDEX

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Book SynopsisBased on course material used by the author at Yale University, this practical text addresses the widening gap found between the mathematics required for upper-level courses in the physical sciences and the knowledge of incoming students.Trade Review`Shankar obviously enjoys his mathematics, and his attitude toward mathematics is simultaneously refreshing and contagious....Dirac notation is intriguingly introduced in the discussion of vector spaces. Finally, the book is richly endowed with well-chosen problems.' American Journal of Physics `Consistent with the needs of science students...a sound mathematical reference for anyone studying or practicing in the physical sciences.' Choice Table of ContentsDifferential Calculus of One Variable. Integral Calculus. Calculus of Many Variables. Infinite Series. Complex Numbers. Functions of a Complex Variable. Vector Calculus. Matrices and Determinants. Linear Vector Spaces. Differential Equations. Answers. Index.

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Book SynopsisTechnical Math For Dummies features easy-to-follow, plain-English guidance on mathematical formulas and methods that professionals use every day in the automotive, health, construction, maintenance and other trades. It shows how to apply concepts of mathematics and formulas related to occupational areas of study.Table of ContentsIntroduction. Part I: Basic Math, Basic Tools. Chapter 1: Math that Works as Hard as You Do. Chapter 2: Discovering Technical Math and the Tools of the Trades. Chapter 3: Zero to One and Beyond. Chapter 4: Easy Come, Easy Go: Addition and Subtraction. Chapter 5: Multiplication and Division: Everybody Needs Them. Chapter 6: Measurement and Conversion. Chapter 7: Slaying the Story Problem Dragon. Part II: Making Non-Basic Math Simple and Easy. Chapter 8: Fun with Fractions. Chapter 9: Decimals: They Have Their Place. Chapter 10: Playing with Percentages. Chapter 11: Tackling Exponents and Square Roots. Part III: Basic Algebra, Geometry, and Trigonometry. Chapter 12: Algebra and the Mystery of X. Chapter 13: Formulas (Secret and Otherwise). Chapter 14: Quick-and-Easy Geometry: The Compressed Version. Chapter 15: Calculating Areas, Perimeters, and Volumes. Chapter 16: Trigonometry, the "Mystery Math". Part IV: Math for the Business of Your Work. Chapter 17: Graphs are Novel and Charts Are Off the Chart. Chapter 18: Hold on a Second: Time Math. Chapter 19: Math for Computer Techs and Users. Part V: The Part of Tens. Chapter 20: Ten Tips for Solving Any Math Problem. Chapter 21: Ten Formulas You’ll Use Most Often. Chapter 22: Ten Ways to Avoid Everyday Math Stress. Glossary. Index.

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Book SynopsisIncisive, self-contained account of tensor analysis and the calculus of exterior differential forms, interaction between the concept of invariance and the calculus of variations. Emphasis is on analytical techniques. Includes problems.

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Book SynopsisThe second edition of this bestselling book provides an overview of the key topics in undergraduate mathematics, allowing beginning graduate students to fill in any gaps in their knowledge. With numerous examples, exercises and suggestions for further reading, it is a must-have for anyone looking to learn some serious mathematics quickly.Trade Review'Reading Garrity is like talking with your favorite uncle - he tells you the essential stories, in a clear and colorful way, and you get just what you need to explore further. The topics are well chosen (and there are more in this new edition). His points of view enrich the reader - not only do you learn what to know, but how to know it. I wish I had had this book when I started graduate school.' John McCleary, Vassar College'I admired one of the intentions behind the first edition of Garrity's All the Math You Missed: to give students the tools to appreciate the applications of mathematics without painting a simplistic picture of 'Applied Mathematics'. In this second edition, he takes this idea to the next level by introducing four additional chapters, dealing primarily with number theory and category theory.' Robert Kotiuga, Boston University'I felt like I was terribly underprepared for graduate school, and Garrity's book helped me fill in some of those gaps. But far more importantly, the welcoming tone made me see that I wasn't alone in feeling anxious, and it made grad school feel less intimidating.' Daniel Erman, University of Wisconsin, Madison'Incoming graduate students would find the book most useful … this book is designed to provide some useful guidance … The writing is clear and easy to read.' Bill Satzer, MAA ReviewsTable of ContentsOn the structure of mathematics; Brief summaries of topics; 1. Linear Algebra; 2. ε and δ real analysis; 3. Calculus for vector-valued functions; 4. Point set topology; 5. Classical Stokes' theorems; 6. Diff erential forms and Stokes' theorem; 7. Curvature for curves and surfaces; 8. Geometry; 9. Countability and the Axiom of Choice; 10. Elementary number theory; 11. Algebra; 12. Algebraic number theory; 13. Complex analysis; 14. Analytic number theory; 15. Lebesgue integration; 16. Fourier analysis; 17. Diff erential equations; 18. Combinatorics and probability theory; 19. Algorithms; 20. Category theory; Appendix A. Equivalence relations; References; Index.

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Book SynopsisAn example- and exercise-filled book for mathematical and scientific modelers with an introductory knowledge of category theory (e.g., readers of Cheng's 'Joy of Abstraction' or Fong & Spivak's 'Invitation to Applied Category Theory') interested in learning to apply the category of polynomial functors to real-world interacting dynamical systems.

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Book SynopsisWritten for senior undergraduates in all disciplines of physical science and engineering, the plain language style of this concise guide to numerical methods concentrates on developing computational skills and avoids potentially intimidating formal mathematical proofs. Including numerous worked examples and exercises, this textbook explains the practical realities of numerical techniques.Table of ContentsPreface; 1. Fitting functions to data; 2. Ordinary differential equations; 3. Two-point boundary conditions; 4. Partial differential equations; 5. Diffusion: parabolic PDEs; 6. Elliptic problems and iterative matrix solution; 7. Fluid dynamics and hyperbolic equations; 8. Boltzmann's equation and its solution; 9. Energy-resolved diffusive transport; 10. Atomistic and particle-in-cell simulation; 11. Monte Carlo techniques; 12. Monte Carlo radiation transport; 13. Next steps; Appendix A. Summary of matrix algebra; Index.

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Book SynopsisThe study of complex variables is beautiful from a purely mathematical point of view, and very useful for solving a wide array of problems arising in applications. This introduction to complex variables, suitable as a text for a one-semester course, has been written for undergraduate students in applied mathematics, science, and engineering. Based on the authors'' extensive teaching experience, it covers topics of keen interest to these students, including ordinary differential equations, as well as Fourier and Laplace transform methods for solving partial differential equations arising in physical applications. Many worked examples, applications, and exercises are included. With this foundation, students can progress beyond the standard course and explore a range of additional topics, including generalized Cauchy theorem, Painlevé equations, computational methods, and conformal mapping with circular arcs. Advanced topics are labeled with an asterisk and can be included in the syllabus or form the basis for challenging student projects.Trade Review'… a stylish, well-written and up to date introduction to complex variable methods for undergraduate (or early graduate) students in applied mathematics, science and engineering … I thoroughly enjoyed reading this book and warmly commend it to anyone seeking a brisk, well-organised account of complex variables with a practical focus on applications and calculational aspects.' Nick Lord, The Mathematical GazetteTable of Contents1. Complex numbers and elementary functions; 2. Analytic functions and integration; 3. Sequences, series and singularities of complex functions; 4. Residue calculus and applications of contour integration; 5. Conformal mappings and applications; Appendix. Answers to selected odd-numbered exercises; References; Index.

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Book SynopsisThis comprehensive textbook/reference provides an in-depth overview of the key aspects of transportation analysis, with an emphasis on modeling real transportation systems and executing the models.Table of ContentsComputational Foundation in Transportation and Transportation Systems Modeling Transportation ModelsTraffic Assignment to Transportation NetworksIntegration Framework and Empirical EvaluationSimulation Tools in TransportationTransportation Use Cases

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Book Synopsis Provides well-written self-contained chapters, including problem sets and exercises, making it ideal for the classroom setting; Introduces applied optimization to the hazardous waste blending problem; Explores linear programming, nonlinear programming, discrete optimization, global optimization, optimization under uncertainty, multi-objective optimization, optimal control and stochastic optimal control; Includes an extensive bibliography at the end of each chapter and an index; GAMS files of case studies for Chapters 2, 3, 4, 5, and 7 are linked to http://www.springer.com/math/book/978-0-387-76634-8; Solutions manual available upon adoptions.Table of Contents1. Introduction.- 2. Linear Programming.- 3. Nonlinear Programming.-4. Discrete Optimization.- 5. Optimization Under Uncertainty.- 6. Multiobjective Optimization.- 7.Optimal Control and Dynamic Optimization.- Index.

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Book SynopsisThis book introduces descriptive statistics and covers a broad range of topics of interest to students and researchers in various applied science disciplines. This includes measures of location, spread, skewness, and kurtosis; absolute and relative measures; and classification of spread, skewness, and kurtosis measures, L-moment based measures, van Zwet ordering of kurtosis, and multivariate kurtosis. Several novel topics are discussed including the recursive algorithm for sample variance; simplification of complicated summation expressions; updating formulas for sample geometric, harmonic and weighted means; divide-and-conquer algorithms for sample variance and covariance; L-skewness; spectral kurtosis, etc. A large number of exercises are included in each chapter that are drawn from various engineering fields along with examples that are illustrated using the R programming language. Basic concepts are introduced before moving on to computational aspects. Some applications in bioinformatics, finance, metallurgy, pharmacokinetics (PK), solid mechanics, and signal processing are briefly discussed. Every analyst who works with numeric data will find the discussion very illuminating and easy to follow.Table of ContentsDescriptive Statistics.- Measures of Location.- Measures of Spread.- Measures of Skewness and Kurtosis.

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Book SynopsisThis textbook presents basic and advanced computational physics in a very didactic style. It contains very-well-presented and simple mathematical descriptions of many of the most important algorithms used in computational physics. The first part of the book discusses the basic numerical methods. The second part concentrates on simulation of classical and quantum systems. Several classes of integration methods are discussed including not only the standard Euler and Runge Kutta method but also multi-step methods and the class of Verlet methods, which is introduced by studying the motion in Liouville space. A general chapter on the numerical treatment of differential equations provides methods of finite differences, finite volumes, finite elements and boundary elements together with spectral methods and weighted residual based methods. The book gives simple but non trivial examples from a broad range of physical topics trying to give the reader insight into not only the numerical treatment but also simulated problems. Different methods are compared with regard to their stability and efficiency. The exercises in the book are realised as computer experiments. Trade ReviewFrom the book reviews:“The well-written monograph about computational physics is based on two-semester lecture courses given by the author on a period of several years for undergraduate physics and biophysics students … . convenient for students and practitioners of computer science, chemistry, and mathematics who are interested in applications of numerical methods in physics and engineering sciences. … well-organized book with a concentration to the important ideas of the methods and physical applications including software, examples, illustrations, and references to further reading.” (Georg Hebermehl, zbMATH, Vol. 1303, 2015)Table of ContentsPart I Numerical Methods.- Error Analysis.- Interpolation.- Numerical Differentiation.- Numerical Integration.- Systems of Inhomogeneous Linear Equations.- Roots and Extremal Points.- Fourier Transformation.- Random Numbers and Monte-Carlo Methods.- Eigenvalue Problems.- Data Fitting.- Discretization of Differential Equations.- Equations of Motion.- Part II Simulation of Classical and Quantum Systems.- Rotational Motion.- Molecular Dynamics.- Thermodynamic Systems.- Random Walk and Brownian Motion.- Electrostatics.- Waves.- Diffusion.- Nonlinear Systems.- Simple Quantum Systems.

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Book SynopsisSociety is complicated. But this book argues that this does not place it beyond the reach of a science that can help to explain and perhaps even to predict social behaviour. As a system made up of many interacting agents – people, groups, institutions and governments, as well as physical and technological structures such as roads and computer networks – society can be regarded as a complex system. In recent years, scientists have made great progress in understanding how such complex systems operate, ranging from animal populations to earthquakes and weather. These systems show behaviours that cannot be predicted or intuited by focusing on the individual components, but which emerge spontaneously as a consequence of their interactions: they are said to be ‘self-organized’. Attempts to direct or manage such emergent properties generally reveal that ‘top-down’ approaches, which try to dictate a particular outcome, are ineffectual, and that what is needed instead is a ‘bottom-up’ approach that aims to guide self-organization towards desirable states.This book shows how some of these ideas from the science of complexity can be applied to the study and management of social phenomena, including traffic flow, economic markets, opinion formation and the growth and structure of cities. Building on these successes, the book argues that the complex-systems view of the social sciences has now matured sufficiently for it to be possible, desirable and perhaps essential to attempt a grander objective: to integrate these efforts into a unified scheme for studying, understanding and ultimately predicting what happens in the world we have made. Such a scheme would require the mobilization and collaboration of many different research communities, and would allow society and its interactions with the physical environment to be explored through realistic models and large-scale data collection and analysis. It should enable us to find new and effective solutions to major global problems such as conflict, disease, financial instability, environmental despoliation and poverty, while avoiding unintended policy consequences. It could give us the foresight to anticipate and ameliorate crises, and to begin tackling some of the most intractable problems of the twenty-first century.Trade ReviewFrom the reviews:“Phil Ball’s little book is one of the best summaries I have come across on complexity theory and its applications. This little triumph of clarity argues that society’s problems are those of highly connected systems. … Nice gentle text. If are a newcomer to complexity sciences, then read this first.” (Urban Models + Spatial Complexity + Smart Cities, August, 2012)Table of ContentsSociety: a Complex Problem.- On the Road: Predicting traffic.- Every Move You Make: Patterns of crowd movement.- Making Your Mind Up: Norms and decisions.- Broken Windows: The spread and control of crime.- The Social Web: Networks and their failures.- Spreading It Around: Mobility, disease and epidemics.- After the Crash: Economic and financial systems.- Love Thy Neighbour: How to foster cooperation.- Living Cities: Urban development as a complex system.- The Transformation of War: Modelling modern conflict.- Towards a Living Earth Simulator: The FuturICT Project.

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Book SynopsisThis book’s aim is to study the mathematical and computational models to analyze the progress, prognosis, prevention, and panacea of breast cancer. The book discusses application of Markov chains and transient mappings, Charlie–Simpson numerical algorithm, models represented by nonlinear reaction–diffusion-type partial differential equations, and related techniques. The book also attempts to design mathematical model of targeted strategic treatments by using Skilled Killer Drugs (SKD1 and SKD2) to suggest the improvisation of future cancer treatments. Both graduate students and researchers of computational biology and oncologists will benefit by studying this book. Researchers of cancer studies and biological sciences will also find this work helpful.Table of ContentsIntroduction.- Statistics: The Backgrounds & The Basis.- Attacker & Defender Model: The Dynamics of the Immune System.- Mathematical Modeling of Metastatic Cancer.- Mathematical/Computational Modeling of Advanced Immunotherapy.- Mathematical Modeling & Computational Studies On The War Against Breast Cancer.- Gene Therapy.- The Smartest Fighters.- Nutritional Therapy.- The Fateful Code & The Future Course.- Conclusion.

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Book SynopsisReplaces the contrived application of the quantum master equation with a satisfactory treatment of quantum fluctuations. This work covers the fluctuations and stochastic methods for describing them. It is of interest to students and researchers in applied mathematics, physics and physical chemistry.Table of ContentsI. Stochastic variablesII. Random eventsIII. Stochastic processesIV. Markov processesV. The master equationVI. One-step processesVII. Chemical reactionsVIII. The Fokker-Planck equationIX. The Langevin approachX. The expansion of the master equationXI. The diffusion typeXII. First-passage problemsXIII. Unstable systemsXIV. Fluctuations in continuous systemsXV. The statistics of jump eventsXVI. Stochastic differential equationsXVII. Stochastic behavior of quantum systems

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Book SynopsisThe eighth edition of Chapra and Canale''s Numerical Methods for Engineers retains the instructional techniques that have made the text so successful. The book covers the standard numerical methods employed by both students and practicing engineers. Although relevant theory is covered, the primary emphasis is on how the methods are applied for engineering problem solving. Each part of the book includes a chapter devoted to case studies from the major engineering disciplines. Numerous new or revised end-of chapter problems and case studies are drawn from actual engineering practice. This edition also includes several new topics including a new formulation for cubic splines, Monte Carlo integration, and supplementary material on hyperbolic partial differential equations.Table of ContentsPart 1 - Modeling, Computers, and Error Analysis1) Mathematical Modeling and Engineering Problem Solving2) Programming and Software3) Approximations and Round-Off Errors4) Truncation Errors and the Taylor SeriesPart 2 - Roots of Equations5) Bracketing Methods6) Open Methods7) Roots of Polynomials8) Case Studies: Roots of EquationsPart 3 - Linear Algebraic Equations9) Gauss Elimination10) LU Decomposition and Matrix Inversion11) Special Matrices and Gauss-Seidel12) Case Studies: Linear Algebraic EquationsPart 4 - Optimization13) One-Dimensional Unconstrained Optimization14) Multidimensional Unconstrained Optimization15) Constrained Optimization16) Case Studies: OptimizationPart 5 - Curve Fitting17) Least-Squares Regression18) Interpolation19) Fourier Approximation20) Case Studies: Curve FittingPart 6 - Numerical Differentiation and Integration21) Newton-Cotes Integration Formulas22) Integration of Equations23) Numerical Differentiation24) Case Studies: Numerical Integration and DifferentiationPart 7 - Ordinary Differential Equations25) Runge-Kutta Methods26) Stiffness and Multistep Methods27) Boundary-Value and Eigenvalue Problems28) Case Studies: Ordinary Differential EquationsPart 8 - Partial Differential Equations29) Finite Difference: Elliptic Equations30) Finite Difference: Parabolic Equations31) Finite-Element Method32) Case Studies: Partial Differential EquationsAppendix A - The Fourier SeriesAppendix B - Getting Started with MatlabAppendix C - Getting Starte dwith MathcadBibliographyIndex

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Book SynopsisSpectral Changes of 1/F Noise in Metals at Clusterization of Light Interstitials.- Analytic Solutions of Boundary Value Problems for Model Kinetic Equations.- Mathematical Models in Non-Linear Systems Thermodynamics.- Critical OpalescenceModels: Experiment.- Methane Combustion Simulation on Multiprocessor Computer Systems.- Computer Simulation of Structural Modifications in the Metal Samples Irradiated by Pulsed Beams.- Visualisation of Grand Challenge Data on Distributed Systems.- Simulation of Electron Transport in Semiconductor Microstructures: Field Emission from Nanotip.- Reliable Computing Experiment in the Study of Generalized Controllability of Linear Functional Differential Systems.- Heat Transfer in Disperse Systems of Various Structures and Configurations.- Some New Results in the Theory of Intelligent Systems.- An Automata Approach to Analysis and Synthesis of Audio and Video Patterns.- A Mathematical Model of Controlling the Portfolio of a Commercial Bank.- Tutoring Process as Object for Situational Control.- Nonlinear Dynamics of Strongly Non-Homogeneous Chains with Symmetric Characteristics.- Models of Directed Self-Avoiding Walks and Statistics of Rigid Polymer Molecules.- Postulate of the Arithmetical Mean and Nonbonded Interactions.- Quantum-Chemical Models of the Structure and the Functions of the Active Centres of the Polynuclear Complexes.- Asymptotics of Transport Equations for Spherical Geometry in L2 with Reflecting Boundary Conditions.- Traveling Heat Waves in High Temperature Medium.- Smooth Lyapunov Manifolds and Correct Mathematical Simulation of Nonlinear Singular Problems in Mathematical Physics.- Computational Methods for the Estimation of the Aerosol Size Distributions.- Two Disperse Particles in the Field of the ElectromagneticRadiation.- Transport Processes in Aerodisperse Systems: Transitional Growth of Nonspherical Particles and Mobility of Ions.- Solution of Some Nonlinear Problems in the Theory of Heating, Vaporization, Burning of Solid Particles and Drops.- On the Irreducible Tensors Method in the Theory of Diffusive Interaction between Particles.- Evaporation and Growth of Single Drops and Finite Array of Interacting Drops of Pure Liquids and Hygroscopic Solutions.Table of Contents1. Models of Nonlinear Phenomena in Physics. 2. Numerical Methods and Computer Simulations. 3. Mathematical Computer Models of Discrete Systems. 4. Mathematical Models in Economics. 5. Nonlinear Models in Chemical Physics and Physical Chemistry. 6. Mathematical Models of Transport Processes in Complex Systems.

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Book SynopsisBy including classical results as well as recent developments in the field of hydrodynamic stability and transition, the book can be used as a textbook for an introductory, graduate-level course in stability theory or for a special-topics fluids course.Trade ReviewFrom the reviews: SIAM REVIEW "This book presents a modern treatment of stability in shear flows. Stability theory has seen a number of classic treatments over the years…Schmid and Henningson’s book builds on these and offers much new material relevant to stability in shear flows…The MATLAB codes included in the appendix and a discussion of the effects of rounding error and resolution on the computations of eigenvalues of linear stability operators will be particularly helpful for students and researchers as they get started with stability computations…As the basis for a course, the first part of the book would permit students to build a solid foundation in classical and modern stability theory, while a selection of advanced topics from the second half of the book could be treated later in the course or through projects and independent study by students." ZENTRALBLATT MATH "The book addresses to graduate students as well as to a broad community of researchers with a basic knowledge of fundamental fluid dynamics…The topics are treated with mathematical rigor while the physical motivation and usefulness of mathematical concepts is kept close at hand. The work is elegantly structured, and the graphical material is very suggestive."Table of Contents1 Introduction and General Results.- 1.1 Introduction.- 1.2 Nonlinear Disturbance Equations.- 1.3 Definition of Stability and Critical Reynolds Numbers.- 1.3.1 Definition of Stability.- 1.3.2 Critical Reynolds Numbers.- 1.3.3 Spatial Evolution of Disturbances.- 1.4 The Reynolds-Orr Equation.- 1.4.1 Derivation of the Reynolds-Orr Equation.- 1.4.2 The Need for Linear Growth Mechanisms.- I Temporal Stability of Parallel Shear Flows.- 2 Linear Inviscid Analysis.- 2.1 Inviscid Linear Stability Equations.- 2.2 Modal Solutions.- 2.2.1 General Results.- 2.2.2 Dispersive Effects and Wave Packets.- 2.3 Initial Value Problem.- 2.3.1 The Inviscid Initial Value Problem.- 2.3.2 Laplace Transform Solution.- 2.3.3 Solutions to the Normal Vorticity Equation.- 2.3.4 Example: Couette Flow.- 2.3.5 Localized Disturbances.- 3 Eigensolutions to the Viscous Problem.- 3.1 Viscous Linear Stability Equations.- 3.1.1 The Velocity-Vorticity Formulation.- 3.1.2 The Orr-Sommerfeld and Squire Equations.- 3.1.3 Squire’s Transformation and Squire’s Theorem.- 3.1.4 Vector Modes.- 3.1.5 Pipe Flow.- 3.2 Spectra and Eigenfunctions.- 3.2.1 Discrete Spectrum.- 3.2.2 Neutral Curves.- 3.2.3 Continuous Spectrum.- 3.2.4 Asymptotic Results.- 3.3 Further Results on Spectra and Eigenfunctions.- 3.3.1 Adjoint Problem and Bi-Orthogonality Condition.- 3.3.2 Sensitivity of Eigenvalues.- 3.3.3 Pseudo-Eigenvalues.- 3.3.4 Bounds on Eigenvalues.- 3.3.5 Dispersive Effects and Wave Packets.- 4 The Viscous Initial Value Problem.- 4.1 The Viscous Initial Value Problem.- 4.1.1 Motivation.- 4.1.2 Derivation of the Disturbance Equations.- 4.1.3 Disturbance Measure.- 4.2 The Forced Squire Equation and Transient Growth.- 4.2.1 Eigenfunction Expansion.- 4.2.2 Blasius Boundary Layer Flow.- 4.3 The Complete Solution to the Initial Value Problem.- 4.3.1 Continuous Formulation.- 4.3.2 Discrete Formulation.- 4.4 Optimal Growth.- 4.4.1 The Matrix Exponential.- 4.4.2 Maximum Amplification.- 4.4.3 Optimal Disturbances.- 4.4.4 Reynolds Number Dependence of Optimal Growth.- 4.5 Optimal Response and Optimal Growth Rate.- 4.5.1 The Forced Problem and the Resolvent.- 4.5.2 Maximum Growth Rate.- 4.5.3 Response to Stochastic Excitation.- 4.6 Estimates of Growth.- 4.6.1 Bounds on Matrix Exponential.- 4.6.2 Conditions for No Growth.- 4.7 Localized Disturbances.- 4.7.1 Choice of Initial Disturbances.- 4.7.2 Examples.- 4.7.3 Asymptotic Behavior.- 5 Nonlinear Stability.- 5.1 Motivation.- 5.1.1 Introduction.- 5.1.2 A Model Problem.- 5.2 Nonlinear Initial Value Problem.- 5.2.1 The Velocity-Vorticity Equations.- 5.3 Weakly Nonlinear Expansion.- 5.3.1 Multiple-Scale Analysis.- 5.3.2 The Landau Equation.- 5.4 Three-Wave Interactions.- 5.4.1 Resonance Conditions.- 5.4.2 Derivation of a Dynamical System.- 5.4.3 Triad Interactions.- 5.5 Solutions to the Nonlinear Initial Value Problem.- 5.5.1 Formal Solutions to the Nonlinear Initial Value Problem.- 5.5.2 Weakly Nonlinear Solutions and the Center Manifold.- 5.5.3 Nonlinear Equilibrium States.- 5.5.4 Numerical Solutions for Localized Disturbances.- 5.6 Energy Theory.- 5.6.1 The Energy Stability Problem.- 5.6.2 Additional Constraints.- II Stability of Complex Flows and Transition.- 6 Temporal Stability of Complex Flows.- 6.1 Effect of Pressure Gradient and Crossflow.- 6.1.1 Falkner-Skan (FS) Boundary Layers.- 6.1.2 Falkner-Skan-Cooke (FSC) Boundary layers.- 6.2 Effect of Rotation and Curvature.- 6.2.1 Curved Channel Flow.- 6.2.2 Rotating Channel Flow.- 6.2.3 Combined Effect of Curvature and Rotation.- 6.3 Effect of Surface Tension.- 6.3.1 Water Table Flow.- 6.3.2 Energy and the Choice of Norm.- 6.3.3 Results.- 6.4 Stability of Unsteady Flow.- 6.4.1 Oscillatory Flow.- 6.4.2 Arbitrary Time Dependence.- 6.5 Effect of Compressibility.- 6.5.1 The Compressible Initial Value Problem.- 6.5.2 Inviscid Instabilities and Rayleigh’s Criterion.- 6.5.3 Viscous Instability.- 6.5.4 Nonmodal Growth.- 7 Growth of Disturbances in Space.- 7.1 Spatial Eigenvalue Analysis.- 7.1.1 Introduction.- 7.1.2 Spatial Spectra.- 7.1.3 Gaster’s Transformation.- 7.1.4 Harmonic Point Source.- 7.2 Absolute Instability.- 7.2.1 The Concept of Absolute Instability.- 7.2.2 Briggs’ Method.- 7.2.3 The Cusp Map.- 7.2.4 Stability of a Two-Dimensional Wake.- 7.2.5 Stability of Rotating Disk Flow.- 7.3 Spatial Initial Value Problem.- 7.3.1 Primitive Variable Formulation.- 7.3.2 Solution of the Spatial Initial Value Problem.- 7.3.3 The Vibrating Ribbon Problem.- 7.4 Nonparallel Effects.- 7.4.1 Asymptotic Methods.- 7.4.2 Parabolic Equations for Steady Disturbances.- 7.4.3 Parabolized Stability Equations (PSE).- 7.4.4 Spatial Optimal Disturbances.- 7.4.5 Global Instability.- 7.5 Nonlinear Effects.- 7.5.1 Nonlinear Wave Interactions.- 7.5.2 Nonlinear Parabolized Stability Equations.- 7.5.3 Examples.- 7.6 Disturbance Environment and Receptivity.- 7.6.1 Introduction.- 7.6.2 Nonlocalized and Localized Receptivity.- 7.6.3 An Adjoint Approach to Receptivity.- 7.6.4 Receptivity Using Parabolic Evolution Equations.- 8 Secondary Instability.- 8.1 Introduction.- 8.2 Secondary Instability of Two-Dimensional Waves.- 8.2.1 Derivation of the Equations.- 8.2.2 Numerical Results.- 8.2.3 Elliptical Instability.- 8.3 Secondary Instability of Vortices and Streaks.- 8.3.1 Governing Equations.- 8.3.2 Examples of Secondary Instability of Streaks and Vortices.- 8.4 Eckhaus Instability.- 8.4.1 Secondary Instability of Parallel Flows.- 8.4.2 Parabolic Equations for Spatial Eckhaus Instability.- 9 Transition to Turbulence.- 9.1 Transition Scenarios and Thresholds.- 9.1.1 Introduction.- 9.1.2 Three Transition Scenarios.- 9.1.3 The Most Likely Transition Scenario.- 9.1.4 Conclusions.- 9.2 Breakdown of Two-Dimensional Waves.- 9.2.1 The Zero Pressure Gradient Boundary Layer.- 9.2.2 Breakdown of Mixing Layers.- 9.3 Streak Breakdown.- 9.3.1 Streaks Forced by Blowing or Suction.- 9.3.2 Freestream Turbulence.- 9.4 Oblique Transition.- 9.4.1 Experiments and Simulations in Blasius Flow.- 9.4.2 Transition in a Separation Bubble.- 9.4.3 Compressible Oblique Transition.- 9.5 Transition of Vortex-Dominated Flows.- 9.5.1 Transition in Flows with Curvature.- 9.5.2 Direct Numerical Simulations of Secondary Instability of Crossflow Vortices.- 9.5.3 Experimental Investigations of Breakdown of Cross-flow Vortices.- 9.6 Breakdown of Localized Disturbances.- 9.6.1 Experimental Results for Boundary Layers.- 9.6.2 Direct Numerical Simulations in Boundary Layers.- 9.7 Transition Modeling.- 9.7.1 Low-Dimensional Models of Subcritical Transition.- 9.7.2 Traditional Transition Prediction Models.- 9.7.3 Transition Prediction Models Based on Nonmodal Growth.- 9.7.4 Nonlinear Transition Modeling.- III Appendix.- A Numerical Issues and Computer Programs.- A.1 Global versus Local Methods.- A.2 Runge-Kutta Methods.- A.3 Chebyshev Expansions.- A.4 Infinite Domain and Continuous Spectrum.- A.5 Chebyshev Discretization of the Orr-Sommerfeld Equation.- A.6 MATLAB Codes for Hydrodynamic Stability Calculations.- A.7 Eigenvalues of Parallel Shear Flows.- B Resonances and Degeneracies.- B.1 Resonances and Degeneracies.- B.2 Orr-Sommerfeld-Squire Resonance.- C Adjoint of the Linearized Boundary Layer Equation.- C.1 Adjoint of the Linearized Boundary Layer Equation.- D Selected Problems on Part I.

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Book SynopsisThe Manchester Physics Series General Editors: D. J. Sandiford; F. Mandl; A. C. Phillips Department of Physics and Astronomy, University of Manchester Properties of Matter B. H. Flowers and E. Mendoza Optics Second Edition F. G. Smith and J. H. Thomson Statistical Physics Second Edition F. Mandl Electromagnetism Second Edition I. S. Grant and W. R. Phillips Statistics R. J. Barlow Solid State Physics Second Edition J. R. Hook and H. E. Hall Quantum Mechanics F. Mandl Particle Physics Second Edition B. R. Martin and G. Shaw The Physics of Stars Second Edition A.C. Phillips Computing for Scientists R. J. Barlow and A. R. Barnett Written by a physicist, Statistics is tailored to the needs of physical scientists, containing and explaining all they need to know. It concentrates on parameter estimation, especially the methods of Least Squares and Maximum Likelihood, but other techniques, such as hypothesis testing, Bayesian statistics and non-parametric methods are also included. Intended foTable of ContentsUsing Statistics. Describing the Data. Theoretical Distributions. Errors. Estimation. Least Squares. Probability and Confidence. Taking Decisions. Ranking Methods. Notes for Number Crunchers. Bibliography. Appendices. Index.

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Book SynopsisTo properly operate a waterworks or wastewater treatment plant and to pass the examination for a waterworks/wastewater operator's license, it is necessary to know how to perform certain calculations. All operators, at all levels of licensure, need a basic understanding of arithmetic and problem-solving techniques to solve the problems they typically encounter in the workplace.Hailed on its first publication as a masterly account written in an engaging, highly readable, user-friendly style, the fully updated Mathematics Manual for Water and Wastewater Treatment Plant Operators: Basic Mathematics for Water and Wastewater Operators introduces and reviews fundamental concepts critical to qualified operators. It builds a strong foundation based on theoretical math concepts, which it then applies to solving practical problems for both water and wastewater operations.Features: Provides a strong foundation based on theoretical math concepts, which it then applieTable of Contents1. Introduction. 2. Basic Units of Measurement, Conversions. 3. Sequence of Operations. 4. Fractions, Decimals & Percent. 5. Rounding & Significant Digits. 6. Powers of Ten and Exponents. 7. Averages (Arithmetic Mean) & Median. 8. Solving for the Unknown. 9. Ratio/Proportion. 10. Electrical Calculations. 11. Circumference, Area & Volume. 12. Force, Pressure & Head, Velocity Calculations. 13. Mass Balance & Measuring Plant Performance. 14. Pumping Calculations. 15. Water Source & Storage Calculations. 16. Waste/Wastewater Laboratory Calculations. 17. Workbook Practice Problems.

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Book SynopsisI Fundamentals.- 1 Ordinary Differential Equations.- 2 Difference Equations.- II Local Analysis.- 3 Approximate Solution of Linear Differential Equations.- 4 Approximate Solution of Nonlinear Differential Equations.- 5 Approximate Solution of Difference Equations.- 6 Asymptotic Expansion of Integrals.- III Perturbation Methods.- 7 Perturbation Series.- 8 Summation of Series.- IV Global Analysis.- 9 Boundary Layer Theory.- 10 WKB Theory.- 11 Multiple-Scale Analysis.Trade Review"This book is a reprint of the original published by McGraw-Hill \ref [MR0538168 (80d:00030)]. The only changes are the addition of the Roman numeral I to the title and the provision of a subtitle, "Asymptotic methods and perturbation theory". This latter improvement is much needed, as the original title suggested that this was a teaching book for undergraduate scientists and engineers. It is not, but is an excellent introduction to asymptotic and perturbation methods for master's degree students or beginning research students. Certain parts of it could be used for a course in asymptotics for final year undergraduates in applied mathematics or mathematical physics. This is a book that has stood the test of time and I cannot but endorse the remarks of the original reviewer. It is written in a fresh and lively style and the many graphs and tables, comparing the results of exact and approximate methods, were in advance of its time. I have owned a copy of the original for over twenty years, using it on a regular basis, and, after the original had gone out of print, lending it to my research students. Springer-Verlag has done a great service to users of, and researchers in, asymptotics and perturbation theory by reprinting this classic." (A.D. Wood, Mathematical Reviews) Table of ContentsI Preface. 1 Ordinary Differential Equations. 2 Difference Equations. 3 Approximate Solution of Linear Differential Equations. 4 Approximate Solution of Nonlinear Equations. 5 Approximate Solution of Difference Equations. 6 Asymptotic Expansion of Integrals. 7 Perturbation Series. 8 Summation of Series. 9 Boundary Layer Theory. 10 WKB Theory. 11 Multiple Scales Analysis. Appendix, References, Index

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Book SynopsisThis book focuses on a development of optimal, flexible, and efficient models and algorithms for cell formation in group technology. Its main aim is to provide a reliable tool that can be used by managers and engineers to design manufacturing cells based on their own preferences and constraints imposed by a particular manufacturing system.Trade Review“The book under review is a very good source … continuing the long term passion of Panos Pardalos and his collaborators in exact solution of difficult problems … . It also adds a very valuable contribution to the body of knowledge of the cell formation problem that can be used in both teaching and research including in bioinformatics.” (Boris Mirkin, Optimization Letters, 2015)Table of Contents1. The problem of cell formation.- 2. ​The p-Median problem.- 3. Application of the PMP to cell formation in group technology.- 4. The minimum multicut problem and an exact model for cell formation.- 5. Multiobjective nature of cell formation.- 6. Pattern-based heuristic for the cell formation problem in group technology.- 7. Branch-and-bound algorithm for bi-criterion cell formation problems.- 8. Summary and conclusions.- A. Solutions to the 35 CF instances from [71].- Index.- References.

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Book SynopsisThis pioneering text provides a comprehensive introduction to systems structure, function, and modeling as applied in all fields of science and engineering. Systems understanding is increasingly recognized as a key to a more holistic education and greater problem solving skills, and is also reflected in the trend toward interdisciplinary approaches to research on complex phenomena. While the concepts and components of systems science will continue to be distributed throughout the various disciplines, undergraduate degree programs in systems science are also being developed, including at the authors' own institutions. However, the subject is approached, systems science as a basis for understanding the components and drivers of phenomena at all scales should be viewed with the same importance as a traditional liberal arts education. Principles of Systems Science contains many graphs, illustrations, side bars, examples, and problems to enhance understanding. Frombasic principles of orgaTrade Review“Principles of systems science consists of 14 chapters organized in five parts. … This book is a feast--full of systems theory and sage guidance about systems practice.” (Ernest Hughes, Computing Reviews, computingreviews.com, August, 2016)Table of ContentsPart I: Introduction to Systems Science.- A Helicopter View.- Systems Principles in the Real World: Understanding Drug Resistant TB.- Part II: Structural and Functional Aspects.- Organized Wholes.- Networks: Connections Within and Without.- Complexity.- Behavior: System Dynamics.- Part III: The Intangible Aspects of Organization: Maintaining and Adapting.- Information, Meaning, Knowledge, and Communications.- Computational Systems.- Cybernetics: The Role of Information and Computation in Systems.- Part IV: Evolution.- Auto-Organization and Emergence.- Evolution.- Part V: Methodological Aspects.- Systems Analysis.- Systems Modeling.- Systems Engineering.

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Book SynopsisThis book offers a user friendly, hands-on, and systematic introduction to applied and computational harmonic analysis: to Fourier analysis, signal processing and wavelets; and to their interplay and applications. The approach is novel, and the book can be used in undergraduate courses, for example, following a first course in linear algebra, but is also suitable for use in graduate level courses. The book will benefit anyone with a basic background in linear algebra. It defines fundamental concepts in signal processing and wavelet theory, assuming only a familiarity with elementary linear algebra. No background in signal processing is needed. Additionally, the book demonstrates in detail why linear algebra is often the best way to go. Those with only a signal processing background are also introduced to the world of linear algebra, although a full course is recommended. The book comes in two versions: one based on MATLAB, and one on Python, demonstrating the feasibility and applications of both approaches. Most of the MATLAB code is available interactively. The applications mainly involve sound and images. The book also includes a rich set of exercises, many of which are of a computational nature.Trade Review“A beginning student who is unfamiliar with the mathematics behind signal processing will find much here that explains the techniques and the issues associated with their use. Altogether the book presents a beautiful introduction to the uses of linear algebra in signal processing.” (MAA Reviews, July 18, 2020)“This book is a very useful textbook for undergraduate students in applied mathematics and engineering disciplines, but it is also suitable for graduate level courses.” (Manfred Tasche, zbMATH 1420.65001, 2019)Table of Contents1. Sound and Fourier series.- 2. Digital Sound and Discrete Fourier Analysis.- 3. Discrete Time Filters.- 4. Motivation for Wavelets and Some Simple Examples.- 5. The Filter Representation of Wavelets.- 6. Constructing Interesting Wavelets.- 7. The Polyphase Representation of Filter Bank Transforms.- 8. Digital Images.- 9. Using Tensor Products to Apply Wavelets to Images.- A Basic Linear Algebra.

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

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

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Book SynopsisThe chapters in this contributed volume showcase current theoretical approaches in the modeling of ocular fluid dynamics in health and disease. By including chapters written by experts from a variety of fields, this volume will help foster a genuinely collaborative spirit between clinical and research scientists. It vividly illustrates the advantages of clinical and experimental methods, data-driven modeling, and physically-based modeling, while also detailing the limitations of each approach. Blood, aqueous humor, vitreous humor, tear film, and cerebrospinal fluid each have a section dedicated to their anatomy and physiology, pathological conditions, imaging techniques, and mathematical modeling. Because each fluid receives a thorough analysis from experts in their respective fields, this volume stands out among the existing ophthalmology literature.Ocular Fluid Dynamics is ideal for current and future graduate students in applied mathematics and ophthalmology who wish to explore the field by investigating open questions, experimental technologies, and mathematical models. It will also be a valuable resource for researchers in mathematics, engineering, physics, computer science, chemistry, ophthalmology, and more.Table of ContentsPart I. Introduction.- Mathematical and physical modeling principles of complex biological systems.- Part II. Blood.- Vascular Anatomy and Physiology of the Eye.- Pathological Consequences of Vascular Hemodynamic Alterations in the Eye.- Measurement of geometrical and functional parameters related to ocular blood flow.- Mathematical modeling of blood flow in the eye.- Part III. Aqueous Humor.- Changes in Parameters of Aqueous Humor Dynamics Throughout Life.- Aqueous Humor Dynamics and its Influence on Glaucoma.- Approaches to Aqueous Humor Outflow Imaging.

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Book SynopsisIn the context of life sciences, we are constantly confronted with information that possesses precise semantic values and appears essentially immersed in a specific evolutionary trend. In such a framework, Nature appears, in Monod’s words, as a tinkerer characterized by the presence of precise principles of self-organization. However, while Monod was obliged to incorporate his brilliant intuitions into the framework of first-order cybernetics and a theory of information with an exclusively syntactic character such as that defined by Shannon, research advances in recent decades have led not only to the definition of a second-order cybernetics but also to an exploration of the boundaries of semantic information. As H. Atlan states, on a biological level "the function self-organizes together with its meaning". Hence the need to refer to a conceptual theory of complexity and to a theory of self-organization characterized in an intentional sense. There is also a need to introduce, at the genetic level, a distinction between coder and ruler as well as the opportunity to define a real software space for natural evolution. The recourse to non-standard model theory, the opening to a new general semantics, and the innovative definition of the relationship between coder and ruler can be considered, today, among the most powerful theoretical tools at our disposal in order to correctly define the contours of that new conceptual revolution increasingly referred to as metabiology. This book focuses on identifying and investigating the role played by these particular theoretical tools in the development of this new scientific paradigm. Nature "speaks" by means of mathematical forms: we can observe these forms, but they are, at the same time, inside us as they populate our organs of cognition. In this context, the volume highlights how metabiology appears primarily to refer to the growth itself of our instruments of participatory knowledge of the world.Table of ContentsChapter 1: On the verge of life: Looking for a new scientific paradigm.- Chapter 2: Drawing a software space for natural evolution.- Chapter 3: Non-standard models and the "construction" of life.- Chapter 4: Regulatory logic, algorithmic information and general semantics.- Chapter 5: The roots of morphogenesis: notes for a new tale.

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Book SynopsisThis book develops analytical methods for studying the dynamical chaos, synchronization, and dynamics of structures in various models of coupled rotators. Rotators and their systems are defined in a cylindrical phase space, and, unlike oscillators, which are defined in Rn, they have a wider “range” of motion: There are vibrational and rotational types for cyclic variables, as well as their combinations (rotational-vibrational) if the number of cyclic variables is more than one. The specificity of rotator phase space poses serious challenges in terms of selecting methods for studying the dynamics of related systems. The book chiefly focuses on developing a modified form of the method of averaging, which can be used to study the dynamics of rotators. In general, the book uses the “language” of the qualitative theory of differential equations, point mappings, and the theory of bifurcations, which helps authors to obtain new results on dynamical chaos in systems with few degrees of freedom. In addition, a special section is devoted to the study and classification of dynamic structures that can occur in systems with a large number of interconnected objects, i.e. in lattices of rotators and/or oscillators. Given its scope and format, the book can be used both in lectures and courses on nonlinear dynamics, and in specialized courses on the development and operation of relevant systems that can be represented by a large number of various practical systems: interconnected grids of various mechanical systems, various types of networks including not only mechanical but also biological systems, etc. Table of ContentsIntroduction.- Autonomous and non-autonomous systems with one degrees-of-freedom. Autonomous and non-autonomous systems with one and a half degrees-of-freedom.- Autonomous systems with two degrees-of-freedom.- Vibration of shafts.- Synchronization in homogeneous lattices.- Physics, existence, fusion and stability Of cluster structures.- Appendix I.- Appendix II.

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Book SynopsisIn simulation tests of dynamic states of the power system (PS), the database of parameters of mathematical models of generating units is most commonly used. In many cases, the parameter values are burdened with large errors. Consequently, the results obtained are not reliable and do not allow drawing true conclusions. This monograph presents the developed methods and tools supporting the process of measurement determination of reliable values of parameters of mathematical models of synchronous generators and excitation systems. Special measurement tests are the basis for determining the parameters. The tests can be carried out in conditions of normal operation of generating units, in which electrical machines operate in the state of saturation of magnetic cores, and voltage regulators can reach limits. This book is intended for specialists in power engineering as well as students of faculties of electrical engineering interested in issues of PS transient states.Table of ContentsIntroduction.- Simulation models of generating unit elements.- Analysis of the sensitivity of generating unit simulation waveforms to changes of model parameters.- Method, algorithm and module of a parameter estimation program for mathematical models of synchronous generator and excitation systems.- Forming and filtration of measurement waveforms.- A system for measuring generator load angle.

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Book SynopsisThis book presents the state-of-the-art in supercomputer simulation. It includes the latest findings from leading researchers using systems from the High Performance Computing Center Stuttgart (HLRS) in 2019. The reports cover all fields of computational science and engineering ranging from CFD to computational physics and from chemistry to computer science with a special emphasis on industrially relevant applications. Presenting findings of one of Europe’s leading systems, this volume covers a wide variety of applications that deliver a high level of sustained performance.The book covers the main methods in high-performance computing. Its outstanding results in achieving the best performance for production codes are of particular interest for both scientists and engineers. The book comes with a wealth of color illustrations and tables of results.Table of ContentsPart 1, Physics.- Part 2, Solid State Physics.- Part 3, Chemistry.- Part 4, Material Science.- Part 5, Reactive Flows.- Part 6, Computational Fluid Dynamics.- Part 7, Transport and Climate.- Part 8, Computer Science.- Part 9, Miscellaneous Topics.

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Book SynopsisThis book presents the state of the art in High Performance Computing on modern supercomputer architectures. It addresses trends in hardware and software development in general. The contributions cover a broad range of topics, from performance evaluations in context with power efficiency to Computational Fluid Dynamics and High Performance Data Analytics. In addition, they explore new topics like the use of High Performance Computers in the field of Artificial Intelligence and Machine Learning. All contributions are based on selected papers presented at the 30th Workshop on Sustained Simulation Performance (WSSP) held at the High Performance Computing Center, University of Stuttgart, Germany in October 2019 and on the papers for the planned Workshop on Sustained Simulation Performance in March 2020, which could not take place due to the Covid-19 pandemic.Table of ContentsPerformance and Power.- Numeric and Optimization.- Data Handling and New Concepts.- Trends in HPC and AI.

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