Mathematical modelling Books

Book SynopsisA comprehensive, thoroughly modern approach to environmental quality assessment The only textbook to combine engineering transport fundamentals and equilibrium aquatic chemistry, Environmental Modeling brings a uniquely contemporary perspective to the assessment of environmental quality. Addressing key questions about fate, transport, and long-term effects of chemical pollutants in the environment, this inherently practical text gives readers the important tools they need to develop and solve their own mathematical models. Contains detailed examples from a wide range of crucial water quality areas-conventional pollutants in rivers, eutrophication of lakes, and toxic organic chemicals and heavy metals in both surface and groundwaters Examines current global issues, including atmospheric deposition, hazardous wastes, soil pollution, global change, and more Features over 200 high-quality illustrations, plus skill-building problems in every chapter <Table of ContentsTransport Phenomena. Chemical Reaction Kinetics. Equilibrium Chemical Modeling. Eutrophication of Lakes. Conventional Pollutants in Rivers. Toxic Organic Chemicals. Modeling Trace Metals. Groundwater Contamination. Atmospheric Deposition and Biogeochemistry. Global Change and Global Cycles. Appendices. Index.

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Book SynopsisUnderstanding how to properly manage urban stormwater is a critical concern to civil and environmental engineers the world over. Mismanagement of stormwater and urban runoff results in flooding, erosion, and water quality problems.Table of ContentsURBAN STORMWATER MANAGEMENT. Urban Drainage Systems: Evolution of Problems. Urban Runoff Quantity and Quality Control Strategies. Urban Stormwater Management Modeling. DATA ANALYSIS. Meteorological Data Analysis. Runoff Quality Data Analysis. DRAINAGE SYSTEM PERFORMANCE ANALYSIS. Elements of Derived Probability Distribution Theory. Model of Urban Drainage System. Quantity Control Analysis of Urban Drainage Systems. Advanced Quantity Control Analysis. Multiple Reservoir Systems. Quality Control Analysis of Urban Drainage Systems. Urban Drainage Systems Analysis: Optimization and SensitivityAnalysis. Appendices. Glossary. Notation. Index.

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Book SynopsisBased around a conference on financial modeling held in Milan in December 1999, this book brings together the leading names in quantitative finance to discuss the modeling techniques in a variety of areas of financial engineering.Table of ContentsPreface The Quantitative Finance Timeline (Paul Wilmott) Part I. New Directions in Equity Modelling Introduction Asymptotic analysis of stochastic volatility models (Henrik Rasmussen and Paul Wilmott) Passport options, a review (Antony Penaud) Equity Dividend Models (David Bakstein and Paul Wilmott) Isoperimetry, log-concavity and elasticity of option prices (Christer Borell) Part II. New Directions in Interest Rate Modelling Introduction Dynamic, deterministic and static optimal portfolio strategies in a mean-variance framework under stochastic interest rates (Isabelle Bajeux-Besnainou and Roland Portrait) Pricing bond options in a worst-case scenario (David Epstein and Paul Wilmott) Part III. New Directions in Risk Management Introduction Implementing VaR by Historical Simulation (Aldo Nassigh, Andrea Piazzetta and Ferdinando Samaria) CrashMetrics (Philip Hua and Paul Wilmott) Herding in financial markets: a role for psychology in explaining investor behaviour? (Henriëtte Prast) Further Reading Author Biographies Index

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Book SynopsisA state-of-the-art approach to urban travel demand modeling Currently used travel forecasting methodology was developed almostthree decades ago, primarily to assess the impacts of large-scalecapital improvement projects, and was not designed to deal withcontemporary urban transportation problems. To be effective today,travel demand models must explicitly represent traveler behavior,must be policy-sensitive, and must be operationally reliable. Urban Travel Demand Modeling: From Individual Choices to GeneralEquilibrium presents an integrated system of models which overhaulthe four traditional phases of travel generation, modal split, tripdistribution, and network assignment. This book shows, for thefirst time, how generalized network equilibrium may be rigorouslyforecast from the optimal travel choices of trip consumerswithout the need to resort to heuristic procedures such asfeedbacks. In addition, models for optimal transportation supplydecisions are integrated with tTable of ContentsModeling Travelers' Decisions as Discrete Choices. Route Choice on Uncongested Networks. Combined Travel Demand Modeling Under Uncongested Conditions. Route Choice Modeling Under Congested Conditions. Combined Travel Demand Modeling Under Congested Conditions. Model Parameter Estimation. Joint Equilibrium Modeling of Activity and Travel Systems. Optimal Transportation Supply. Appendices. Bibliography. Indexes.

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Book SynopsisBioremediation and Natural Attenuation: Process Fundamentals and Mathematical Models provides, under one cover, the current methodology needed by groundwater scientists and engineers in their efforts to evaluate contamination problems, to estimate risk to human health and ecosystems, and to design and formulate remediation strategies.Trade Review"…does a very good job of bringing together material form disparate sources…readers new to the field will be well served by it." (Ground Water, March-April 2007) "The topic is important; both theory and state-of-the-art are well discussed…this is an excellent book." (Journal of Hazardous Materials, September 1, 2006) “… a reference book for practitioners, regulators, and researchers dealing with contaminant hydrogeology and correction action.” (Environmental Geology, December 2006)Table of ContentsPreface. 1. Introduction to Bioremediation. 2. Geochemical Attenuation Mechanisms. 3. Biodegradation Principles. 4. Fundamentals of Ground Water Flow and Contaminant Transport Processes. 5. Fate and Transport Equations and Analytical Models for Natural Attenuation. 6. Numerical Modeling of Contaminant Transport, Transformation, and Degradation Processes. 7. Field and Laboratory Techniques to Determine Site-Specific Parameters for Modeling the Fate and Transport of Groundwater Pollutants. 8. Bioremediation Technologies. 9. Performance Assessment and Demonstration of Bioremediation and Natural Attenuation. Appendix A: Chemical Properties of Various Compounds. Appendix B: Free Energy and Thermodynamic Feasibility of Chemical and Biochemical Reactions. Appendix C: Commonly Used Numerical Groundwater Flow and Solute Transport Codes (Modified after Wiedemeier et al., 1999). Appendix D: Nonparametric Statistical Tests for Determining the Effectiveness of Natural Attenuation (after Wisconsin Department of Natural Resources). Appendix E: Critical Values of the Student t-Distribution. Glossary. Index.

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Book SynopsisGraphical models----a subset of log--linear models----reveal the interrelationships between multiple variables and features of the underlying conditional independence.Table of ContentsIndependence and Interaction. Independence Graphs. Information Divergence. The Inverse Variance. Graphical Gaussian Models. Graphical Log-Linear Models. Model Selection. Methods for Sparse Tables. Regression and Graphical Chain Models. Models for Mixed Variables. Decompositions and Decomposability. Appendices. References. Author Index. Subject Index.

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Book SynopsisThe first book to provide a comprehensive treatment integrating finite-time thermodynamics and optimal control, giving an overview of important breakthroughs in the last 20 years. It presents a survey of the optimization technique, including the basics of optimal control theory, and the principal thermodynamic concepts and equations.Table of ContentsMathematical Modeling of Thermodynamic Systems. Optimization Methods. Optimal Control Methods. Limiting Possibilities of Heat-Mechanical Systems with One Reservoir. Heat-Exchange Processes with Minimal Dissipation. Optimization and Estimates of the Limiting Possibilities of Heat-Mechanical Systems with a Number of Reservoirs. Limiting Possibilities of Complex Systems with a Number of Heat-Mechanical Systems. Mass Transfer Processes with Minimal Irreversibility. Thermodynamic Analysis of Separation Processes and Chemical Reactions. Commodity Exchange in Economic Systems. Bibliography. Index.

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Book SynopsisThis text focuses on the issue of non-linear modelling of high frequency financial data. Non-linearity refers to situations in which there is a high degree of apparent randomness to the way in which a particular financial measure, price, interest rate, or exchange rate moves with time.Table of ContentsHIGH FREQUENCY MODELS IN FINANCE: MOTIVATIONS AND THEORETICAL ISSUES. Modelling with High Frequency Data: A Growing Interest for Financial Economists and Fund Managers (M. Gavridis). High Frequency Foreign Exchange Rates: Price Behavior Analysis and 'True Price' Models (J. Moody & L. Wu). DETECTING NONLINEARITIES IN HIGH FREQUENCY DATA: EMPIRICAL TESTS AND MODELLING IMPLICATIONS. Testing Linearity with Information-Theoretic Statistics and the Bootstrap (F. Acosta). Testing for Linearity: A Frequency Domain Approach (J. Drunat, et al.). Stochastic or Chaotic Dynamics in High Frequency Financial Data (D. Guégan & L. Mercier). F-consistency, De-volatization and Normalization of High Frequency Financial Data (B. Zhou). PARAMETRIC MODELS FOR NONLINEAR FINANCIAL TIME SERIES. High Frequency Financial Time Series Data: Some Stylized Facts and Models of Stochastic Volatility (E. Ghysels, et al.). Modelling Short-term Volatility with GARCH and HARCH Models (M. Dacorogna, et al.). High Frequency Switching Regimes: A Continuous-time Threshold Process (R. Dacco' & S. Satchell). Modelling Burst Phenomena: Bilinear and Autoregressive Exponential Models (J. Drunat, et al.). NON-PARAMETRIC MODELS FOR NONLINEAR FINANCIAL TIME SERIES. Application of Neural Networks to Forecast High Frequency Data: Foreign Exchange (P. Bolland, et al.). An Application of Genetic Algorithms to High Frequency Trading Models: A Case Study (C. Dunis, et al.). High Frequency Exchange Rate Forecasting by the Nearest Neighbours Method (H. Alexandre, et al.). Index.

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Book SynopsisThis general introduction to the ideas and techniques required for the mathematical modelling of diseases begins with an outline of some disease statistics dating from Daniel Bernoulli's 1760 smallpox data. The authors then describe simple deterministic and stochastic models in continuous and discrete time for epidemics taking place in either homogeneous or stratified (non-homogeneous) populations. Several techniques for constructing and analysing models are provided, mostly in the context of viral and bacterial diseases of human populations. These models are contrasted with models for rumours and vector-borne diseases like malaria. Questions of fitting data to models, and their use in understanding methods for controlling the spread of infection, are discussed. Exercises and complementary results at the end of each chapter extend the scope of the text, which will be useful for students taking courses in mathematical biology who have some basic knowledge of probability and statistics.Trade Review'… It gives an excellent general introduction to epidemic modelling, starting with an interesting historical account and then describing the most important and useful models which can be used.' Robert MacMillan, Mathematical Gazette'The book will be accessible … and its study highly rewarding, to anyone with an interest in epidemic models…' V. S. Isham, Short Book Reviews'Daley and Gani's monograph is a concise and useful presentation of a variety of epidemiological models.' Daniel Haydon, Trends in Ecology and Evolution'… gives an excellent general introduction to epidemic modelling … should certainly be available to undergraduates.' Robert MacMillan, The Mathematical Gazette'This book had us hooked … [it] remains an important reference in our library and is frequently consulted for advice on how to think about modelling in related contexts.' Darfiana Nur and Kerrie L. Mengersen, The Australian and New Zealand Journal of Statistics'… the book is clear and well written … could serve as course literature for graduate, or possibly last year undergraduate, course in epidemic modelling.' Statistics in Medicine'I found the book very clear, concise and useful … I recommend the book very strongly as a teaching tool and as a research tool to academics and scientists who are interested in epidemic modeling. I also strongly recommend the book to applied mathematicians who are intetrested in stochastic models in general.' Mathematics TodayTable of ContentsPreface; 1. Some history; 2. Deterministic models; 3. Stochastic models in continuous time; 4. Stochastic models in discrete time; 5. Rumours: modelling spread and its cessation; 6. Fitting epidemic data; 7. The control of epidemics; References and author index; Subject index.

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Book SynopsisUnderstanding wind stress (drag) over the ocean is central to many facets of air-sea interaction, which in turn is vital for models of weather prediction and climate modelling. Wind Stress over the Ocean, first published in 2001, brings together thirty of the world's leading experts in air-sea interaction, under the auspices of the Scientific Committee on Oceanic Research. Wind Stress over the Ocean provides a thorough re-examination of the physical processes that transfer momentum between the atmosphere and the ocean. As well as describing the established fundamentals, the book also explores active areas of research and controversy. The book will form a comprehensive guide and reference for researchers and graduate students in physical oceanography, meteorology, fluid dynamics and coastal engineering.Trade ReviewReview of the hardback: '… helpful and handy for people who want timely, authoritative information about the different processes that affect the wind stress over the sea.' EOSReview of the hardback: '… a very useful book … It will be much referenced.' Grant Bigg, WeatherReview of the hardback: ' … this publication is an essential reference text owing to the rapidly changing nature of scientific progress. It will be a general guide and reference document for researchers and graduates in physical oceanography, meteorology, fluid dynamics and coastal engineering. Many who read this book will be inspired to carry out research in those areas which still have many specific problems to be solved.' BulletinTable of ContentsPreface; 1. Overview; Part I: 2. Historical drag expression; 3. Atmospheric and oceanic boundary layer physics; 4. Ocean wave spectra and integral properties; 5. Drag generation mechanisms; 6. Coupling mechanisms; 7. The measurement of surface stress; Part II: 8. The influence of swell on the drag; 9. The influence of unsteadiness; 10. The dependence on wave age; 11. The influence on mesoscale atmospheric processes; 12. Wind, stress and wave directions; 13. The influence of surface tension; 14. The influence of spatial inhomogeneity; 15. Basin boundaries; References; Index.

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Book SynopsisThis book is an introduction to the study of mathematical models of electrically active cells, which play an essential role in, for example, nerve conduction and cardiac functions. This is an important and vigorously researched field. In the book, Dr Cronin synthesizes and reviews this material and provides a detailed discussion of the Hodgkin-Huxley model for nerve conduction, which forms the cornerstone of this body of work. Her treatment includes a derivation of the Hodgkin-Huxley model, which is a system of four nonlinear differential equations; a discussion of the validity of this model; and a summary of some of the mathematical analysis carried out on this model. Special emphasis is placed on singular perturbation theory, and arguments, both mathematical and physiological, for using the perturbation viewpoint are presented.Table of Contents1. Introduction; 2. Nerve conduction: the work of Hodgkin and Huxley; 3. Nerve conduction: other mathematical models; 4. Models of other electrically excitable cells; 5. Mathematical theory; 6. Mathematical analysis of physiological models; Appendix; References.

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Book SynopsisThe book gives a comprehensive and lucid account of the science of the atmospheric boundary layer (ABL). There is an emphasis on the application of the ABL to numerical modelling of the climate. The book comprises nine chapters, several appendices (data tables, information sources, physical constants) and an extensive reference list. Chapter 1 serves as an introduction, with chapters 2 and 3 dealing with the development of mean and turbulence equations, and the many scaling laws and theories that are the cornerstone of any serious ABL treatment. Modelling of the ABL is crucially dependent for its realism on the surface boundary conditions, and chapters 4 and 5 deal with aerodynamic and energy considerations, with attention to both dry and wet land surfaces and sea. The structure of the clear-sky, thermally stratified ABL is treated in chapter 6, including the convective and stable cases over homogeneous land, the marine ABL and the internal boundary layer at the coastline. Chapter 7 thTrade Review'An excellent review of the current state of affairs on boundary-layer meteorology research.' Bulletin of the American Meteorological Society.'I find that it compares favourably to good texts that have appeared recently; I strongly recommend it as a synthesis of present thinking on physical processes in the atmospheric boundary layer.' Waves in Random Media.Table of Contents1. The atmospheric boundary layer; 2. Basic equations for mean and fluctuating quantites; 3. Scaling laws for mean and turbulent quantites; 4. Surface roughness and local advection; 5. Energy fluxes at the land surface; 6. The thermally stratified ABL; 7. The cloud topped boundary layer; 8. ABL modelling and parameterisation schemes; 9. The impact of the ABL on climate.

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Book SynopsisFor many applications a randomized algorithm is either the simplest algorithm available, or the fastest, or both. This tutorial presents the basic concepts in the design and analysis of randomized algorithms. The first part of the book presents tools from probability theory and probabilistic analysis that are recurrent in algorithmic applications. Algorithmic examples are given to illustrate the use of each tool in a concrete setting. In the second part of the book, each of the seven chapters focuses on one important area of application of randomized algorithms: data structures; geometric algorithms; graph algorithms; number theory; enumeration; parallel algorithms; and on-line algorithms. A comprehensive and representative selection of the algorithms in these areas is also given. This book should prove invaluable as a reference for researchers and professional programmers, as well as for students.Trade Review'The techniques described by Rajeev Motwani and Prabhaker Raghavan are wide-ranging and powerful, so this book is an important one. As far as I have been able to find out this is the only book on the entire subject … this excellent volume does us proud!' American Scientist'This book can serve as an excellent basis for a graduate course. It is highly recommended for students and researchers who wish to deepen their knowledge of the subject. Finally, I believe that the book, with its vast coverage, will be an invaluable source for active researchers in the field.' Y. Aumann, Computing ReviewsTable of ContentsPart I. Tools and Techniques: 1. Introduction; 2. Game-theoretic techniques; 3. Moments and deviations; 4. Tail inequalities; 5. The probabilistic method; 6. Markov chains and random walks; 7. Algebraic techniques; Part II. Applications: 8. Data structures; 9. Geometric algorithms and linear programming; 10. Graph algorithms; 11. Approximate counting; 12. Parallel and distributed algorithms; 13. Online algorithms; 14. Number theory and algebra; Appendix A: notational index; Appendix B: mathematical background; Appendix C: basic probability theory.

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Book SynopsisThis introductory textbook on mathematical biology focuses on discrete models across a variety of biological subdisciplines. Biological topics treated include linear and non-linear models of populations, Markov models of molecular evolution, phylogenetic tree construction, genetics, and infectious disease models. The coverage of models of molecular evolution and phylogenetic tree construction from DNA sequence data is unique among books at this level. Computer investigations with MATLAB are incorporated throughout, in both exercises and more extensive projects, to give readers hands-on experience with the mathematical models developed. MATLAB programs accompany the text. Mathematical tools, such as matrix algebra, eigenvector analysis, and basic probability, are motivated by biological models and given self-contained developments, so that mathematical prerequisites are minimal.Trade Review'… many institutions, like mine, are looking into ways of adding a mathematical modeling component into the undergraduate curriculum for general biology students. This book will be a great asset to these institutions … a very interesting and challenging book for undergraduate students with a strong interest in biology …'. Mei Zhu, Pacific Lutheran University'I found this book interesting since many institutions, like mine, are looking into ways of adding a mathematical modeling component into the undergraduate curriculum for general biology students. This book will be a great asset to these institutions … Overall, this is a very interesting and challenging book for undergraduate students with a strong interest in biology, but not necessarily with a calculus background. Students with a strong mathematical background will also benefit from this book … This book is also a good reference book for biologists who are interested in learning mathematical modeling or integrating it into teaching their undergraduate biology courses.' Mei Zhu, Pacific Lutheran University'… eminently suitable for their target undergraduate audiences and, indeed, for anyone curious to learn more about this increasingly important and undeniably exciting area of applied mathematics.' The Mathematical Gazette'… an attractive introduction to the modeling of biological processes at a very elementary level.' Zentralblatt MATH'This is an attractive introduction into the modelling of biological processes at a very elementary level. … Many exercises motivate the reader to acquire a deeper understanding of the topics treated. Also a substantial number of MATLAB projects are suggested to give the students hands-on experience.' Monatshefte für MathematikTable of Contents1. Dynamic modeling with different equations; 2. Linear models of structured populations; 3. Non-linear models of interactions; 4. Modeling molecular evolution; 5. Constructing phylogenic trees; 6. Genetics; 7. Infectious disease modeling; 8. Curve fitting and biological modeling; Appendix A. Basic analysis of numerical data; Appendix B. For further reading.

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Book SynopsisThis is an up-to-date textbook of model theory taking the reader from first definitions to Morley's theorem and the elementary parts of stability theory.Trade Review'… up-to-date … can serve as an introduction to applications of model theory in computer science.' L'Enseignement Mathématique' … a very readable introduction to the subject.' Mathematika'This book contains rich material for a good introductory course in model theory …' European Mathematical Society'I have talked with students who first learned about model theory from this text, and overall it served them well. From his impressive work of 1993, Hodges has distilled an accessible introductory account. In doing so he has provided a valuable resource for a first study of model theory.' Carol Wood, International Journal of Symbolic LogicTable of Contents1. Naming of parts; 2. Classifying structures; 3. Structures that look alike; 4. Interpretations; 5. The first order case: compactness; 6. The countable case; 7. The existential case; 8. Saturation; 9. Structure and categoricity.

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Book SynopsisIn this book, first published in 2006, the authors' main aims are first to present classical results in a way that's accessible to non-specialists. Second, to describe results of Smirnov in conformal invariance. It is essential reading for all working in this exciting area.Trade Review'This book contains a complete account of most of the important results in the fascinating area of percolation. Elegant and straightforward proofs are given with minimal background in probability or graph theory. It is self-contained, accessible to a wide readership and widely illustrated with numerous examples. It will be of considerable interest for both beginners and advanced searchers alike.' Zentralblatt MATHTable of ContentsPreface; 1. Basic concepts; 2. Probabilistic tools; 3. Percolation on Z2 - the Harris-Kesten theorem; 4. Exponential decay and critical probabilities - theorems of Menshikov and Aizenman & Barsky; 5. Uniqueness of the infinite open cluster and critical probabilities; 6. Estimating critical probabilities; 7. Conformal invariance - Smirnov's theorem; 8. Continuum percolation; Bibliography; Index; List of notation.

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Book SynopsisWritten to suit a wide audience (including physical sciences), these two volumes will become the reference of choice on the Hilbert transform, whatever the subject background of the reader. The author explains all the common Hilbert transforms, mathematical techniques for evaluating them, and has detailed discussions of their application.Trade Review"The author gives detailed and exhaustive information on almost all properties of the Hilbert transform... the selected topics are presented in an easy-to-use style." Lasha Ephremidze, Mathematical ReviewsTable of ContentsPreface; List of symbols; List of abbreviations; Volume I: 1. Introduction; 2. Review of some background mathematics; 3. Derivation of the Hilbert transform relations; 4. Some basic properties of the Hilbert transform; 5. Relationship between the Hilbert transform and some common transforms; 6. The Hilbert transform of periodic functions; 7. Inequalities for the Hilbert transform; 8. Asymptotic behavior of the Hilbert transform; 9. Hilbert transforms of some special functions; 10. Hilbert transforms involving distributions; 11. The finite Hilbert transform; 12. Some singular integral equations; 13. Discrete Hilbert transforms; 14. Numerical evaluation of Hilbert transforms; References; Subject index; Author index.

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Book SynopsisThis text gives a self-contained and detailed treatment of presently known results, and new theorems on hyperbolicity, shadowing, complicated motion, and robustness. The book is intended to provide a dependable reference for researchers wishing to apply such results. This book will be of particular interest to researchers and students interested in dynamical systems, particularly in noninvertible maps and infinite dimensional semi-flows or maps and global analysis.Table of ContentsIntroductionHyperbolic operators, projections , diagonalizationSequence spaces and substitution operatorsHyperbolic setsShadowing and persistence of hyperbolic setsTransversal homoclinic orbitsAppendixNotationReferences

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Book SynopsisQuantitative Methods for Finance and Investments ensures that readers come away from reading it with a reasonable degree of comfort and proficiency in applying elementary mathematics to several types of financial analysis.Trade Review"This excellent text patiently guides the reader through a wide array of mathematics, ranging from elementary matrix algebra to differential and integral calculus. The quantitative methods are illustrated with a rich and captivating assortment of applications to the analysis of portfolios, derivatives, exchange, fixed income instruments, and equities. Undergraduate and MBA-level students who have read this book will feel comfortable with the mathematics in their finance courses and their professors can focus on teaching finance as it should be taught." Kose John, Stern School of Business, New York University <1--end--> "This volume provides a comprehensive review of mathematics which will prove invaluable for students of finance. It is a reference book for the nonmathematician and a clear and concise text that will help fill the gaps in students' knowledge. Although the topic is quantitative methods, the organization, emphasis, applications, and numerous examples are all geared to the student of finance. Having Teall and Hasan on your bookshelf provides an essential safety net for students, teachers, and practitioners." Paul Wachtel, Stern School of Business, New York UniversityTable of ContentsPreface. Acknowledgments. 1. Introduction and Overview:. The Importance of Mathematics in Finance. Mathematical and Computer Modeling in Finance. Money, Securities, and Markets. Time Value, Risk, Arbitrage, and Pricing. The Organization of this Book. 2. Review of Elementary Mathematics: Functions and Operations:. Introduction. Variables, Equations, and Inequalities. Exponents. The Order of Arithmetic Operations and the Rules of Algebra. The Number e. Logarithms. Subscripts. Summations. Double Summations. Products. Factorial Products. Permutations and Combinations. Exercises. Appendix: An Introduction to the ExcelT Spreadsheet. 3. A Review of Elementary Mathematics: Algebra and Solving Equations:. Algebraic Manipulations. The Quadratic Formula. Solving Systems of Equations that Contain Multiple Variables. Geometric Expansions. Functions and Graphs. Exercises. Appendix: Solving Systems of Equations on a Spreadsheet. 4. The Time Value of Money:. Introduction and Future Value. Simple Interest. Compound Interest. Fractional Period Compounding of Interest. Continuous Compounding of Interest. Annuity Future Values. Discounting and Present Value. Present Value of a Series of Cash Flows. Annuity Present Values. Amortization. Perpetuity Models. Single-stage Growth Models. Multiple-stage Growth Models. Exercises. Appendix: Time Value Spreadsheet Applications. 5. Return, Risk, and Co-movement:. Return on Investment. Geometric Mean Return on Investment. Internal Rate of Return. Bond Yields. An Introduction to Risk. Expected Return. Variance and Standard Deviation. Historical Variance and Standard Deviation. Covariance. The Coefficient of Correlation and the Coefficient of Determination. Exercises. Appendix: Return and Risk Spreadsheet Applications. 6. Elementary Portfolio Mathematics:. An Introduction to Portfolio Analysis. Portfolio Return. Portfolio Variance. Diversification and Efficiency. The Market Portfolio and Beta. Deriving the Portfolio Variance Expression. Exercises. 7. Elements of Matrix Mathematics:. An Introduction to Matrices. Matrix Arithmetic. Inverting Matrices. Solving Systems of Equations. Spanning the State Space. Exercises. Appendix: Matrix mathematics on a Spreadsheet. 8. Differential Calculus:. Functions and Limits. Slopes, Derivatives, Maxima, and Minima. Derivatives of Polynomials. Partial and Total Derivatives. The Chain Rule, Product Rule, and Quotient Rule. Logarithmic and Exponential Functions. Taylor Series Expansions. The Method of LaGrange Multipliers. Exercises. Appendix: Derivatives of Polynomials. Appendix: A Table of Rules for Finding Derivatives. Appendix: Portfolio Risk Minimization on a Spreadsheet. 9. Integral Calculus:. Antidifferentiation and the Indefinite Integral. Riemann Sums. Definite Integrals and Areas. Differential Equations. Exercises. Appendix: Rules for Finding Integrals. Appendix: Riemann sums on a spreadsheet. 10. Elements of Options Mathematics:. An Introduction to Stock Options. Binomial Option Pricing: One Time Period. Binomial Option Pricing: Multiple Time Periods. The Black–Scholes Option Pricing Model. Puts and Valuation. Black–Scholes Model Sensitivities. Estimating Implied Volatilities. Exercises. References. Appendix A: Solutions to Exercises. Appendix B: The z-Table. Appendix C: Notation. Appendix D: Glossary. Index.

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Book SynopsisQuantitative Methods for Finance and Investments ensures that readers come away from reading it with a reasonable degree of comfort and proficiency in applying elementary mathematics to several types of financial analysis.Trade Review"This excellent text patiently guides the reader through a wide array of mathematics, ranging from elementary matrix algebra to differential and integral calculus. The quantitative methods are illustrated with a rich and captivating assortment of applications to the analysis of portfolios, derivatives, exchange, fixed income instruments, and equities. Undergraduate and MBA-level students who have read this book will feel comfortable with the mathematics in their finance courses and their professors can focus on teaching finance as it should be taught." Kose John, Stern School of Business, New York University <1--end--> "This volume provides a comprehensive review of mathematics which will prove invaluable for students of finance. It is a reference book for the nonmathematician and a clear and concise text that will help fill the gaps in students' knowledge. Although the topic is quantitative methods, the organization, emphasis, applications, and numerous examples are all geared to the student of finance. Having Teall and Hasan on your bookshelf provides an essential safety net for students, teachers, and practitioners." Paul Wachtel, Stern School of Business, New York UniversityTable of ContentsPreface Acknowledgments 1 Introduction and Overview 1 1.1 The importance of mathematics in finance 1 1.2 Mathematical and computer modeling in finance 2 1.3 Money, securities, and markets 3 1.4 Time value, risk, arbitrage, and pricing 5 1.5 The organization of this book 6 2 A Review of Elementary Mathematics: Functions and Operations 7 2.1 Introduction 7 2.2 Variables, equations, and inequalities 7 2.3 Exponents 8 Application 2.1: Interest and future value 9 2.4 The order of arithmetic operations and the rules of algebra 10 Application 2.2: Initial deposit amounts 11 2.5 The number e 11 2.6 Logarithms 12 Application 2.3: The time needed to double your money 13 2.7 Subscripts 14 2.8 Summations 14 Application 2.4: Mean values 15 2.9 Double summations 16 2.10 Products 17 Application 2.5: Geometric means 17 Application 2.6: The term structure of interest rates 18 2.11 Factorial products 19 Application 2.7: Deriving the number e 19 2.12 Permutations and combinations 20 Exercises 21 Appendix 2.A An introduction to the Excel™ spreadsheet 23 3 A Review of Elementary Mathematics: Algebra and Solving Equations 25 3.1 Algebraic manipulations 25 Application 3.1: Purchase power parity 27 Application 3.2: Finding break-even production levels 28 Application 3.3: Solving for spot and forward interest rates 29 3.2 The quadratic formula 29 Application 3.4: Finding break-even production levels 30 Application 3.5: Finding the perfectly hedged portfolio 31 3.3 Solving systems of equations that contain multiple variables 32 Application 3.6: Pricing factors 35 Application 3.7: External financing needs 35 3.4 Geometric expansions 38 Application 3.8: Money multipliers 40 3.5 Functions and graphs 41 Application 3.9: Utility of wealth 43 Exercises 44 Appendix 3.A Solving systems of equations on a spreadsheet 48 4 The Time Value of Money 51 4.1 Introduction and future value 51 4.2 Simple interest 51 4.3 Compound interest 52 4.4 Fractional period compounding of interest 53 Application 4.1: APY and bank account comparisons 55 4.5 Continuous compounding of interest 56 4.6 Annuity future values 57 Application 4.2: Planning for retirement 59 4.7 Discounting and present value 60 4.8 The present value of a series of cash flows 61 4.9 Annuity present values 62 Application 4.3: Planning for Retirement, Part Ii 64 Application 4.4: Valuing a bond 64 4.10 Amortization 65 Application 4.5: Determining the mortgage payment 66 4.11 Perpetuity models 67 4.12 Single-stage growth models 68 Application 4.6: Stock valuation models 70 4.13 Multiple-stage growth models 72 Exercises 73 Appendix 4.A Time value spreadsheet applications 77 5 Return, Risk, and Co-movement 79 5.1 Return on investment 79 Application 5.1: Fund performance 81 5.2 Geometric mean return on investment 82 Application 5.2: Fund Performance, Part Ii 83 5.3 Internal rate of return 84 5.4 Bond yields 87 5.5 An introduction to risk 88 5.6 Expected return 88 5.7 Variance and standard deviation 89 5.8 Historical variance and standard deviation 91 5.9 Covariance 93 5.10 The coefficient of correlation and the coefficient of determination 94 Exercises 95 Appendix 5.A Return and risk spreadsheet applications 99 6 Elementary Portfolio Mathematics 103 6.1 An introduction to portfolio analysis 103 6.2 Portfolio return 103 6.3 Portfolio variance 104 6.4 Diversification and efficiency 106 6.5 The market portfolio and beta 110 6.6 Deriving the portfolio variance expression 111 Exercises 113 7 Elements of Matrix Mathematics 115 7.1 An introduction to matrices 115 Application 7.1: Portfolio mathematics 116 7.2 Matrix arithmetic 117 Application 7.2: Portfolio Mathematics, Part Ii 120 Application 7.3: Put–call parity 121 7.3 Inverting matrices 123 7.4 Solving systems of equations 125 Application 7.4: External funding requirements 126 Application 7.5: Coupon bonds and deriving yield curves 127 Application 7.6: Arbitrage with riskless bonds 130 Application 7.7: Fixed income portfolio dedication 131 Application 7.8: Binomial option pricing 132 7.5 Spanning the state space 133 Application 7.9: Using options to span the state space 136 Exercises 137 Appendix 7.A Matrix mathematics on a spreadsheet 142 8 Differential Calculus 145 8.1 Functions and limits 145 Application 8.1: The natural log 146 8.2 Slopes, derivatives, maxima, and minima 147 8.3 Derivatives of polynomials 149 Application 8.2: Marginal utility 151 Application 8.3: Duration and immunization 153 Application 8.4: Portfolio risk and diversification 156 8.4 Partial and total derivatives 157 8.5 The chain rule, product rule, and quotient rule 158 Application 8.5: Plotting the Capital Market Line 159 8.6 Logarithmic and exponential functions 165 8.7 Taylor series expansions 166 Application 8.6: Convexity and immunization 167 Exercises 172 Appendix 8.A Derivatives of polynomials 176 Appendix 8.B A table of rules for finding derivatives 177 Appendix 8.C Portfolio risk minimization on a spreadsheet 178 9 Integral Calculus 180 9.1 Antidifferentiation and the indefinite integral 180 9.2 Riemann sums 181 9.3 Definite integrals and areas 185 Application 9.1: Cumulative densities 186 Application 9.2: Expected value and variance 188 Application 9.3: Valuing continuous dividend payments 189 Application 9.4: Expected option values 191 9.4 Differential equations 191 Application 9.5: Security returns in continuous time 193 Application 9.6: Annuities and growing annuities 194 Exercises 195 Appendix 9.A Rules for finding integrals 198 Appendix 9.B Riemann sums on a spreadsheet 199 10 Elements of Options Mathematics 203 10.1 An introduction to stock options 203 10.2 Binomial option pricing: one time period 205 10.3 Binomial option pricing: multiple time periods 207 10.4 The Black–Scholes option pricing model 210 10.5 Puts and valuation 212 10.6 Black–Scholes model sensitivities 213 10.7 Estimating implied volatilities 215 Exercises 219 References 222 Appendix A Solutions to Exercises 224 Appendix B The z-Table 266 Appendix C Notation 267 Appendix D Glossary 270 Index 274

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Book Synopsisaeo provides all the specialist knowledge, understanding and confidence needed to use models aeo focuses on life--cycle modelling, from the commissioning of a building through to demolition aeo offers practitioners an insight through detailed case studies to use of models.Table of ContentsPreface. Chapter 1 Heat Transfer in Building Elements. 1.1 Heat and mass transfer processes in buildings. 1.2 Heat transfer through external walls and roofs. 1.3 Analytical methods for solving the one-dimensional transient heat conduction equation. 1.4 Lumped capacitance methods. 1.5 Heat transfer through glazing. Chapter 2 Modelling Heat Transfer in Building Envelopes. 2.1 Finite Difference Method – A Numerical Method for Solving the Heat Conduction Equation. 2.2 Heat Transfer in Building Spaces. 2.3 Synthesis of Heat Transfer Methods. 2.4 Latent Loads and Room Moisture Content Balance. Chapter 3 Mass Transfer, Air Movement and Ventilation. Chapter 4 Steady-State Plant Modelling. 4.1 Model Formulations for Plant. 4.2 Mathematical Models of Air-conditioning Equipment using Equation-fitting. 4.3 A Detailed Steady-state Cooling and Dehumidifying Coil Model. 4.4 Modelling Distribution Networks. 4.5 Modelling Air-conditioning Systems. Chapter 5 Modelling Control Systems. 5.1 Distributed System Modelling. 5.2 Modelling Control Elements. 5.3 Modelling Control Algorithms. 5.4 Solution Schemes. Chapter 6 Modeling in Practice I. 6.1 Developments in General. 6.2 Internal Ventilation Problems6.3 Wind Flow Around Buildings. 6.4 Applications to Plant. 6.5 Applications to Control and Fault Detection. Chapter 7 Modeling in Practice II. 7.1 Interrelationships Between Methodologies. 7.2 Tools and Their Integration. 7.3 Validation and Verification. References. Appendix A. Appendix B. Index

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Book SynopsisServes as a how-to guide for developing mathematical models in biology. Starting at an elementary level of mathematical modeling, this title gradually builds from classic models in ecology and evolution to more intricate class-structured and probabilistic models. It provides primers with instructive exercises.Trade ReviewHonorable Mention for the 2007 Best Professional/Scholarly Book in Biological Sciences, Association of American Publishers "A gentle but thorough introduction to the mathematical techniques employed in ecological and evolutionary theory. Readers who ... finish this well-written book will be prepared to read and understand a sizeable fraction of the current literature."--Donald L. DeAngelis, Quarterly Review of Biology "At long last, Sally Otto and Troy Day have provided relief for biologists and epidemiologists in search of an easily read, practical, and thorough starting point from which to learn mathematical modeling... We would recommend this book over shorter texts that are labeled as 'introductory'... The depth and detail that Otto and Day have included in this text arc appealing rather than intimidating, and the structure of the text is empowering rather than didactic or formulaic."--Sanjay Basu and Alison P. Galvani, Siam Review "[T]he great value of the Otto/Day book is that it attempts pedagogical soundness, and so is useful for teaching. Besides being perfectly readable, it engages and impresses the reader quickly not only with the subject matter, but also with the quality of printing and layout which have to be seen to be believed. These praises may sound lavish by many a reader of these columns but first see the book or better still buy the volume and you will see our passion and rage for going all out in praise of this volume."--Current Engineering Practice "I highly recommend this book for every university biology department because it provides both a unique, and often uplifting, introduction and a comprehensive reference of techniques for building and analysing mathematical models."--Volker Grimm, Basic and Applied Ecology "I cannot help but think that future textbook authors will want to have Otto and Day front and center on the work desk, for this is a valuable source of material... This book stands out, and its contribution is quite apparent. In sum, this book is a valuable contribution to the literature, and one to which I expect to refer regularly in connection with my teaching and writing duties."--Steven G. Krantz, UMAP Journal "[A] great textbook... [M]asterful use of figures and illustrations and exercises ... provide the reader with valuable practice in constructing models and implementing related mathematical techniques. I certainly recommend this text and can attest to its usefulness for budding researchers in the biological sciences."--Jason M. Graham, MAA ReviewsTable of ContentsPreface ix Chapter 1: Mathematical Modeling in Biology 1 1.1 Introduction 1 1.2 HIV 2 1.3 Models of HIV/AIDS 5 1.4 Concluding Message 14 Chapter 2: How to Construct a Model 17 2.1 Introduction 17 2.2 Formulate the Question 19 2.3 Determine the Basic Ingredients 19 2.4 Qualitatively Describe the Biological System 26 2.5 Quantitatively Describe the Biological System 33 2.6 Analyze the Equations 39 2.7 Checks and Balances 47 2.8 Relate the Results Back to the Question 50 2.9 Concluding Message 51 Chapter 3: Deriving Classic Models in Ecology and Evolutionary Biology 54 3.1 Introduction 54 3.2 Exponential and Logistic Models of Population Growth 54 3.3 Haploid and Diploid Models of Natural Selection 62 3.4 Models of Interactions among Species 72 3.5 Epidemiological Models of Disease Spread 77 3.6 Working Backward--Interpreting Equations in Terms of the Biology 79 3.7 Concluding Message 82 Primer 1: Functions and Approximations 89 P1.1 Functions and Their Forms 89 P1.2 Linear Approximations 96 P1.3 The Taylor Series 100 Chapter 4: Numerical and Graphical Techniques--Developing a Feeling for Your Model 110 4.1 Introduction 110 4.2 Plots of Variables Over Time 111 4.3 Plots of Variables as a Function of the Variables Themselves 124 4.4 Multiple Variables and Phase-Plane Diagrams 133 4.5 Concluding Message 145 Chapter 5: Equilibria and Stability Analyses--One-Variable Models 151 5.1 Introduction 151 5.2 Finding an Equilibrium 152 5.3 Determining Stability 163 5.4 Approximations 176 5.5 Concluding Message 184 Chapter 6: General Solutions and Transformations--One-Variable Models 191 6.1 Introduction 191 6.2 Transformations 192 6.3 Linear Models in Discrete Time 193 6.4 Nonlinear Models in Discrete Time 195 6.5 Linear Models in Continuous Time 198 6.6 Nonlinear Models in Continuous Time 202 6.7 Concluding Message 207 Primer 2: Linear Algebra 214 P2.1 An Introduction to Vectors and Matrices 214 P2.2 Vector and Matrix Addition 219 P2.3 Multiplication by a Scalar 222 P2.4 Multiplication of Vectors and Matrices 224 P2.5 The Trace and Determinant of a Square Matrix 228 P2.6 The Inverse 233 P2.7 Solving Systems of Equations 235 P2.8 The Eigenvalues of a Matrix 237 P2.9 The Eigenvectors of a Matrix 243 Chapter 7: Equilibria and Stability Analyses--Linear Models with Multiple Variables 254 7.1 Introduction 254 7.2 Models with More than One Dynamic Variable 255 7.3 Linear Multivariable Models 260 7.4 Equilibria and Stability for Linear Discrete-Time Models 279 7.5 Concluding Message 289 Chapter 8: Equilibria and Stability Analyses--Nonlinear Models with Multiple Variables 294 8.1 Introduction 294 8.2 Nonlinear Multiple-Variable Models 294 8.3 Equilibria and Stability for Nonlinear Discrete-Time Models 316 8.4 Perturbation Techniques for Approximating Eigenvalues 330 8.5 Concluding Message 337 Chapter 9: General Solutions and Tranformations--Models with Multiple Variables 347 9.1 Introduction 347 9.2 Linear Models Involving Multiple Variables 347 9.3 Nonlinear Models Involving Multiple Variables 365 9.4 Concluding Message 381 Chapter 10: Dynamics of Class-Structured Populations 386 10.1 Introduction 386 10.2 Constructing Class-Structured Models 388 10.3 Analyzing Class-Structured Models 393 10.4 Reproductive Value and Left Eigenvectors 398 10.5 The Effect of Parameters on the Long-Term Growth Rate 400 10.6 Age-Structured Models--The Leslie Matrix 403 10.7 Concluding Message 418 Chapter 11: Techniques for Analyzing Models with Periodic Behavior 423 11.1 Introduction 423 11.2 What Are Periodic Dynamics? 423 11.3 Composite Mappings 425 11.4 Hopf Bifurcations 428 11.5 Constants of Motion 436 11.6 Concluding Message 449 Chapter 12: Evolutionary Invasion Analysis 454 12.1 Introduction 454 12.2 Two Introductory Examples 455 12.3 The General Technique of Evolutionary Invasion Analysis 465 12.4 Determining How the ESS Changes as a Function of Parameters 478 12.5 Evolutionary Invasion Analyses in Class-Structured Populations 485 12.6 Concluding Message 502 Primer 3: Probability Theory 513 P3.1 An Introduction to Probability 513 P3.2 Conditional Probabilities and Bayes' Theorem 518 P3.3 Discrete Probability Distributions 521 P3.4 Continuous Probability Distributions 536 P3.5 The (Insert Your Name Here) Distribution 553 Chapter 13: Probabilistic Models 567 13.1 Introduction 567 13.2 Models of Population Growth 568 13.3 Birth-Death Models 573 13.4 Wright-Fisher Model of Allele Frequency Change 576 13.5 Moran Model of Allele Frequency Change 581 13.6 Cancer Development 584 13.7 Cellular Automata--A Model of Extinction and Recolonization 591 13.8 Looking Backward in Time--Coalescent Theory 594 13.9 Concluding Message 602 Chapter 14: Analyzing Discrete Stochastic Models 608 14.1 Introduction 608 14.2 Two-State Markov Models 608 14.3 Multistate Markov Models 614 14.4 Birth-Death Models 631 14.5 Branching Processes 639 14.6 Concluding Message 644 Chapter 15: Analyzing Continuous Stochastic Models--Diffusion in Time and Space 649 15.1 Introduction 649 15.2 Constructing Diffusion Models 649 15.3 Analyzing the Diffusion Equation with Drift 664 15.4 Modeling Populations in Space Using the Diffusion Equation 684 15.5 Concluding Message 687 Epilogue: The Art of Mathematical Modeling in Biology 692 Appendix 1: Commonly Used Mathematical Rules 695 A1.1 Rules for Algebraic Functions 695 A1.2 Rules for Logarithmic and Exponential Functions 695 A1.3 Some Important Sums 696 A1.4 Some Important Products 696 A1.5 Inequalities 697 Appendix 2: Some Important Rules from Calculus 699 A2.1 Concepts 699 A2.2 Derivatives 701 A2.3 Integrals 703 A2.4 Limits 704 Appendix 3: The Perron-Frobenius Theorem 709 A3.1: Definitions 709 A3.2: The Perron-Frobenius Theorem 710 Appendix 4: Finding Maxima and Minima of Functions 713 A4.1 Functions with One Variable 713 A4.2 Functions with Multiple Variables 714 Appendix 5: Moment-Generating Functions 717 Index of Definitions, Recipes, and Rules 725 General Index 727

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Book SynopsisDarren Bridger is a consultant to designers and marketers, advising on using and analyzing data that tap into consumers' non-conscious thinking and motivations. He was one of the original pioneers of the Consumer Neuroscience industry, helping to pioneer two of the first companies in the field then joining the world's largest agency, Neurofocus (now part of the Nielsen company). He is currently Head of Insights at NeuroStrata. Trade Review"A super, easy-to-read book demystifying the world of neuro design, addressing the balance between the role of human creativity and that of neuroscience in modern design. If you think neuro design is about creating bland designs by deconstructing beauty, you need to read this book. It's not about that at all. Darren Bridger introduces all the major themes, key methods and tools underlying the science in engaging, manageable chunks. Any book that explains the allure of memes has to get five stars from me." * Jamie Croggon, Design Director, SharkNinja *"With solid science as the starting point, Darren Bridger provides an eminently practical guide to designing for your customer's brain. Neuro Design is packed with actionable strategies and techniques, and is a must-read for every marketer and designer." * Roger Dooley, author of Brainfluence *"A topic which should be of great importance to anyone in the business of retailing, advertising and marketing. Darren Bridger deals with complex topics in an engaging and practical manner, covering all aspects of the interplay between brain function and product design. Such an understanding is crucial for ensuring consumers stop and buy, rather than walking on by." * Dr David Lewis, Chairman of Mindlab International & Author of The Brain Sell *Table of Contents Section - 01: What is Neuro Design?; Section - 02: Neuroaesthetics; Section - 03: Processing Fluency; Section - 04: How First Impressions Work; Section - 05: Multisensory and Emotional Design; Section - 06: Visual Saliency Maps; Section - 07: Visual Persuasion and Behavioural Economics; Section - 08: Designing for Screens; Section - 09: Viral Designs; Section - 10: Designing Presentation Slides; Section - 11: Conducting Neuro Design Research; Section - 12: Conclusion;

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Book SynopsisWritten for students, researchers, consultants, professionals, and scholars, Logic Modeling Methods in Program Evaluation provides a step-by-step explanation of logic modeling and its importance in connecting theory with implementation and outcomes in program evaluation in the social sciences.Trade Review"The book is definitely worth buying. Both program developers and evaluators will find the text useful." (Journal of Multidisciplinary Evaluation, March 2008)Table of ContentsList of Figures. Preface. 1. Evaluation and Logic Models. 2. The Uses of Logic Models. 3. The Components of a Logic Model. 4. The Connections in a Logic Model. 5. Developing Logic Models to Support Evaluation. 6. Developing Logic Models of Differing Complexity. 7. Using a Logic Model to Identify Evaluation Questions. 8. Using a Logic Model to Support Explanatory Evaluation. 9. Challenges in Developing Logic Models. 10. Developing Logic Models for Complex Projects. 11. Using Logic Models to Evaluate a Family of Projects. 12. Using the Logic Model to Provide Technical Assistance. Appendix: The Phases of an Evaluation. About the Author. Glossary. References.

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Book SynopsisMathematical Models for Structural Reliability Analysis offers mathematical models for describing load and material properties in solving structural engineering problems. Examples are provided, demonstrating how the models are implemented, and the limitations of the models are clearly stated. Analytical solutions are also discussed, and methods are clearly distinguished from models. The authors explain both theoretical models and practical applications in a clear, concise, and readable fashion.Table of ContentsStochastic Process Models (F. Casciati and M. Di Paola)IntroductionThe Orthogonal-Increment ModelThe Correlation-Stationary Model Time-Invariant Linear Systems Models of Common UseThe Evolutionary Model Time-Invariant Linear SystemsMarkov Processes A Model of Common Use Itô Stochastic Differential Equation Some Examples Approximation of Mechanical Processes: Physical versus Itô EquationsThe Random Pulse Train Model The Delta-Correlated Model Fokker Planck and Moment Equations for Parametric Delta Correlated Input Quasi-Linear Systems Simulation of Delta Correlated Processes and Response Simulation of Normal White Noise Input and Response Orthogonal-Increment Model for Delta Correlated ProcessesMultidegree-of-Freedom Systems Under Parametric Delta Correlated Input Moment Equation Approach for MDOF Systems Simulation of Multivariate Delta Correlated Processes and ResponseConclusions and ReferencesAppendix Characterization of Random Variables Joint Characterization of Random Variables Operation on Stochastic Processes Kronecker Algebra: Some FundamentalsDimension Reduction and Discretization in Stochastic Problems by Regression Method (O. Ditlevsen)IntroductionLinear RegressionNormal DistributionNon-Gaussian Distributions and Linear RegressionMarginally Transformed Gaussian Processes and FieldsDiscretized Fields Defined by Linear Regression on a Finite Set of Field ValuesDiscretization Defined by Linear Regression on a Finite Set of Linear FunctionalsPoisson Load Field ExampleStochastic Finite Element Methods and Reliability CalculationsClassical versus Statistical-Stochastic Interpolation Formulated on the Basis of the Principle of Maximum LikelihoodComputational Practicability of the Statistical-Stochastic Interpolation MethodField Modeling on the Basis of Measured Noisy DataDiscretization Defined by L

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Book SynopsisWritten by leading researchers from the USA, Canada and Europe, this is an essential reference tool for researchers and advanced students in animal nutrition. Farm livestock have evolved digestive systems that are capable of digesting fibrous materials and by-products unsuited for man. Throughout the world, production from farm livestock is concerned with providing food and clothing of animal origin for man. Animal production science underpins this goal and provides the scientific basis for livestock management practices. Feed evaluation concerns the use of methods to describe animal feedstuffs with respect to their ability to sustain different types and levels of animal performance. The main themes of the book are methods of feed evaluation, current feeding systems, and mechanistic mathematical modelling. No other title brings together methods, systems and models under one cover.Table of Contents1: Feed Evaluation for Animal Production, J France, MK Theodorou, RS Lowman and DE Beever 2: Feed Characterisation, A Chesson 3: Intake, Passage and Digestibility, DP Poppi, J France and SR McLennan 4: In Vitro and In Situ Methods for Estimating Digestibility with Reference to Protein Degradability, GA Broderick and RC Cochran 5: Measurement of Energy Metabolism, C K Reynolds 6: Feeding Systems for Dairy Cows, S Tamminga and G Hof 7: Feeding Systems for Beef Cattle, JG Buchanan-Smith and DG Fox 8: Feeding Systems for Sheep, LA Sinclair and RG Wilkinson 9: Feeding Systems for Pigs, LI Chiba 10: Feeding Systems for Poultry, S Leeson and JD Summers 11: Feeding Systems for Horses, D Cuddeford 12: Prediction of Response to Nutrients by Ruminants Through Mathematical Modelling and Improved Feed Characterization, DE Beever, J France and G Alderman 13: Analyses of Modelling Whole Rumen Function, J Dijkstra and A Bannink 14: Modelling the Lactating Dairy Cow, RL Baldwin and KC Donovan 15: Modelling Growth and Wool Production in Ruminants, WJ Gerrits and J Dijkstra 16: Modelling Growth and Lactation in Pigs, JL Black 17: Modelling the Utilization of Dietary Energy and Amino Acids by Poultry, MG MacLeod 18: Modelling Growth in Fish, Y Cui and S Xie 19: The Nutrition of Companion Animals, AC Longland, MK Theodorou and IH Burger 20: Index

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Book SynopsisMathematical modeling - the ability to apply mathematical concepts and techniques to real-life systemsâhas expanded considerably over the last decades, making it impossible to cover all of its aspects in one course or textbook. Continuum Modeling in the Physical Sciences provides an extensive exposition of the general principles and methods of this growing field with a focus on applications in the natural sciences. The authors present a thorough treatment of mathematical modeling from the elementary level to more advanced concepts. Most of the chapters are devoted to a discussion of central issues such as dimensional analysis, conservation principles, balance laws, constitutive relations, stability, robustness, and variational methods, and are accompanied by numerous real-life examples. Readers will benefit from the exercises placed throughout the text and the Challenging Problems sections found at the ends of several chapters.

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Book SynopsisModern financial mathematics relies on the theory of random processes in time, reflecting the erratic fluctuations in financial markets. This book introduces the fascinating area of financial mathematics and its calculus in an accessible manner for undergraduate students. Using little high-level mathematics, the author presents the basic methods for evaluating financial options and building financial simulations. By emphasising relevant applications and illustrating concepts with colour graphics, Elementary Calculus of Financial Mathematics presents the crucial concepts needed to understand financial options among these fluctuations. Among the topics covered are the binomial lattice model for evaluating financial options, the BlackâScholes and FokkerâPlanck equations, and the interpretation of Ito's formula in financial applications. Each chapter includes exercises for student practice and the appendices offer MATLAB and SCILAB code as well as alternate proofs of the FokkerâPlanck equ

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Book SynopsisThis hands-on text demystifies numerical modelling for early-stage physics and engineering students, with each chapter focusing on an intriguing physics problem. Developed over many years of teaching a computational modelling course, this stand-alone book gives students an essential numerical modelling toolkit for today's data-driven landscape.Table of ContentsPreface; How to use this book; First steps; 1. Rectangular finite quantum well – Stationary Schrödinger Equation in 1D; 2. Diffraction of light on a slit; 3. Pendulum as a standard unit of time; 4. Planetary system; 5. Gravitation inside a star; 6. Normal modes in a cylindrical waveguide; 7. Thermal insulation properties of a wall; 8. Cylindrical capacitor; 9. Coupled harmonic oscillators; 10. The Fermi-Pasta-Ulam problem; 11. Cold hydrogen star; 12. Rectangular quantum well filled with electrons – The idea of self-consistent calculations; 13. Time dependent Schrödinger Equation Dawid Dworzański; 14. Poisson equation in 2D; Appendices; Further Reading; Index.

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Book Synopsis

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Book SynopsisQuantitative Finance with Python: A Practical Guide to Investment Management, Trading and Financial Engineering bridges the gap between the theory of mathematical finance and the practical applications of these concepts for derivative pricing and portfolio management. The book provides students with a very hands-on, rigorous introduction to foundational topics in quant finance, such as options pricing, portfolio optimization and machine learning. Simultaneously, the reader benefits from a strong emphasis on the practical applications of these concepts for institutional investors. Features Useful as both a teaching resource and as a practical tool for professional investors. Ideal textbook for first year graduate students in quantitative finance programs, such as those in master's programs in Mathematical Finance, Quant Finance or Financial Engineering. Includes a perspective on the future of quant finaTable of ContentsSection I. Foundations of Quant Modeling. 1. Setting the Stage: Quant Landscape. 1.1. Introduction. 1.2. Quant Finance Institutions. 1.3. Most Common Quant Career Paths. 1.4. Types of Financial Instruments. 1.5. Stages of a Quant Project. 1.6. Trends: Where is Quant Finance Going? 2. Theoretical Underpinnings of Quant Modeling: Modeling the Risk Neutral Measure. 2.1. Introduction. 2.2. Risk Neutral Pricing & No Arbitrage. 2.3. Binomial Trees. 2.4. Building Blocks of Stochastic Calculus. 2.5. Stochastic Differential Equations. 2.6. Itô’s Lemma. 2.7. Connection between SDEs and PDES. 2.8. Girsanov’s Theorem. 3. Theoretical Underpinnings of Quant Modeling: Modeling the Physical Measure. 3.1. Introduction: Forecasting vs. Replication. 3.2. Market Efficiency and Risk Premia. 3.3. Linear Regression Models. 3.4. Time Series Models. 3.5. Panel Regression Models. 3.6. Core Portfolio and Investment Concepts. 3.7. Bootstrapping. 3.8. Principal Component Analysis. 3.9. Conclusions: Comparison to Risk Neutral Measure Modelling. 4. Python Programming Environment. 4.1. The Python Programming Language. 4.2. Advantages and Disadvantages of Python. 4.3. Python Development Environments. 4.4. Basic Programming Concepts in Python. 5. Programming Concepts in Python. 5.1. Introduction. 5.2. Numpy Library. 5.3. Pandas Library. 5.4. Data Structures in Python. 5.5. Implementation of Quant Techniques in Python. 5.6. Object-Oriented Programming in Python. 5.7. Design Patterns. 5.8. Search Algorithms. 5.9. Sort Algorithms. 6. Working with Financial Datasets. 6.1. Introduction. 6.2. Data Collection. 6.3. Common Financial Datasets. 6.4. Common Financial Data Sources. 6.5. Cleaning Different Types of Financial Data. 6.6. Handling Missing Data. 6.7. Outlier Detection. 7. Model Validation. 7.1. Why Is Model Validation So Important? 7.2. How Do We Ensure Our Models Are Correct? 7.3. Components of a Model Validation Process. 7.4. Goals of Model Validation. 7.5. Trade-off between Realistic Assumptions and Parsimony in Models. Section II. Options Modeling. 8. Stochastic Models. 8.1. Simple Models. 8.2. Stochastic Volatility Models. 8.3. Jump Diffusion Models. 8.4. Local Volatility Models. 8.5. Stochastic Local Volatility Models. 8.6. Practicalities of using these Models. 9. Options Pricing Techniques for European Options. 9.1. Models with Closed Form Solutions or Asymptotic Approximations. 9.2. Option Pricing via Quadrature. 9.3. Option Pricing via FFT. 9.4. Root Finding. 9.5. Optimization Techniques. 9.6. Calibration of Volatility Surfaces. 10. Options Pricing Techniques for Exotic Options. 10.1. Introduction. 10.2. Simulation. 10.3. Numerical Solutions to PDEs. 10.4. Modeling Exotic Options in Practice. 11. Greeks and Options Trading. 11.1. Introduction. 11.2. Black-Scholes Greeks. 11.3. Theta vs. Gamma. 11.4. Model Dependence of Greeks. 11.5. Greeks for Exotic Options. 11.6. Estimation of Greeks via Finite Differences. 11.7. Smile Adjusted Greeks. 11.8. Hedging in Practice. 11.9. Common Options Trading Structures. 11.10. Volatility as an Asset Class. 11.11. Risk Premia in the Options Market: Implied vs. Realized Volatility. 11.12. Case Study: GameStop Reddit Mania. 12. Extraction of Risk Neutral Densities. 12.1. Motivation. 12.2. Breden—Litzenberger. 12.3. Connection Between Risk Neutral Distributions and Market Instruments. 12.4. Optimization Framework for Non-Parametric Density Extraction. 12.5. Weigthed Monte Carlo. 12.6. Relationship between Volatility skew and Risk Neutral Densities. 12.7. Risk Premia in the Options Market: Comparison OF Risk Neutral vs. Physical Measures. 12.8. Conclusions & Assessment of Parametric vs. Non-Parametric Methods. Section III. Quant Modelling in Different Markets. 13. Interest Rate Markets. 13.1. Market Setting. 13.2. Bond Pricing Concepts. 13.3. Main Components of a Yield Curve. 13.4. Market Rates. 13.5. Yield Curve Construction. 13.6. Modelling Interest Rate Derivatives. 13.7 Modeling Volatility for a Single Rate: Caps / Floors. 13.8. Modeling Volatility for a Single Rate: Swaptions. 13.9. Modelling the Term Structure: Short Rate Models. 13.10. Modelling the Term Structure: Forward Rate Models. 13.11. Exotic Options. 13.12. Investment Perspective: Traded Structures. 13.13. Case Study: Introduction of Negative Rates. 14. Credit Markets. 14.1. Market Setting. 14.2. Modeling Default Risk: Hazard Rate Models. 14.3. Risky Bond. 14.4. Credit Default Swaps. 14.5. CDS vs. Corporate Bonds. 14.6. Bootstrapping a Survival Curve. 14.7. Indices of Credit Default Swaps. 14.8. Market Implied vs. Empirical Default Probabilities. 14.9. Options on CDS & CDX Indices. 14.10. Modeling Correlation: CDOS. 14.11. Models Connecting Equity and Credit. 14.12. Mortgage-backed Securities. 14.13. Investment Perspective: Traded Structures. 15. Foreign Exchange Markets. 15.1. Market Setting. 15.2. Modeling in a Currency Setting. 15.3. Volatility Smiles IN Foreign Exchange Markets. 15.4. Exotic Options in Foreign Exchange Markets. 15.5. Investment Perspective: Traded Structures. 15.6. Case Study: CHF Peg Break in 2015. 16. Equity & Commodity Markets. 16.1. Market Setting. 16.2. Futures Curves in Equity & Commodity Markets. 16.3. Volatility Surfaces in Equity & Commodity Markets. 16.4. Exotic Options in Equity & Commodity Markets. 16.5. Investment Perspective: Traded Structures. 16.6. Case Study: Nat Gas Short Squeeze. 16.7. Case Study: Volatility ETP Apocalypse of 2018. Section IV. Portfolio Construction & Risk Management. 17. Portfolio Construction & Optimization Techniques. 17.1. Theoretical Background. 17.2. Mean-Variance Optimization. 17.3. Challenges Associated with Mean-Variance Optimization. 17.4. Capital Asset Pricing Model. 17.5. Black-Litterman. 17.6. Resampling. 17.7. Downside Risk Based Optimization. 17.8. Risk Parity. 17.9. Comparison OF Methodologies. 18. Modelling Expected Returns and Covariance Matrices. 18.1. Single & Multi-Factor Models for Expected Returns. 18.2. Modelling Volatility. 19. Risk Management. 19.1. Motivation & Setting. 19.2. Common Risk Measures. 19.3. Calculation of Portfolio VAR and CVAR. 19.4. Risk Management of Non-Linear Instruments. 19.5. Risk Management in Rates & Credit Markets. 20. Quantitative Trading Models. 20.1. Introduction to Quant Trading Models. 20.2. Back-Testing. 20.3. Common Stat-Arb Strategies. 20.4. Systematic Options Based Strategies. 20.5. Combining Quant Strategies. 20.6. Principles of Discretionary vs. Systematic Investing. 21. Incorporating Machine Learning Techniques. 21.1. Machine Learning Framework. 21.2. Supervised vs. Unsupervised Learning Methods. 21.3. Clustering. 21.4. Classification Techniques. 21.5. Feature Importance & Interpretability. 21.6. Other Applications OF Machine Learning. Bibliography. Index

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Book SynopsisThis textbook intends to be a comprehensive and substantially self-contained two-volume book covering performance, reliability, and availability evaluation subjects. The volumes focus on computing systems, although the methods may also be applied to other systems. The first volume covers Chapter 1 to Chapter 14, whose subtitle is ``Performance Modeling and Background. The second volume encompasses Chapter 15 to Chapter 25 and has the subtitle ``Reliability and Availability Modeling, Measuring and Workload, and Lifetime Data Analysis.This text is helpful for computer performance professionals for supporting planning, design, configuring, and tuning the performance, reliability, and availability of computing systems. Such professionals may use these volumes to get acquainted with specific subjects by looking at the particular chapters. Many examples in the textbook on computing systems will help them understand the concepts covered in each chapter. The text may also be helpful for the instructor who teaches performance, reliability, and availability evaluation subjects. Many possible threads could be configured according to the interest of the audience and the duration of the course. Chapter 1 presents a good number of possible courses programs that could be organized using this text.Volume II is composed of the last two parts. Part III examines reliability and availability modeling by covering a set of fundamental notions, definitions, redundancy procedures, and modeling methods such as Reliability Block Diagrams (RBD) and Fault Trees (FT) with the respective evaluation methods, adopts Markov chains, Stochastic Petri nets and even hierarchical and heterogeneous modeling to represent more complex systems. Part IV discusses performance measurements and reliability data analysis. It first depicts some basic measuring mechanisms applied in computer systems, then discusses workload generation. After, we examine failure monitoring and fault injection, and finally, we discuss a set of techniques for reliability and maintainability data analysis.

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Book SynopsisSpreadsheet Problem Solving and Programming for Engineers and Scientists provides a comprehensive resource essential to a full understanding of modern spreadsheet skills needed for engineering and scientific computations.Beginning with the basics of spreadsheets and programming, this book builds on the authors' decades of experience teaching spreadsheets and programming to both university students and professional engineers and scientists. Following on from this, it covers engineering economics, key numerical methods, and applied statistics. Finally, this book details the Visual Basic for Applications (VBA) programming system that accompanies Excel.With each chapter including examples and a set of exercises, this book is an ideal companion for all engineering courses and also for self-study. Based on the latest version of Excel (Microsoft Excel for Microsoft 365), it is also compatible with earlier versions of Excel dating back to Version 2013. Including numerTable of ContentsChapter 1 Spreadsheet Basics Chapter 2 Charts and GraphsChapter 3 Engineering and Scientific FormulasChapter 4 Table-based CalculationsChapter 5 Case Studies and TargetingChapter 6 Financial CalculationsChapter 7 Numerical MethodsChapter 8 Applied StatisticsChapter 9 Introduction to VBA and MacrosChapter 10 User-defined FunctionsChapter 11 VBA ProgrammingChapter 12 User InterfacesAppendix A: Matrix Algebra ReviewAppendix B: Shortcut Keys and Key Combinations

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Book SynopsisMechatronics is a mongrel, a crossbreed of classic mechanical engineering, the relatively young pup of computer science, the energetic electrical engineering, the pedigree mathematics and the bloodhound of Control Theory.All too many courses in control theory consist of a diet of Everything you could ever need to know about the Laplace Transform' rather than answering What happens when your servomotor saturates?' Topics in this book have been selected to answer the questions that the mechatronics student is most likely to raise.That does not mean that the mathematical aspects have been left out, far from it. The diet here includes matrices, transforms, eigenvectors, differential equations and even the dreaded z transform. But every effort has been made to relate them to practical experience, to make them digestible. They are there for what they can do, not to support pages of mathematical rigour that defines their origins.The theme running throughout the Table of Contents1. Why Do You Need Control Theory? 2. Modelling Time .3. A Simulation Environment 4. Step Length Considerations. 5. Modelling a Second-Order System .6. The Complication of Motor Drive Limits. 7. Practical Controller Design 8. Adding Dynamics to the Controller 9. Sensors and Actuators. 10. Analogue Simulation. 11. Matrix State Equations. 12. Putting It into Practice. 13. Observers 14. More about the Mathematics 15. Transfer Functions 16. Solving the State Equations 17. Discrete Time and the z Operator. 18. Root locus. 19. More about the Phase Plane. 20. Optimisation and an Experiment. 21. Problem Systems. 22. Final Comments.

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Book SynopsisWith Python, C++, FORTRAN, and a friendly conversational tone peppered with attempted humor, Modeling and Simulation of Everyday Things takes us on a journey through constructing models and simulations of systems and processes in everyday life and beyond. Readers can access an exampleâpacked online repository of programs in each of the three languages, including seldom covered work in generalized geometries and 3D.This second edition is a wonderful confluence of development of Python and C++ applications and will cultivate a broad perspective in the readership through having translations of major programs available in Python, C++, and FORTRAN (as we move forward, software engineers and researchers are recognizing the value of legacy programming). In addition to leveraging the best of the three languages, the readership can explore versatility in visualization by using native Python graphics as well as POV Raytracer and thirdâparty animation tools. We approach modeling of a system by introducing the theoretical framework of the system, followed by its discretized form, and then with narrated programs and sample results that also appear in the online repository.Readers will be able to critically think through constructing models and simulations of a vast array of systems, interpreting results, and visualizing them (which includes examples for visually and auditorily impaired individuals). Most importantly, their confidence will propel them forward to meet the challenges of the field and to think outside the book. Leveraging the best of three coding languages, two tracks for visualization, a conversational tone, and numerous examples, this book is extremely versatile and can be used by students from high school through science undergraduates in 2âyear and 4âyear institutions. The text is also ideal for use in Data Science as well as Professional Science Masterâs programs.

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Book SynopsisThe field of nonlinear dispersive waves has developed enormously since the work of Stokes, Boussinesq and Kortewegâde Vries (KdV) in the nineteenth century. In the 1960s, researchers developed effective asymptotic methods for deriving nonlinear wave equations, such as the KdV equation, governing a broad class of physical phenomena that admit special solutions including those commonly known as solitons. This book describes the underlying approximation techniques and methods for finding solutions to these and other equations. The concepts and methods covered include wave dispersion, asymptotic analysis, perturbation theory, the method of multiple scales, deep and shallow water waves, nonlinear optics including fiber optic communications, mode-locked lasers and dispersion-managed wave phenomena. Most chapters feature exercise sets, making the book suitable for advanced courses or for self-directed learning. Graduate students and researchers will find this an excellent entry to a thriving Trade Review'[This] is an up-to-date teaching resource that will prepare students for work in nonlinear waves as the subject appears today in applications, especially in nonlinear optics. It is clear that Mark Ablowitz's book is a welcome addition to the literature that will be particularly useful to anyone planning a course on nonlinear waves.' Peter D. Miller, SIAM NewsTable of ContentsPreface; Acknowledgements; Part I. Fundamentals and Basic Applications: 1. Introduction; 2. Linear and nonlinear wave equations; 3. Asymptotic analysis of wave equations; 4. Perturbation analysis; 5. Water waves and KdV type equations; 6. Nonlinear Schrödinger models and water waves; 7. Nonlinear Schrödinger models in nonlinear optics; Part II. Integrability and Solitons: 8. Solitons and integrable equations; 9. Inverse scattering transform for the KdV equation; Part III. Novel Applications of Nonlinear Waves: 10. Communications; 11. Mode-locked lasers; 12. Nonlinear photonic lattices; References; Index.

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Book SynopsisRecent technological advances have enabled comprehensive determination of the molecular composition of living cells. The chemical interactions between many of these molecules are known, giving rise to genome-scale reconstructed biochemical reaction networks underlying cellular functions. Mathematical descriptions of the totality of these chemical interactions lead to genome-scale models that allow the computation of physiological functions. Reflecting these recent developments, this textbook explains how such quantitative and computable genotype-phenotype relationships are built using a genome-wide basis of information about the gene portfolio of a target organism. It describes how biological knowledge is assembled to reconstruct biochemical reaction networks, the formulation of computational models of biological functions, and how these models can be used to address key biological questions and enable predictive biology. Developed through extensive classroom use, the book is designed Trade Review'One of the defining challenges of systems biology is to determine the structures and mechanisms by which complex networks of genes, proteins and metabolites control cell processes and molecular dynamics. Bernhard Ø. Palsson is a leading pioneer in constructing and analyzing genome-scale models of such networks. Here Palsson offers students an insider's guided tour of the concepts, principles and techniques underlying this emerging field. The book is brilliantly laid out and offers professors well-structured, much-needed material for a graduate-level course in systems biology and network science.' James J. Collins, Massachusetts Institute of Technology'This is a real tour de force. With enormous clarity, Bernhard Ø. Palsson sets out the what, why and how of network and systems biology, and of the important role of genome-wide reconstructions - especially, to date, of metabolism - in realising it … this is a masterful survey of the field by one of its leading practitioners. The development is nicely logical … If you are interested in network biology at all, then this book is for you.' Douglas Kell, University of Manchester'Systems Biology is an excellent resource for familiarizing researchers and students with the process of reconstructing genome-scale metabolic models and the types of data needed. A number of thorough studies are included that shed light on a range of queries that genome-scale models are well suited to answer. In addition to models, a number of algorithmic techniques are described for analyzing models and inferring organizational principles of metabolism or ways to re-engineer them. A great teaching and reference resource!' Costas Maranas, Pennsylvania State University'… a very important and novel contribution to the systems biology literature. The field of systems biology is still in the phase of being defined as an independent field with a clear curriculum, but Palsson gives his very clear contributions to this. His definition of the paradigm of systems biology as components, networks, computer models and physiology is clearly explained and linked to educational modules, educational values and specific prerequisites. Thus, not only is he providing a fantastic novel textbook that enables teaching about network reconstruction and analysis, but he is also clearly defining this as the core of systems biology. I am therefore confident that the very well thought through structure of this textbook, where the reader is introduced to the different layers of network reconstruction and analysis, will be widely used for teaching systems biology worldwide.' Jens Nielsen, Chalmers University of Technology'Bernhard Ø. Palsson is the leading pioneer of genome-scale models in biology today, and this book provides a beautiful view into his unique and powerful brand of systems biology. What lies in these pages is a masterful synthesis of a cohesive mathematical framework for representing biological processes that ties directly to experimental biology. While centered on metabolism - the powerhouse of the cell - this book teaches approaches that can be universally applied across all biochemical processes. This book will be a tremendous resource for students and researchers alike, and will help drive applications ranging from the environment to human health.' Nathan Price, Institute for Systems Biology'[This textbook] offers a truly authoritative treatment of genome-scale systems biology modelling. [It] covers all aspects of this rapidly growing field from theory to basic and applied uses, also detailing open challenges with an emphasis on the multitude of constraint-based approaches by which phenotypic behavior can be inferred from biochemical wiring diagrams. The book is generously illustrated by figures and despite its great depth and breadth, it remains readily accessible … researchers [will find it] a go-to guide for many years to come.' Balázs Papp, Biological Research Centre, Hungarian Academy of SciencesTable of ContentsPreface; 1. Introduction; Part I. Network Reconstruction: 2. Network reconstruction: the concept; 3. Network reconstruction: the process; 4. Metabolism in Escherichia coli; 5. Prokaryotes; 6. Eukaryotes; 7. Biochemical reaction networks; 8. Metastructures of genomes; Part II. Mathematical Properties of Reconstructed Networks: 9. The stoichiometric matrix; 10. Simple topological network properties; 11. Fundamental network properties; 12. Pathways; 13. Use of pathway vectors; 14. Randomized sampling; Part III. Determining the Phenotypic Potential of Reconstructed Networks: 15. Dual causality; 16. Functional states; 17. Constraints; 18. Optimization; 19. Determining capabilities; 20. Equivalent states; 21. Distal causation; Part IV. Basic and Applied Uses: 22. Environmental parameters; 23. Genetic parameters; 24. Analysis of omic data; 25. Model driven discovery; 26. Adaptive laboratory evolution; 27. Model driven design; Part V. Conceptual Foundations: 28. Teaching systems biology; 29. Epilogue; References; Index.

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Book SynopsisDesigning engineering components that make optimal use of materials requires consideration of the nonlinear static and dynamic characteristics associated with both manufacturing and working environments. The modeling of these characteristics can only be done through numerical formulation and simulation, which requires an understanding of both the theoretical background and associated computer solution techniques. By presenting nonlinear solid mechanics, dynamic conservation laws and principles, and the associated finite element techniques together, the authors provide in this second book a unified treatment of the dynamic simulation of nonlinear solids. Alongside a number of worked examples and exercises are user instructions, program descriptions, and examples for two MATLAB computer implementations for which source codes are available online. While this book is designed to complement postgraduate courses, it is also relevant to those in industry requiring an appreciation of the way tTrade Review'… the software can be useful to readers in testing different options of the codes, building their own simple examples, and acquiring some additional experience and knowledge about continuum mechanics and numerical methods for their simulations.' Josip Tambaca, Society for Industrial and Applied Mathematics ReviewTable of Contents1. Introduction; 2. Dynamic analysis of 3-D trusses; 3. Dynamic equilibrium of deformable solids; 4. Discretization and solution; 5. Conservation laws in solid dynamics; 6. Thermodynamics; 7. Space and time discretization of conservation laws in solid dynamics; 8. Computer implementation for displacement-based dynamics; 9. Computational implementation for conservation-law-based explicit fast dynamics; Appendix. Shocks; Bibliography; Index.

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Book SynopsisThe Earth and environmental sciences are becoming progressively more quantitative due to the increased use of mathematical models and new data analysis techniques. This accessible introduction presents an overview of the mathematical methods essential for understanding Earth processes, providing an invaluable resource for students and early career researchers who may have missed (or forgotten) the mathematics they need to succeed as scientists. Topics build gently from basic methods such as calculus to more advanced techniques including linear algebra and differential equations. The practical applications of the mathematical methods to a variety of topics are discussed, ranging from atmospheric science and oceanography to biogeochemistry and geophysics. Including over 530 exercises and end-of-chapter problems, as well as additional computer codes in Python and MATLAB, this book supports readers in applying appropriate analytical or computational methods to solving real research questioTable of ContentsPreface; 1. Estimation and dimensional analysis; 2. Derivatives and integrals; 3. Series and summations; 4. Scalars, vectors, and matrices; 5. Probability; 6. Ordinary differential equations; 7. Vectors and calculus; 8. Special functions; 9. Fourier series and integral transforms; 10. Partial differential equations; 11. Tensors; Appendix A. Units and dimensions; Appendix B. Tables of useful formulae; Appendix C. Complex numbers; Notes; References; Index.

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Book SynopsisIdeal for teaching and self study, this practical book demonstrates how cognitive scientists can conduct Bayesian analyses for many real-life modeling problems. Supported by examples, exercises, computer code and additional resources available online, readers will learn to take full advantage of the exciting possibilities that the Bayesian approach affords.Trade Review'This book provides the best practical guide to date on how to do Bayesian modeling in cognitive science.' Jay Myung, Ohio State University'This is a very powerful exposition of how Bayesian methods, and WinBUGS in particular, can be used to deal with cognitive models that are apparently intractable. When we produced WinBUGS, we had no idea it could be used like this - it's amazing and gratifying to see these applications.' David Spiegelhalter, Winton Professor for the Public Understanding of Risk, Statistical Laboratory, Centre for Mathematical Sciences, CambridgeTable of ContentsPart I. Getting Started: 1. The basics of Bayesian analysis; 2. Getting started with WinBUGS; Part II. Parameter Estimation: 3. Inferences with binomials; 4. Inferences with Gaussians; 5. Some examples of data analysis; 6. Latent mixture models; Part III. Model Selection: 7. Bayesian model comparison; 8. Comparing Gaussian means; 9. Comparing binomial rates; Part IV. Case Studies: 10. Memory retention; 11. Signal detection theory; 12. Psychophysical functions; 13. Extrasensory perception; 14. Multinomial processing trees; 15. The SIMPLE model of memory; 16. The BART model of risk taking; 17. The GCM model of categorization; 18. Heuristic decision-making; 19. Number concept development.

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Book SynopsisGeomathematics provides a comprehensive summary of the mathematical principles behind key topics in geophysics and geodesy, covering the foundations of gravimetry, geomagnetics and seismology. Theorems and their proofs explain why physical realities in geoscience are the logical mathematical consequences of basic laws. The book also derives and analyzes the theory and numerical aspects of established systems of basis functions; and presents an algorithm for combining different types of trial functions. Topics cover inverse problems and their regularization, the Laplace/Poisson equation, boundary-value problems, foundations of potential theory, the Poisson integral formula, spherical harmonics, Legendre polynomials and functions, radial basis functions, the Biot-Savart law, decomposition theorems (orthogonal, Helmholtz, and Mie), basics of continuum mechanics, conservation laws, modelling of seismic waves, the Cauchy-Navier equation, seismic rays, and travel-time tomography. Each chapter ends with review questions, with solutions for instructors available online, providing a valuable reference for graduate students and researchers.Table of Contents1. Introduction; 2. Required Mathematical Basics; 3. Gravitation and Harmonic Functions; 4. Basis Functions; 5. Inverse Problems; 6. The Magnetic Field; 7. Mathematical Models in Seismology; Appendix A. Hints for the Exercises; Appendix B. Questions for Understanding; References; Index.

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Book SynopsisThe study of electronic structure of materials is at a momentous stage, with new computational methods and advances in basic theory. Many properties of materials can be determined from the fundamental equations, and electronic structure theory is now an integral part of research in physics, chemistry, materials science and other fields. This book provides a unified exposition of the theory and methods, with emphasis on understanding each essential component. New in the second edition are recent advances in density functional theory, an introduction to Berry phases and topological insulators explained in terms of elementary band theory, and many new examples of applications. Graduate students and research scientists will find careful explanations with references to original papers, pertinent reviews, and accessible books. Each chapter includes a short list of the most relevant works and exercises that reveal salient points and challenge the reader.Trade Review'… this 2nd edition is … very welcome and timely, as it has been significantly expanded to cover the 'new' topics. The core of the book remains unchanged in scope, focusing on 'independent particle methods' such as DFT and Hartree-Fock theory, and their extensions. This is … a worthy … and is strongly recommended for anyone working in the field of electronic structure.' Matt Probert, Contemporary PhysicsTable of ContentsPreface; Acknowledgments; Notation; Part I. Overview and background topics: 1. Introduction; 2. Overview; 3. Theoretical background; 4. Periodic solids and electron bands; 5. Uniform electron gas and sp-bonded metals; Part II. Density functional theory: 6. Density functional theory: foundations; 7. The Kohn–Sham auxiliary system; 8. Functionals for exchange and correlation I; 9. Functionals for exchange and correlation II; Part III. Important preliminaries on atoms: 10. Electronic structure of atoms; 11. Pseudopotentials; Part IV. Determination of electronic structure: the basic methods: 12. Plane waves and grids: basics; 13. Plane waves and real space methods: full calculations; 14. Localized orbitals: tight-binding; 15. Localized orbitals: full calculations; 16. Augmented functions: APW, KKR, MTO; 17. Augmented functions: linear methods; 18. Locality and linear scaling O(N) methods; Part V. From Electronic Structure to Properties of Matter: 19. Quantum molecular dynamics (QMD); 20. Response functions: phonons, magnons, . . .; 21. Excitation spectra and optical properties; 22. Surfaces, interfaces, and lower dimensional systems; 23. Wannier functions; 24. Polarization, localization, and Berry phases; Part VI. Electronic Structure and Topology: 25. Topology of the electronic structure of a crystal: introduction; 26. Two band models: Berry phase, winding and topology; 27. Topological insulators I: Two dimensions; 28. Topological insulators II: Three dimensions; Part VII. APPENDICES: A. Functional equations; B. LSDA and GGA functionals; C. Adiabatic approximation; D. Perturbation Theory, response functions and Green's functions; E. Dielectric functions and optical properties; F. Coulomb interactions in extended systems; G. Stress from electronic structure; H. Energy and stress densities; I. Alternative force expressions; J. Scattering and phase shifts; K. Useful relations and formulas; L. Numerical methods; M. Iterative methods in electronic structure; N. Two-center matrix elements: expressions for arbitrary angular momentum l; O. Dirac equation and spin-orbit interaction; P. Berry phase, curvature and Chern numbers; Q. Quantum Hall effect and edge conductivity; R. Codes for electronic structure calculations for solids; References; Index.

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Book SynopsisResistivity and induced polarization methods are used for a wide range of near-surface applications, including hydrogeology, civil engineering and archaeology, as well as emerging applications in the agricultural and plant sciences. This comprehensive reference text covers both theory and practice of resistivity and induced polarization methods, demonstrating how to measure, model and interpret data in both the laboratory and the field. Marking the 100 year anniversary of the seminal work of Conrad Schlumberger (1920), the book covers historical development of electrical geophysics, electrical properties of geological materials, instrumentation, acquisition and modelling, and includes case studies that capture applications to societally relevant problems. The book is also supported by a full suite of forward and inverse modelling tools, allowing the reader to apply the techniques to a wide range of applications using digital datasets provided online. This is a valuable reference for grTrade Review'Binley and Slater are two of the best electrical geophysicists in the world, and together have written a comprehensive, accessible textbook for anyone interested in electrical methods. By including a history of the methods, open-source software, and sections on theory, instrumentation, forward and inverse modelling, and applications, they've produced a 'one-stop shop' for all things electrical. This book starts with a primer on the most fundamental mathematics and builds up from there to topics outlining the state of the science, including helpful figures and sidebar information along the way. I strongly recommend this book to any student or practitioner interested in learning more about how to apply electrical geophysical techniques to shallow-Earth problems, and look forward to sharing it with my research students.' Kamini Singha, Colorado School of Mines'This is without doubt the most comprehensive and thorough treatment of electrical geophysics anywhere in the literature. It is a brilliantly written book, covering theory and practice, with numerous real-world examples of the use of resistivity and induced polarization. It will certainly be first on my recommended reading list for students, researchers and practitioners working in the field of geoelectrics and near-surface geophysics.' Jonathan Chambers, British Geological Survey'Andrew Binley and Lee Slater, two experienced scientists in the field of near-surface geophysics, have compiled a modern textbook that describes the development and the state of the art of resistivity and IP technology. The book provides deep insight into the theoretical fundamentals, and presents the breadth of application of these geophysical methods. Considering the wealth of information and the clearly arranged presentation, the textbook will be useful both for academic education and as a reference work for researchers and practitioners. This book will certainly inspire further research work and practical application of resistivity and IP methods.' Andreas Weller, Technische Universität ClausthalTable of ContentsPreface; Acknowledgements; List of symbols; 1. Introduction; 2. Electrical properties of the near surface Earth; 3. Instrumentation and laboratory measurements; 4. Field configuration and acquisition; 5. Forward and inverse modelling; 6. Case studies; 7. Future developments; Appendix A. Modelling tools; Index.

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Book SynopsisLearn to master basic programming tasks from scratch with real-life, scientifically relevant examples and solutions drawn from both science and engineering. Students and researchers at all levels are increasingly turning to the powerful Python programming language as an alternative to commercial packages and this fast-paced introduction moves from the basics to advanced concepts in one complete volume, enabling readers to gain proficiency quickly. Beginning with general programming concepts such as loops and functions within the core Python 3 language, and moving on to the NumPy, SciPy and Matplotlib libraries for numerical programming and data visualization, this textbook also discusses the use of Jupyter Notebooks to build rich-media, shareable documents for scientific analysis. The second edition features a new chapter on data analysis with the pandas library and comprehensive updates, and new exercises and examples. A final chapter introduces more advanced topics such as floating-pTable of ContentsAcknowledgments; 1. Introduction; 2. The core Python language I; 3. Interlude: simple plots and charts; 4. The core Python language II; 5. IPython and Jupyter Notebook; 6. NumPy; 7. Matplotlib; 8. SciPy; 9. Data analysis with pandas; 10. General scientific programming; Appendix A. Solutions; Appendix B. Differences between Python versions 2 and 3; Appendix C. SciPy's odeint ordinary differential equation solver; Glossary; Index.

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Book SynopsisNumerical relativity has emerged as the key tool to model gravitational waves - recently detected for the first time - that are emitted when black holes or neutron stars collide. This book provides a pedagogical, accessible, and concise introduction to the subject. Relying heavily on analogies with Newtonian gravity, scalar fields and electromagnetic fields, it introduces key concepts of numerical relativity in a context familiar to readers without prior expertise in general relativity. Readers can explore these concepts by working through numerous exercises, and can see them ''in action'' by experimenting with the accompanying Python sample codes, and so develop familiarity with many techniques commonly employed by publicly available numerical relativity codes. This is an attractive, student-friendly resource for short courses on numerical relativity, as well as providing supplementary reading for courses on general relativity and computational physics.Trade Review'Computational general relativity has now become a central tool for the exploration of the astrophysical universe, and gravitational-wave astronomy would not be possible without it. A burgeoning or seasoned astrophysicist who wishes to be up to date must therefore acquire an awareness of the field's methods and main achievements. But where to begin? With this book! Baumgarte and Shapiro are leading experts (indeed, founding experts) of this field, and with their trademark lucid and engaging prose, they take us gently by the hand on a comprehensive guided tour. Mysterious notions (lapse, shift, extrinsic curvature, constraint equations) are introduced seamlessly, and the book features a gallery of the field's most important results to date. A superb achievement for the great benefit of the scientific community.' Eric Poisson, University of Guelph; author of A Relativist's Toolkit'Numerical relativity well deserves its reputation as a subject of great beauty yet prodigious conceptual difficulty and daunting technical complexity. This outstanding text, by two leading practitioners of the field, is a wonderful Rosetta Stone for those seeking an efficient path toward a working knowledge of the subject. For me it will serve as an essential reference. I'm sorry only that it was not available sooner.' Robert Eisenstein, Massachusetts Institute of Technology'This is an excellent book explaining the general relativistic two-body problem and its numerical treatment in a highly pedagogical manner to a broad scientific audience. Besides the main topic, readers will also gain some unexpected insight and new viewpoints on numerous wider aspects of Einstein's theory.' Ulrich Sperhake, University of Cambridge'Black holes and gravitational waves are, thanks to new observations, fast-advancing frontiers of astronomy that attract wide interest. Their implications are best addressed by powerful computers, so this text, by two acknowledged world experts, is especially welcome and timely.' Martin Rees, Astronomer Royal; author of Gravity's Fatal AttractionTable of ContentsPreface; 1. Newton's and Einstein's gravity; 2. Foliations of spacetime: constraint and evolution equations; 3. Solving the constraint equations; 4 Solving the evolution equations; 5. Numerical simulations of black-hole binaries; Epilogue; Appendix A. A brief review of tensor properties; Appendix B. A brief introduction to some numerical techniques; Appendix C. A very brief introduction to matter sources; Appendix D. A summary of important results; Appendix E. Answers to selected problems; References; 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 SynopsisA modern approach to mathematical modeling, featuring unique applications from the field of mechanics An Introduction to Mathematical Modeling: A Course in Mechanics is designed to survey the mathematical models that form the foundations of modern science and incorporates examples that illustrate how the most successful models arise from basic principles in modern and classical mathematical physics. Written by a world authority on mathematical theory and computational mechanics, the book presents an account of continuum mechanics, electromagnetic field theory, quantum mechanics, and statistical mechanics for readers with varied backgrounds in engineering, computer science, mathematics, and physics. The author streamlines a comprehensive understanding of the topic in three clearly organized sections: Nonlinear Continuum Mechanics introduces kinematics as well as force and stress in deformable bodies; mass and momentum; balance of linear and angular momeTrade Review “The book also serves as a valuable reference for professionals working in the areas of modeling and simulation, physics, and computational engineering.” (Zentralblatt MATH, 2012) Table of ContentsPreface xiii I Nonlinear Continuum Mechanics 1 1 Kinematics of Deformable Bodies 3 1.1 Motion 4 1.2 Strain and Deformation Tensors 7 1.3 Rates of Motion 10 1.4 Rates of Deformation 13 1.5 The Piola Transformation 15 1.6 The Polar Decomposition Theorem 19 1.7 Principal Directions and Invariants of Deformation and Strain 20 1.8 The Reynolds' Transport Theorem 23 2 Mass and Momentum 25 2.1 Local Forms of the Principle of Conservation of Mass 26 2.2 Momentum 28 3 Force and Stress in Deformable Bodies 29 4 The Principles of Balance of Linear and Angular Momentum 35 4.1 Cauchy's Theorem: The Cauchy Stress Tensor 36 4.2 The Equations of Motion (Linear Momentum) 38 4.3 The Equations of Motion Referred to the Reference Configuration: The Piola-Kirchhoff Stress Tensors 40 4.4 Power 42 5 The Principle of Conservation of Energy 45 5.1 Energy and the Conservation of Energy 45 5.2 Local Forms of the Principle of Conservation of Energy 47 6 Thermodynamics of Continua and the Second Law 49 7 Constitutive Equations 53 7.1 Rules and Principles for Constitutive Equations 54 7.2 Principle of Material Frame Indifference 57 7.2.1 Solids 57 7.2.2 Fluids 59 7.3 The Coleman-Noll Method: Consistency with the Second Law of Thermodynamics 60 8 Examples and Applications 63 8.1 The Navier-Stokes Equations for Incompressible Flow 63 8.2 Flow of Gases and Compressible Fluids: The Compressible Navier-Stokes Equations 66 8.3 Heat Conduction 67 8.4 Theory of Elasticity 69 II Electromagnetic Field Theory and Quantum Mechanics 73 9 Electromagnetic Waves 75 9.1 Introduction 75 9.2 Electric Fields 75 9.3 Gauss's Law 79 9.4 Electric Potential Energy 80 9.4.1 Atom Models 80 9.5 Magnetic Fields 81 9.6 Some Properties of Waves 84 9.7 Maxwell's Equations 87 9.8 Electromagnetic Waves 91 10 Introduction to Quantum Mechanics 93 10.1 Introductory Comments 93 10.2 Wave and Particle Mechanics 94 10.3 Heisenberg's Uncertainty Principle 97 10.4 Schrödinger's Equation 99 10.4.1 The Case of a Free Particle 99 10.4.2 Superposition in Rn 101 10.4.3 Hamiltonian Form 102 10.4.4 The Case of Potential Energy 102 10.4.5 Relativistic Quantum Mechanics 102 10.4.6 General Formulations of Schrödinger's Equation 103 10.4.7 The Time-Independent Schrödinger Equation 104 10.5 Elementary Properties of the Wave Equation 104 10.5.1 Review 104 10.5.2 Momentum 106 10.5.3 Wave Packets and Fourier Transforms 109 10.6 The Wave-Momentum Duality 110 10.7 Appendix: A Brief Review of Probability Densities 111 11 Dynamical Variables and Observables in Quantum Mechanics: The Mathematical Formalism 115 11.1 Introductory Remarks 115 11.2 The Hilbert Spaces L2(R) (or L2(Rd)) and H1(R) (or H1(Rd)) 116 11.3 Dynamical Variables and Hermitian Operators 118 11.4 Spectral Theory of Hermitian Operators: The Discrete Spectrum 121 11.5 Observables and Statistical Distributions 125 11.6 The Continuous Spectrum 127 11.7 The Generalized Uncertainty Principle for Dynamical Variables 128 11.7.1 Simultaneous Eigenfunctions 130 12 Applications: The Harmonic Oscillator and the Hydrogen Atom 131 12.1 Introductory Remarks 131 12.2 Ground States and Energy Quanta: The Harmonic Oscillator 131 12.3 The Hydrogen Atom 133 12.3.1 Schrödinger Equation in Spherical Coordinates 135 12.3.2 The Radial Equation 136 12.3.3 The Angular Equation 138 12.3.4 The Orbitals of the Hydrogen Atom 140 12.3.5 Spectroscopic States 140 13 Spin and Pauli's Principle 145 13.1 Angular Momentum and Spin 145 13.2 Extrinsic Angular Momentum 147 13.2.1 The Ladder Property: Raising and Lowering States 149 13.3 Spin 151 13.4 Identical Particles and Pauli's Principle 155 13.5 The Helium Atom 158 13.6 Variational Principle 161 14 Atomic and Molecular Structure 165 14.1 Introduction 165 14.2 Electronic Structure of Atomic Elements 165 14.3 The Periodic Table 169 14.4 Atomic Bonds and Molecules 173 14.5 Examples of Molecular Structures 180 15 Ab Initio Methods: Approximate Methods and Density Functional Theory 189 15.1 Introduction 189 15.2 The Born-Oppenheimer Approximation 190 15.3 The Hartree and the Hartree-Fock Methods 194 15.3.1 The Hartree Method 196 15.3.2 The Hartree-Fock Method 196 15.3.3 The Roothaan Equations 199 15.4 Density Functional Theory 200 15.4.1 Electron Density 200 15.4.2 The Hohenberg-Kohn Theorem 205 15.4.3 The Kohn-Sham Theory 208 III Statistical Mechanics 213 16 Basic Concepts: Ensembles, Distribution Functions, and Averages 215 16.1 Introductory Remarks 215 16.2 Hamiltonian Mechanics 216 16.2.1 The Hamiltonian and the Equations of Motion 218 16.3 Phase Functions and Time Averages 219 16.4 Ensembles, Ensemble Averages, and Ergodic Systems 220 16.5 Statistical Mechanics of Isolated Systems 224 16.6 The Microcanonical Ensemble 228 16.6.1 Composite Systems 230 16.7 The Canonical Ensemble 234 16.8 The Grand Canonical Ensemble 239 16.9 Appendix: A Brief Account of Molecular Dynamics 240 16.9.1 Newtonian's Equations of Motion 241 16.9.2 Potential Functions 242 16.9.3 Numerical Solution of the Dynamical System 245 17 Statistical Mechanics Basis of Classical Thermodynamics 249 17.1 Introductory Remarks 249 17.2 Energy and the First Law of Thermodynamics 250 17.3 Statistical Mechanics Interpretation of the Rate of Work in Quasi-Static Processes 251 17.4 Statistical Mechanics Interpretation of the First Law of Thermodynamics 254 17.4.1 Statistical Interpretation of Q 256 17.5 Entropy and the Partition Function 257 17.6 Conjugate Hamiltonians 259 17.7 The Gibbs Relations 261 17.8 Monte Carlo and Metropolis Methods 262 17.8.1 The Partition Function for a Canonical Ensemble 263 17.8.2 The Metropolis Method 264 17.9 Kinetic Theory: Boltzmann's Equation of Nonequilibrium Statistical Mechanics 265 17.9.1 Boltzmann's Equation 265 17.9.2 Collision Invariants 268 17.9.3 The Continuum Mechanics of Compressible Fluids and Gases: The Macroscopic Balance Laws 269 Exercises 273 Bibliography 317 Index 325

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Book SynopsisA powerful, unified approach to mathematical and computational modeling in science and engineering Mathematical and computational modeling makes it possible to predict the behavior of a broad range of systems across a broad range of disciplines. This text guides students and professionals through the axiomatic approach, a powerful method that will enable them to easily master the principle types of mathematical and computational models used in engineering and science. Readers will discover that this axiomatic approach not only enables them to systematically construct effective models, it also enables them to apply these models to any macroscopic physical system. Mathematical Modeling in Science and Engineering focuses on models in which the processes to be modeled are expressed as systems of partial differential equations. It begins with an introductory discussion of the axiomatic formulation of basic models, setting the foundation for further topics such as:Table of ContentsPreface xiii 1 AXIOMATIC FORMULATION OF THE BASIC MODELS 1 1.1 Models 1 1.2 Microscopic and macroscopic physics 2 1.3 Kinematics of continuous systems 3 1.3.1 Intensive properties 6 1.3.2 Extensive properties 8 1.4 Balance equations of extensive and intensive properties 9 1.4.1 Global balance equations 9 1.4.2 The local balance equations 10 1.4.3 The role of balance conditions in the modeling of continuous systems 13 1.4.4 Formulation of motion restrictions by means of balance equations 14 1.5 Summary 16 2 MECHANICS OF CLASSICAL CONTINUOUS SYSTEMS 23 2.1 One-phase systems 23 2.2 The basic mathematical model of one-phase systems 24 2.3 The extensive/intensive properties of classical mechanics 25 2.4 Mass conservation 26 2.5 Linear momentum balance 27 2.6 Angular momentum balance 29 2.7 Energy concepts 32 2.8 The balance of kinetic energy 33 2.9 The balance of internal energy 34 2.10 Heat equivalent of mechanical work 35 2.11 Summary of basic equations for solid and fluid mechanics 35 2.12 Some basic concepts of thermodynamics 36 2.12.1 Heat transport 36 2.13 Summary 38 3 MECHANICS OF NON-CLASSICAL CONTINUOUS SYSTEMS 45 3.1 Multiphase systems 45 3.2 The basic mathematical model of multiphase systems 46 3.3 Solute transport in a free fluid 47 3.4 Transport by fluids in porous media 49 3.5 Flow of fluids through porous media 51 3.6 Petroleum reservoirs: the black-oil model 52 3.6.1 Assumptions of the black-oil model 53 3.6.2 Notation 53 3.6.3 Family of extensive properties 54 3.6.4 Differential equations and jump conditions 55 3.7 Summary 57 4 SOLUTE TRANSPORT BY A FREE FLUID 63 4.1 The general equation of solute transport by a free fluid 64 4.2 Transport processes 65 4.2.1 Advection 65 4.2.2 Diffusion processes 65 4.3 Mass generation processes 66 4.4 Differential equations of diffusive transport 67 4.5 Well-posed problems for diffusive transport 69 4.5.1 Time-dependent problems 70 4.5.2 Steady state 71 4.6 First-order irreversible processes 71 4.7 Differential equations of non-diffusive transport 73 4.8 Well-posed problems for non-diffusive transport 73 4.8.1 Well-posed problems in one spatial dimension 74 4.8.2 Well-posed problems in several spatial dimensions 79 4.8.3 Well-posed problems for steady-state models 80 4.9 Summary 80 5 FLOW OF A FLUID IN A POROUS MEDIUM 85 5.1 Basic assumptions of the flow model 85 5.2 The basic model for the flow of a fluid through a porous medium 86 5.3 Modeling the elasticity and compressibility 87 5.3.1 Fluid compressibility 87 5.3.2 Pore compressibility 88 5.3.3 The storage coefficient 90 5.4 Darcy's law 90 5.5 Piezometric level 92 5.6 General equation governing flow through a porous medium 94 5.6.1 Special forms of the governing differential equation 95 5.7 Applications of the jump conditions 96 5.8 Well-posed problems 96 5.8.1 Steady-state models 97 5.8.2 Time-dependent problems 99 5.9 Models with a reduced number of spatial dimensions 99 5.9.1 Theoretical derivation of a 2-D model for a confined aquifer 100 5.9.2 Leaky aquitard method 102 5.9.3 The integrodifferential equations approach 104 5.9.4 Other 2-D aquifer models 108 5.10 Summary 111 6 SOLUTE TRANSPORT IN A POROUS MEDIUM 117 6.1 Transport processes 118 6.1.1 Advection 118 6.2 Non-conservative processes 118 6.2.1 First-order irreversible processes 119 6.2.2 Adsorption 119 6.3 Dispersion-diffusion 121 6.4 The equations for transport of solutes in porous media 123 6.5 Well-posed problems 125 6.6 Summary 125 7 MULTIPHASE SYSTEMS 129 7.1 Basic model for the flow of multiple-species transport in a multiple-fluid- phase porous medium 129 7.2 Modeling the transport of species i in phase a 130 7.3 The saturated flow case 133 7.4 The air-water system 137 7.5 The immobile air unsaturated flow model 142 7.6 Boundary conditions 143 7.7 Summary 145 8 ENHANCED OIL RECOVERY 149 8.1 Background on oil production and reservoir modeling 149 8.2 Processes to be modeled 151 8.3 Unified formulation of EOR models 151 8.4 The black-oil model 152 8.5 The Compositional Model 156 8.6 Summary 160 9 LINEAR ELASTICITY 165 9.1 Introduction 165 9.2 Elastic Solids 166 9.3 The Linear Elastic Solid 167 9.4 More on the Displacement Field Decomposition 170 9.5 Strain Analysis 171 9.6 Stress Analysis 173 9.7 Isotropic materials 175 9.8 Stress-strain relations for isotropic materials 177 9.9 The governing differential equations 179 9.9.1 Elastodynamics 180 9.9.2 Elastostatics 180 9.10 Well-posed problems 181 9.10.1 Elastostatics 181 9.10.2 Elastodynamics 181 9.11 Representation of solutions for isotropic elastic solids 182 9.12 Summary 183 10 FLUID MECHANICS 189 10.1 Introduction 189 10.2 Newtonian fluids: Stokes' constitutive equations 190 10.3 Navier-Stokes equations 192 10.4 Complementary constitutive equations 193 10.5 The concepts of incompressible and inviscid fluids 193 10.6 Incompressible fluids 194 10.7 Initial and boundary conditions 195 10.8 Viscous incompressible fluids: steady states 196 10.9 Linearized theory of incompressible fluids 196 10.10 Ideal fluids 197 10.11 Irrotational flows 198 10.12 Extension of Bernoulli's relations to compressible fluids 199 10.13 Shallow-water theory 200 10.14 Inviscid compressible fluids 202 10.14.1 Small perturbations in a compressible fluid: the theory of sound 203 10.14.2 Initiation of motion 204 10.14.3 Discontinuous models and shock conditions 206 10.15 Summary 208 A: PARTIAL DIFFERENTIAL EQUATIONS 211 A. 1 Classification 211 A.2 Canonical forms 213 A.3 Well-posed problems 213 A.3.1 Boundary-value problems: the elliptic case 214 A.3.2 Initial-boundary-value problems 214 B: SOME RESULTS FROM THE CALCULUS 217 B.l Notation 217 B.2 Generalized Gauss Theorem 218 C: PROOF OF THEOREM 221 D: THE BOUNDARY LAYER INCOMPRESSIBILITY APPROXIMATION 225 E: INDICIAL NOTATION 229 E.l General 229 E.2 Matrix algebra 230 E.3 Applications to differential calculus 232 Index 235

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