Maths for engineers Books

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 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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Book SynopsisAnthony 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.Table of ContentsPreface xvii Acknowledgements xix Chapter 1 Review of algebraic techniques 1Chapter 2 Engineering functionsChapter 3 The trigonometric functionsChapter 4 Coordinate systemsChapter 5 Discrete mathematicsChapter 6 Sequences and seriesChapter 7 VectorsChapter 8 Matrix algebraChapter 9 Complex numbersChapter 10 Di erentiationChapter 11 Techniques of di erentiationChapter 12 Applications of di erentiationChapter 13 IntegrationChapter 14 Techniques of integrationChapter 15 Applications of integrationChapter 16 Further topics in integrationChapter 17 Numerical integrationChapter 18 Taylor polynomials, Taylor series and Maclaurin seriesChapter 19 Ordinary di erential equations IChapter 20 Ordinary di erential equations IIChapter 21 The Laplace transformChapter 22 Di erence equations and the z transformChapter 23 Fourier seriesChapter 24 The Fourier transformChapter 25 Functions of several variablesChapter 26 Vector calculusChapter 27 Line integrals and multiple integralsChapter 28 ProbabilityChapter 29 Statistics and probability distributionsAppendix I Representing a continuous function and a sequence as a sum of weighted impulsesAppendix II The Greek alphabetAppendix III SI units and prefixesAppendix IV The binomial expansion of (n−N)/nnIndex

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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 SynopsisKuldeep Singh is Senior Lecturer in Mathematics at the School of Physics, Astronomy and Mathematics at the University of Hertfordshire, UK. He teaches mathematics to a wide range of engineering and science students.Trade ReviewOnline reviews: Very clear. Concise. A joy to learn from. I can't be more happy with a book that allows such depth to be absorbed.- Amazon reviewer This book has been my trusted reference since its first edition and is the best book on the topic that I have ever encountered. It takes you from a round-up of 'the stuff from school' all the way to differential equations; but in contrast to other books, you don't get lost on the way. Every chapter is well structured and full of great explanations, examples and illustrations, as well as related to real-world engineering problems; this makes it extra fun to work through. An amazing piece of work! - Amazon reviewer A brilliant book very well written, definitely outstanding in the field of instruction on basic and advanced maths. The author has the great ability to explain in great detail, and the text, walks the student step by step, through each and every process. Never have I seen such a splendid approach to mathematics...I highly recommend this book for the desk of each High School student, and Advanced Engineering student, or any student, who is required to know maths, from basic to advanced levels. - Barnes & Noble reviewer Published reviews of the first edition: 'The unique quality of this book is the wealth of examples applying the mathematical techniques taught here. These examples span mechanics, aerodynamics, electronics, engineering, fluid dynamics and other areas of applied mathematics. These are not just the usual examples involving differential equations and equations of motion, but real and thoughtful applications that will be relevant to the student.' - Jill Russell, Open University, UK. 'If you teach a first year mathematics module to a diverse engineering group, this book should be at the top of your list for consideration as a core text. It aims to encourage their [the students] learning through setting the mathematics within the context of engineering examples. With its very readable text it is suitable for both self-study and as support for a taught module. The book covers the requirements of most first year engineering mathematics modules with a fairly gentle reminder of arithmetic and algebra by way of introduction. Examples are drawn from such diverse subjects as electricity, control theory, heat flow, structures, fluid mechanics, signal processing, thermodynamics etc with the largest group being from mechanics. The examples are simple enough to be understood by most engineering students but sufficiently specific to allow students to see that mathematics is relevant to their own engineering discipline. I liked the presentation of the text - the questions posed to the reader, the full labelling in diagrams and the indication to students of the discipline of the examples. Helpful extra information is occasionally provided in subscript format to indicate the method used to move from one line to the next.' - Dr Ian Taylor, Faculty of Engineering at The University of Ulster, Engineering Subject Centre, Northern Ireland. 'The book starts with the basics of mathematics making it suitable for those with little background in mathematics. This also makes it appealing to a wide variety of readers with different mathematical backgrounds. The book is a good size covering all the essential topics to adequate depth. It covers topics similar to other books targeted at the same audience; however it differs in that it does not assume readers to have a mathematical background. The book's approach of using examples is effective. Its use of examples is motivating. The engineering example generates interest by illustrating the importance and relevance of mathematics in engineering. A definite plus is the provision of online interactive questions, which enable users to test their understanding. This extra support makes it an ideal text for self-study and distance learning.' - Dr Lawrence Chirwa, School of Electrical and Mechanical Engineering at The University of Ulster, Engineering Subject Centre, Northern Ireland. 'This is a book that is designed to cover the basics thoroughly and then move on. As a reminder of useful techniques, the book is definitely valuable. What is most refreshing is that it explains everything that you need to know in order to cover the basics of a given subject. The fact that there is almost no assumed knowledge is reassuring, and takes some of the mental strain away from getting your head around eigenvectors again... Essentially, if you want to remind yourself how to do those things that you once thought were straightforward, this is the book for you. A very useful book to have on your shelf.' - Edward Hoare, The Institution of Structural Engineers, UK. 'Excellent engineering examples not found in other texts' - Stephen Farrell, Lancaster University, UK 'Displaying questions/examples from different engineering disciplines demonstrates to students that mathematics is not a subject that must simply be endured but that it is an important tool for the professional engineer.' - Frank Doheny, Althone Institute of Technology, Ireland 'I think this is an excellent second edition. The strengths of the book include its being aimed at weaker students who have difficulty bridging the gap between A level and university. The contents match up well with our syllabuses. It has also a wealth of questions based on practical engineering examples.' Ian Jones, Liverpool John Moores University, UK Lecturer feedback: 'I really like this book. There are plenty of end-of-chapter questions and the explanations within the chapters are very well laid out. Topics have been given a thorough treatment.' - Saudagar Jagdev, Department of Engineering, Leeds City College, UK 'This text is brilliant! Easy to read and understand. It also uses an excellent spread of engineering sectors in the end-of-chapter questions.' - Christopher Collins, School of Construction, Lincoln College, UK 'Excellent text - detailed explanation of topics, relevant examples and attractive presentation.' - Aine Ni She, Department of Mathematics, Cork Institute of Technology, Ireland 'An excellent textbook for students undertaking mathematics as part of their core engineering studies.' - Allister Ross Smith, Fife College, UKTable of ContentsIntroduction: Arithmetic for Engineers Engineering Formulae Visualizing Engineering Formulae Functions on Engineering Trigonometry and Waveforms Logarithmic, Exponential and Hyperbolic Functions Differentiation Engineering Applications of Differentiation Integration Engineering Applications of Integration Complex Numbers Matrices Vectors First Order Differential Equations Second Order Linear Differential Equations Partial Differentiation Probability and Statistics Solutions Appendix: Standard Normal Distribution Table.

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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 SynopsisMeasurement is a fundamental concept that underpins almost every aspect of the modern world. It is central to the sciences, social sciences, medicine, and economics, but it affects everyday life. We measure everything - from the distance of far-off galaxies to the temperature of the air, levels of risk, political majorities, taxes, blood pressure, IQ, and weight. The history of measurement goes back to the ancient world, and its story has been one of gradual standardization. Today there are different types of measurement, levels of accuracy, and systems of units, applied in different contexts. Measurement involves notions of variability, accuracy, reliability, and error, and challenges such as the measurement of extreme values.In this Very Short Introduction, David Hand explains the common mathematical framework underlying all measurement, the main approaches to measurement, and the challenges involved. Following a brief historical account of measurement, he discusses measurement as used in the physical sciences and engineering, the life sciences and medicine, the social and behavioural sciences, economics, business, and public policy.ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.Table of ContentsREFERENCES; FURTHER READING; INDEX

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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 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 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 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 SynopsisThe fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For studentsand otherswith a mathematical background, these derivations provide a starting point to machine learning texts. Forthoselearning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book''s web site.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 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 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 SynopsisThis comprehensive new textbook bridges the gap between mathematical theory and practical engineering applications. Organized into eight chapters, it introduces programming skills in MATLAB and Python alongside essential mathematical concepts, progressing from basic computation and linear algebra to more advanced topics such as differential equations, Fourier series, and Laplace transforms. The book develops both mathematical reasoning and computational proficiency, equipping students with essential tools for modern engineering practice. It includes numerous MATLAB and Python scripts, presented within the text and available through a dedicated GitHub repository for hands-on learning and reproducibility. Each chapter concludes with problemsâmany with solutionsâthat reinforce understanding and encourage practical application. By integrating theory with coding exercises, the book ensures that students not only grasp key concepts but also gain the skills to apply them in real-world contexts. The book is intended for undergraduate engineering students in Civil, Mechanical, Electrical, and Chemical Engineering. It is particularly suited for modules in Engineering Mathematics, Programming, Computations, and Analytical Studies, and can also serve as a supplementary reference for postgraduate students seeking applied mathematical and computational skills. Instructors will find it a valuable teaching resource that integrates theory with practice, adaptable for both semester- and year-long courses.The GitHub repository can be accesses at https://github.com/prog871/CRC-book2025.

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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 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 SynopsisComplex analysis is a classic and central area of mathematics, which is studied and exploited in a range of important fields, from number theory to engineering. This book offers a detailed presentation of elementary topics, to reflect the knowledge base of students.Trade ReviewReview from previous edition Priestley's book is an unqualified success. * THES *[This] is THE undergraduate textbook on the subject. * Peter Cameron, QMW *The conciseness of the text is one of its many good features * Chris Ridler-Rowe, Imperial College *Table of ContentsComplex numbers ; Geometry in the complex plane ; Topology and analysis in the complex plane ; Holomorphic functions ; Complex series and power series ; A menagerie of holomorphic functions ; Paths ; Multifunctions: basic track ; Conformal mapping ; Cauchy's theorem: basic track ; Cauchy's theorem: advanced track ; Cauchy's formulae ; Power series representation ; Zeros of holomorphic functions ; Further theory of holomorphic functions ; Singularities ; Cauchy's residue theorem ; Contour integration: a technical toolkit ; Applications of contour integration ; The Laplace transform ; The Fourier transform ; Harmonic functions and holomorphic functions ; Bibliography ; Notation index ; 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 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 SynopsisExamines a nonlinear system of parabolic partial differential equations (PDE) arising in mathematical biology and statistical mechanics. This book describes the mathematical and physical principles: derivation of a series of equations, biological modeling based on biased random walks, and quantized blowup mechanism based on several PDE techniques.Trade ReviewFrom the reviews: "This book is primarily concerned with systems of partial differential equations of elliptic-parabolic type. Such systems are special cases of systems of pdes that occur naturally in biochemistry, biophysics, molecular biology, and in chemical thermodynamics and statistical mechanics—in short wherever chemical kinetics and diffusive processes are present in a system…. The book itself is well organized and readable although very technical. It is a book about the mathematics of systems and not biology or thermodynamics…. [It] certainly belongs on the bookshelf of specialists in nonlinear pde/math biology." —Bulletin of the AMS “This book is introductory in the sense of being accessible to students not only of mathematics, but also of the physical and the engineering sciences once they have mastered the introductory mathematical courses. …Overall, the presentation is quite detailed regarding the needs of the practitioner with many examples to engineering, earth sciences, etc. (among others elasticity, vibrations, heat transfer, fluid flow; also eigenvalue problems), and special but important items not so often covered in other texts, e.g., how to cope with the specific difficulties arising in polar coordinates. Both numerous exercises and codes in Ansys, Fortran, Mathematica® and MATLAB direct the reader towards experimentation of his own.” (Monatshefte fur Mathematik) "This book examines a nonlinear system of parabolic partial differential equations (PDEs) arising in mathematical biology and statistical mechanics. … Free Energy and Self-Interacting Particles is suitable for researchers and graduate students of mathematics and applied mathematics who are interested in non-linear PDEs in stochastic processes, cellular automata, variational methods, and their applications to natural sciences. It is also suitable for researchers in other fields such as physics, chemistry, biology, and engineering." (Christopher Mayer, Simulation News Europe, Vol. 16 (1), 2006)Table of Contents* Dedication * Preface * Summary * Background * Fundamental Theorem * Trudinger–Moser Inequality * The Green's Function * Equilibrium States * Blowup Analysis for Stationary Solutions * Multiple Existence * Dynamical Equivalence * Formation of Collapses * Finiteness of Blowup Points * Concentration Lemma * Weak Solution * Hyperparabolicity * Quantized Blowup Mechanism * Theory of Dual Variation * References * 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 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 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 book comprises the proceedings of the 4th International Conference on Computational Engineering (ICCE 2017), held in Darmstadt, Germany on September 28-29, 2017. The conference is intended to provide an interdisciplinary meeting place for researchers and practitioners working on computational methods in all disciplines of engineering, applied mathematics and computer science. The aims of the conference are to discuss the state of the art in this challenging field, exchange experiences, develop promising perspectives for future research and initiate further cooperation.Computational Engineering is a modern and multidisciplinary science for computer-based modeling, simulation, analysis, and optimization of complex engineering applications and natural phenomena. The book contains an overview of selected approaches from numerics and optimization of Partial Differential Equations as well as uncertainty quantification techniques, typically in multiphysics environments. Where possible, application cases from engineering are integrated.The book will be of interest to researchers and practitioners of Computational Engineering, Applied Mathematics, Engineering Sciences and Computer Science.Table of ContentsOptimization of design parameters of CIP spray cleaning nozzle using Genetic Algorithm.- Multilevel Optimization of Fluid-Structure Interaction based on Reduced Order Models.- An investigation of airfoil noise prediction using hybrid LES/RANS models.- A high-order local Discontinuous Galerkin scheme for viscoelastic fluid flow.- A Bramble-Pasciak conjugate gradient method for discrete Stokes problems with lognormal random viscosity.- Linear Solvers for the Finite Pointset Method.- Additional degrees of parallelism within the Adomian decomposition method.- Integrated modeling and validation for phase change with natural convection.- A weighted reduced basis method for parabolic PDEs with random data.- Modeling of the compressed-air flow impact for thermoforming simulations.- Monolithic simulation of convection-coupled phase-change -- verification and reproducibility.

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Book SynopsisThis book addresses a range of aging intensity functions, which make it possible to measure and compare aging trends for lifetime random variables. Moreover, they can be used for the characterization of lifetime distributions, also with bounded support. Stochastic orders based on the aging intensities, and their connections with some other orders, are also discussed. To demonstrate the applicability of aging intensity in reliability practice, the book analyzes both real and generated data. The estimated, properly chosen, aging intensity function is mainly recommended to identify data’s lifetime distribution, and secondly, to estimate some of the parameters of the identified distribution. Both reliability researchers and practitioners will find the book a valuable guide and source of inspiration. Table of ContentsBasic reliability functions.- Aging intensity of nonnegative univariate absolutely continuous Distributions.- Aging intensities of discrete distributions.- Aging intensities vector for bivariate absolutely continuous distributions.- Aging intensities vectors for bivariate discrete distributions.- Generalized aging intensity functions.- G-generalized aging intensity functions.- Support dependent G-generalized aging intensity functions.- Conclusions and Final Remarks.

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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 presents new ideas in the framework of novel, finite element discretization schemes for solids and structure, focusing on the mechanical as well as the mathematical background. It also explores the implementation and automation aspects of these technologies. Furthermore, the authors highlight recent developments in mixed finite element formulations in solid mechanics as well as novel techniques for flexible structures at finite deformations. The book also describes automation processes and the application of automatic differentiation technique, including characteristic problems, automatic code generation and code optimization. The combination of these approaches leads to highly efficient numerical codes, which are fundamental for reliable simulations of complicated engineering problems. These techniques are used in a wide range of applications from elasticity, viscoelasticity, plasticity, and viscoplasticity in classical engineering disciplines, such as civil and mechanical engineering, as well as in modern branches like biomechanics and multiphysics.Table of ContentsNotes on Basic Concepts of the Finite Element Method for Elliptic Problems.- Sensitivity Analysis Based Automation of Computational Problems.- Equilibrated Stress Reconstruction and a Posteriori Error Estimation for Linear Elasticity.- A Concept for the Extension of the Assumed Stress Finite Element Method to Hyperelasticity.- Simple Equilibrium Finite Elements for Geometrically Exact Bernoulli-Euler Beams and Kirchhoff-Love Shells.- Isogeometric Analysis of Solids in Boundary Representation.

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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 examines recent methods for data-driven fault diagnosis of multimode continuous processes. It formalizes, generalizes, and systematically presents the main concepts, and approaches required to design fault diagnosis methods for multimode continuous processes. The book provides both theoretical and practical tools to help readers address the fault diagnosis problem by drawing data-driven methods from at least three different areas: statistics, unsupervised, and supervised learning.Table of ContentsData-driven Fault Diagnosis.- Multimode Continuous Processes.- Multimode Continuous Processes Clustering.- Multimode Continuous Processes Monitoring.

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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 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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Book SynopsisThis compact textbook provides a foundation in mathematics for STEM students entering university. The book helps students from different disciplines and backgrounds make the transition to university. Based on the author’s teaching for many years, the book can be used as a textbook and a resource for lecturers and professors. Its accessibility is such that it is can also be used by students in their final year in school before university and help them continue their mathematical studies at college. The book is designed so that students will return to the book repeatedly as their undergraduate careers progress. Although compact and concise, it loses no rigour. All the topics are carefully explained meaningfully, not just presented as a set of rules or rote-learned procedures. Table of ContentsTrigonometry.- Real and Complex Numbers.- Vector Algebra.- Matrices.- Differentiation.

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Book SynopsisSimulating the behavior of a human heart, predicting tomorrow's weather, optimizing the aerodynamics of a sailboat, finding the ideal cooking time for a hamburger: to solve these problems, cardiologists, meteorologists, sportsmen, and engineers can count on math help. This book will lead you to the discovery of a magical world, made up of equations, in which a huge variety of important problems for our life can find useful answers.Trade Review“By providing tools and current examples on modeling issues ... the book makes a contribution answering the becoming more and more prevalent presence of Mathematics in our daily lives. The examples come essentially from the physical and natural sciences, but the book can be relied on in other areas, including the humanities, aside seminal works on mathematical modeling ... . The journey consists in eight rigorous and enjoying chapters.” (Lisa Morhaim, zbMATH 1519.00001, 2023)Table of Contents1 The model, aka the magic box.- 2 Weather Forecast Models.- 3 Epidemics: the Mathematics of Contagion.- 4 Mathematical Hearth.- 5 Mathematics in the Wind.- 6 Flying on Sun Power.- 7 The taste for Mathematics.- 8 Conclusions.

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Book SynopsisUsing a novel integration of mathematics and Python codes, this book illustrates the fundamental concepts that link probability, statistics, and machine learning, so that the reader can not only employ statistical and machine learning models using modern Python modules, but also understand their relative strengths and weaknesses. To clearly connect theoretical concepts to practical implementations, the author provides many worked-out examples along with "Programming Tips" that encourage the reader to write quality Python code. The entire text, including all the figures and numerical results, is reproducible using the Python codes provided, thus enabling readers to follow along by experimenting with the same code on their own computers. Modern Python modules like Pandas, Sympy, Scikit-learn, Statsmodels, Scipy, Xarray, Tensorflow, and Keras are used to implement and visualize important machine learning concepts like the bias/variance trade-off, cross-validation, interpretability, and regularization. Many abstract mathematical ideas, such as modes of convergence in probability, are explained and illustrated with concrete numerical examples. This book is suitable for anyone with undergraduate-level experience with probability, statistics, or machine learning and with rudimentary knowledge of Python programming.Table of ContentsIntroduction.- Part 1 Getting Started with Scientific Python.- Installation and Setup.- Numpy.- Matplotlib.- Ipython.- Jupyter Notebook.- Scipy.- Pandas.- Sympy.- Interfacing with Compiled Libraries.- Integrated Development Environments.- Quick Guide to Performance and Parallel Programming.- Other Resources.- Part 2 Probability.- Introduction.- Projection Methods.- Conditional Expectation as Projection.- Conditional Expectation and Mean Squared Error.- Worked Examples of Conditional Expectation and Mean Square Error Optimization.- Useful Distributions.- Information Entropy.- Moment Generating Functions.- Monte Carlo Sampling Methods.- Useful Inequalities.- Part 3 Statistics.- Python Modules for Statistics.- Types of Convergence.- Estimation Using Maximum Likelihood.- Hypothesis Testing and P-Values.- Confidence Intervals.- Linear Regression.- Maximum A-Posteriori.- Robust Statistics.- Bootstrapping.- Gauss Markov.- Nonparametric Methods.- Survival Analysis.- Part 4 Machine Learning.- Introduction.- Python Machine Learning Modules.- Theory of Learning.- Decision Trees.- Boosting Trees.- Logistic Regression.- Generalized Linear Models.- Regularization.- Support Vector Machines.- Dimensionality Reduction.- Clustering.- Ensemble Methods.- Deep Learning.- Notation.- References.- Index.

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Book SynopsisThis textbook offers a comprehensive treatment of vehicle dynamics using an innovative, compelling approach, suitable for engineering students and professionals alike. Written by an authoritative contributor in the fields of applied mathematics and mechanics, it focuses on the development of vehicle models paying special attention to all the relevant assumptions, and providing explanations for each step. Some classical concepts of vehicle dynamics are revisited and reformulated, making this book also interesting for experienced readers. Using clear definitions, sound mathematics, and worked-out exercises, the book helps readers to truly understand the essence of vehicle dynamics for solving practical problems. With respect to the previous edition, which was the recipient of a 2019 TAA Textbook Excellence Award, this thoroughly revised third edition presents a more extensive and in-depth analysis of braking and handling of race cars.Table of ContentsIntroduction.- Mechanics of the Wheel with Tire.- Vehicle Model for Handling and Performance.- Braking Performance.

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Book SynopsisThis book offers a thought-provoking exploration of dynamic geometry and its connections to self-reference and theoretical biology. The authors explore how a self-referential boundary can be translated into remarkable relations between expanding geometrical forms, with a particular focus on triangles and circles.The essence of this work lies in revealing not only how these forms expand and interact with others but also how their interactions lead to closed loops of definitions between processes, where triangles and circles reciprocally define one another. These unique geometrical relations offer fresh perspectives on the interaction and emergence of forms. Through the introduction of time and a fixed velocity of expansions, a rich tapestry of encounters and coalescences unfolds, pushing beyond the boundaries of traditional insights on context dependence and state transitions of systems.These captivating movements elude prediction other than by numerical approximation within unpredictable durations. Unlike cellular automata, they defy stepwise progression on a predefined grid, presenting themselves as unprogrammable construction processes that leave readers in awe of their unexpected elegance.This book is essential reading for researchers and students in theoretical biology seeking to deepen their understanding of the intersections of geometry and systems theory and seeking to gain new insights into the processes that underlie the origination of complexity."What is unique to the authors' attempt is to shed a new light on extending the notion of cohesive interaction so as to make it applicable even to biology at large without offending the established physics so far. To the best of my knowledge, their work has been the first attempt of this kind in explicating the intricate relationship between geometric topology of the network and the realizable temporal cohesion to be observed widely in biology." (Professor Koichiro Matsuno, 1st foreword to this book) "I am delighted that the authors use Robert Rosen's (M,R)-systems — impredicative networks that are inherently geometrical — to illustrate (see Chapter 4 of this book) their self-referential systems of geometrical expansions." (dr. Aloisius Louie, 2nd foreword to this book)Table of ContentsIntroductory remarks.- A self-referential boundary.- Expanding forms: the geometrical representation.- The geometrical expansions as a relational network.- The geometrical representation and its computability.- Conclusion.- References.

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Book SynopsisStudy of dust devils in a laboratory experiment.- Corner circulation scaling laws of turbulent Rayleigh-Bénard convection in a cubic cell.- Direct numerical simulation of turbulent open channel ?ow: Streamwise turbulence intensity scaling and its relation to large-scale coherent motions.

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