Maths for engineers Books

Book SynopsisMATLAB and Simulink Crash Course for Engineers is a reader-friendly introductory guide to the features, functions, and applications of MATLAB and Simulink. The book provides readers with real-world examples, exercises, and applications, and offers highly illustrated, step-by-step demonstrations of techniques for the modelling and simulation of complex systems. MATLAB coverage includes vectors and matrices, programs and functions, complex numbers, visualization, solving equations, numerical methods, optimization problems, and graphical user interfaces. The Simulink coverage includes commonly used Simulink blocks, control system simulation, electrical circuit analysis, electric power systems, power electronics, and renewable energy technology. This powerful tutorial is a great resource for students, engineers, and other busy technical professionals who need to quickly acquire a solid understanding of MATLAB and Simulink.Table of ContentsIntroduction to MATLAB.- Vectors and Matrices.- Programs and Functions.- Complex Numbers.- Visualization.- Solving Equations.- Numerical Methods in MATLAB.- Electrical Circuit Analysis.- Control System and MATLAB.- Optimization Problem.- App Designer and Graphical User Interface in MATLAB.- Introduction to Simulink.- Control System in Simulink.- Commonly Used Simulink Blocks.- Electrical Circuit Analysis in Simulink.- Application of Simulink in Power Systems.- Application of Simulink in Power Electronics.- Application of Simulink in Renewable Energy Technology.

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

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

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Book SynopsisThis book offers a complete and detailed introduction to the theory of discrete dynamical systems, with special attention to stability of fixed points and periodic orbits. It provides a solid mathematical background and the essential basic knowledge for further developments such as, for instance, deterministic chaos theory, for which many other references are available (but sometimes, without an exhaustive presentation of preliminary notions). Readers will find a discussion of topics sometimes neglected in the research literature, such as a comparison between different predictions achievable by the discrete time model and the continuous time model of the same application. Another novel aspect of this book is an accurate analysis of the way a fixed point may lose stability, introducing and comparing several notions of instability: simple instability, repulsivity, and complete instability. To help the reader and to show the flexibility and potentiality of the discrete approach to dynamics, many examples, numerical simulations, and figures have been included. The book is used as a reference material for courses at a doctoral or upper undergraduate level in mathematics and theoretical engineering.Trade Review“The book is well written, easy to read and has many exciting examples to motivate the results. Therefore, it is a book which deserves to be read.” (José S. Cánovas Peña, Mathematical Reviews, January, 2023)“This quite small book belonging to a series entitled ‘Mathematical Engineering’ is a self-contained introduction to discrete- time systems. Motivated by applications arising from physics, engineering … economics and other natural sciences, it is mainly addressed to students, aiming to show that discrete dynamics deserves its own interest and is not easy to study. … The reviewed book can be considered … as a preliminary study for more complete monographs … .” (Vladimir Răsvan, zbMATH 1492.37001, 2022)Table of ContentsDiscrete dynamical systems.- Stability and attraction.- Bifurcations.- Positive linear systems.

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

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

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

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

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

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Book SynopsisSince Additive Manufacturing (AM) techniques allow the manufacture of complex-shaped structures the combination of lightweight construction, topology optimization, and AM is of significant interest. Besides the established continuum topology optimization methods, less attention is paid to algorithm-driven optimization based on linear optimization, which can also be used for topology optimization of truss-like structures.To overcome this shortcoming, we combined linear optimization, Computer-Aided Design (CAD), numerical shape optimization, and numerical simulation into an algorithm-driven product design process for additively manufactured truss-like structures. With our Ansys SpaceClaim add-in construcTOR, which is capable of obtaining ready-for-machine-interpretation CAD data of truss-like structures out of raw mathematical optimization data, the high performance of (heuristic-based) optimization algorithms implemented in linear programming software is now available to the CAD community.Table of ContentsIntroduction.- Physical and Technical Background.- Optimization of Truss Structures.- Bridging Algorithm-Driven Truss Optimization and Additive Manufacturing.- Mixed-Integer Linear Programming for Truss Optimization.- CAD-Based Mathematical Optimization.- Computational Study.- Conclusion and Outlook.

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Book SynopsisThis book presents the state-of-the-art in simulation on supercomputers. Leading researchers present results achieved on systems of the High Performance Computing Center Stuttgart (HLRS) for the year 2012. The reports cover all fields of computational science and engineering ranging from CFD via computational physics and chemistry to computer science with a special emphasis on industrially relevant applications. Presenting results for both vector-systems and micro-processor based systems the book allows to compare performance levels and usability of various architectures. As HLRS operates not only a large cluster system but also one of the largest NEC vector systems in the world this book gives an excellent insight also into the potential of vector systems. The book covers the main methods in high performance computing. Its outstanding results in achieving highest performance for production codes are of particular interest for both the scientist and the engineer. The book comes with a wealth of coloured illustrations and tables of results. ​Table of Contents1. Physics.- 2. Solid State Physics.- 3. Reacting Flows.- 4. Computational Fluid Dynamics.- 5. Transport and Climate.- 6. Miscellaneous Topics.

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

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

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Book SynopsisThis book introduces Python programming language and fundamental concepts in algorithms and computing. Its target audience includes students and engineers with little or no background in programming, who need to master a practical programming language and learn the basic thinking in computer science/programming. The main contents come from lecture notes for engineering students from all disciplines, and has received high ratings. Its materials and ordering have been adjusted repeatedly according to classroom reception. Compared to alternative textbooks in the market, this book introduces the underlying Python implementation of number, string, list, tuple, dict, function, class, instance and module objects in a consistent and easy-to-understand way, making assignment, function definition, function call, mutability and binding environments understandable inside-out. By giving the abstraction of implementation mechanisms, this book builds a solid understanding of the Python programming language.Trade Review“There are 11 chapters, each of which has a selection of exercises at the end. The problems are well written and generally increase in complexity. … Tailored to the instructor, it provides a good foundation.” (David Bellin, Computing Reviews, October, 2015)Table of ContentsIntroduction.- The first Python program.- More mathematical power.- The need of flow control.- Loops and problem solving.- Functions and better organizing of code.- Lists, mutability and efficiency.- Solving more complex problems.- Data organization.- More on functions.- More Python syntax.- Customized types.- Summary.

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

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

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Book SynopsisThis open access book contains review papers authored by thirteen plenary invited speakers to the 9th International Congress on Industrial and Applied Mathematics (Valencia, July 15-19, 2019). Written by top-level scientists recognized worldwide, the scientific contributions cover a wide range of cutting-edge topics of industrial and applied mathematics: mathematical modeling, industrial and environmental mathematics, mathematical biology and medicine, reduced-order modeling and cryptography. The book also includes an introductory chapter summarizing the main features of the congress. This is the first volume of a thematic series dedicated to research results presented at ICIAM 2019-Valencia Congress.Table of Contents1 M. Berger, Asteroid-Generated Tsunamis: A Review.- 2 A. Bermúdez, Some Case Studies in Environmental and Industrial Mathematics.- 3 Z. Cai et al., Hyperbolic Model Reduction for Kinetic Equations.- 4 A. Cohen et al., State Estimation - The Role of Reduced Models.- 5 C. Conca, Modelling Our Sense Of Smell.- 6 L. Edelstein-Keshet, Pattern formation inside living cells.- 7 M. Garzon et al., Efficient Algorithms for Tracking Moving Interfaces.- 8 K. Lauter, Private AI: Machine Learning on Encrypted Data.- 9 C. Le Bris, Mathematical approaches for contemporary materials science: Addressing defects in the microstructure.- 10 H. Leng et al., An iterative thresholding method for topology optimization for the Navier-Stokes flow.- 11 K. Sako, Cryptography and Digital Transformation.- 12 H. Suito et al., Numerical Study for Blood Flows in Thoracic Aorta.- 13 J.A.C. Weideman, Dynamics of Complex Singularities of Nonlinear PDEs: Analysis and Computation.

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

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

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

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Book SynopsisComprehensive, classic introduction to space-flight engineering for advanced undergraduate and graduate students provides basic tools for quantitative analysis of the motions of satellites and other vehicles in space.

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

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

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Book SynopsisThis comprehensive guide to Bayesian methods in astronomy enables hands-on work by supplying complete R, JAGS, Python, and Stan code, to use directly or to adapt. A must-have for astronomers, its concrete focus on modeling, analysis, and interpretation will also be attractive to researchers in the sciences more broadly.Trade Review'This volume is a very welcome addition to the small but growing library of resources for advanced analysis of astronomical data. Astronomers are often confronted with complex constrained regression problems, situations that benefit from computationally intensive Bayesian approaches. The authors provide a unique and sophisticated guide with tutorials in methodology and software implementation. The worked examples are impressive. Many astronomers use Python and will benefit from the less familiar capabilities of R, Stan, and JAGS for Bayesian analysis. I suspect the work will also be useful to scientists in other fields who venture into the world of Bayesian computational statistics.' Eric D. Feigelson, Pennsylvania State University, author of Modern Statistical Methods for Astronomy'Encyclopaedic in scope, a treasure trove of ready code for the hands-on practitioner.' Ben Wandelt, Paris Institute of Astrophysics, Institut Lagrange de Paris, Université Paris-Sorbonne'This informative book is a valuable resource for astronomers, astrophysicists, and cosmologists at all levels of their career. From students starting out in the field to researchers at the frontiers of data analysis, everyone will find insightful techniques accompanied by helpful examples of code. With this book, Hilbe, de Souza, and Ishida are firmly taking astrostatistics into the twenty-first century.' Roberto Trotta, Imperial College London, author of The Edge of the Sky'… the focus of the book is not on providing a full understanding of how the distributions arise, but to give guidelines on how to write code for applications, including building multi-level models, and here it succeeds well, and is an excellent resource in conjunction with powerful packages such as STAN and JAGS.' Alan Heavens, The ObservatoryTable of ContentsPreface; 1. Astrostatistics; 2. Prerequisites; 3. Frequentist vs Bayesian methods; 4. Normal linear models; 5. GLM part I - continuous and binomial models; 6. GLM part II - count models; 7. GLM part III - zero-inflated and hurdle models; 8. Hierarchical GLMMs; 9. Model selection; 10. Astronomical applications; 11. The future of astrostatistics; Appendix A. Bayesian modeling using INLA; Bibliography; Index.

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Book SynopsisADVANCED ENGINEERING MATHEMATICS AND ANALYSIS: VOLUME 1 offers a straightforward approach to understanding the theory of several engineering tools that are used to compute, evaluate, and analyse practical problems. It is a mathematics textbook that can be used by students, instructors, and technical carriers. Throughout the five chapters of the book, besides the pure mathematical examples, several practical issues from different fields are modelled and solved to illustrate the relation between the theory and its applications. The book elucidates the subjects in a self-contained style. This volume contains the basics and advanced topics of linear algebra and matrix theory, two-chapter ordinary differential equations to elaborate many classes, Laplace transforms with fundamental applications, and a complete engineering course of numerical methods. Each chapter ends with exercises that are arranged according to the chapter sections. The readers will find the answers at the end of the book.Table of ContentsPreface; Acknowledgements; Linear Algebra and Matrices; Differential Equations: Part I; Differential Equations: Part II; Laplace Transforms; Numerical Methods; Answers to Selected Exercises; References; Index.

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Book SynopsisGrid generation deals with the use of grids (meshes) in the numerical solution of partial differential equations by finite elements, finite volume, finite differences and boundary elements. Grid generation is applied in the aerospace, mechanical engineering and scientific computing fields. This book presents new research in the field.

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Book SynopsisCryptography is the study of methods to transform information from its original comprehensible form into a scrambled incomprehensible form, such that its content can only be disclosed to some qualified persons. In the past, cryptography helped ensure secrecy in important communications, such as those of spies, military leaders, and diplomats. In recent decades, it has expanded in two main ways: firstly, it provides mechanisms for more than just keeping secrets through schemes like digital signatures, digital cash, etc; secondly, cryptography is used by almost all computer users as it is embedded into the infrastructure for computing and telecommunications. Cryptography ensures secure communications through confidentiality, integrity, authenticity and non-repudiation. Cryptography has evolved over the years from Julius Cesar''s cipher, which simply shifts the letters of the words a fixed number of times, to the sophisticated RSA algorithm, which was invented by Ronald L. Rivest, Adi Shamir and Leonard M. Adleman, and the elegant AES cipher (Advanced Encryption Standard), which was invented by Joan Daemen and Vincent Rijmen. The need for fast but secure cryptographic systems is growing bigger. Therefore, dedicated hardware for cryptography is becoming a key issue for designers. With the spread of reconfigurable hardware such as FPGAs, embedded cryptographic hardware became cost-effective. Nevertheless, it is worthy to note that nowadays, even hardwired cryptographic algorithms are not safe. Attacks based on power consumption and electromagnetic Analysis, such as SPA, DPA and EMA have been successfully used to retrieve secret information stored in cryptographic devices. Besides performance in terms of area and throughput, designer of embedded cryptographic hardware must worry about the leakage of their implementations. The content of this book is divided into three main parts, which are focused on new trends in cryptographic hardware, arithmetic and factoring.

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Book SynopsisResearch and development in scientific computing and computational science has considerably increased the power of numerical simulation. Engineers and researchers are now able to solve large and complex problems which were impossible to solve in the past. This new book presents some techniques, methods and algorithms for solving engineering problems arising in energy and environment applications.

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Book SynopsisLinear algebra has become the subject to know for people in quantitative disciplines of all kinds. No longer the exclusive domain of mathematicians and engineers, it is now used everywhere there is data and everybody who works with data needs to know more. This new book from Professor Gilbert Strang, author of the acclaimed Introduction to Linear Algebra, now in its fifth edition, makes linear algebra accessible to everybody, not just those with a strong background in mathematics. It takes a more active start, beginning by finding independent columns of small matrices, leading to the key concepts of linear combinations and rank and column space. From there it passes on to the classical topics of solving linear equations, orthogonality, linear transformations and subspaces, all clearly explained with many examples and exercises. The last major topics are eigenvalues and the important singular value decomposition, illustrated with applications to differential equations and image compression. A final optional chapter explores the ideas behind deep learning.

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Book Synopsis Scientific Computing for Scientists and Engineers is designed to teach undergraduate students relevant numerical methods and required fundamentals in scientific computing. Most problems in science and engineering require the solution of mathematical problems, most of which can only be done on a computer. Accurately approximating those problems requires solving differential equations and linear systems with millions of unknowns, and smart algorithms can be used on computers to reduce calculation times from years to minutes or even seconds. This book explains: How can we approximate these important mathematical processes? How accurate are our approximations? How efficient are our approximations? Scientific Computing for Scientists and Engineers covers: An introduction to a wide range of numerical methods for linear systems, eigenvalue problems, differential equations, numerical integration, and nonlinear problems; Scientific computing fundamentals like floating point representation of numbers and convergence; Analysis of accuracy and efficiency; Simple programming examples in MATLAB to illustrate the algorithms and to solve real life problems; Exercises to reinforce all topics.

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Book Synopsis

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Book SynopsisThis book is a new edition of Tensors and Manifolds: With Applications to Mechanics and Relativity which was published in 1992. It is based on courses taken by advanced undergraduate and beginning graduate students in mathematics and physics, giving an introduction to the expanse of modern mathematics and its application in modern physics. It aims to fill the gap between the basic courses and the highly technical and specialised courses which both mathematics and physics students require in their advanced training, while simultaneously trying to promote, at an early stage, a better appreciation and understanding of each other''s discipline. The book sets forth the basic principles of tensors and manifolds, describing how the mathematics underlies elegant geometrical models of classical mechanics, relativity and elementary particle physics. The existing material from the first edition has been reworked and extended in some sections to provide extra clarity, as well as additional problemTrade ReviewReview from previous edition Clearly written and self-contained and, in particular, the author has succeeded in combining mathematical rigor with a certain degree of informality in a satisfactory way. As such, this work will certainly be appreciated by a wide audience. * Mathematical Reviews, August 1993 *Table of Contents1. Vector spaces ; 2. Multilinear mappings and dual spaces ; 3. Tensor product spaces ; 4. Tensors ; 5. Symmetric and skew-symmetric tensors ; 6. Exterior (Grassmann) algebra ; 7. The tangent map of real cartesian spaces ; 8. Topological spaces ; 9. Differentiable manifolds ; 10. Submanifolds ; 11. Vector fields, 1-forms and other tensor fields ; 12. Differentiation and integration of differential forms ; 13. The flow and the Lie derivative of a vector field ; 14. Integrability conditions for distributions and for pfaffian systems ; 15. Pseudo-Riemannian manifolds ; 16. Connection 1-forms ; 17. Connection on manifolds ; 18. Mechanics ; 19. Additional topics in mechanics ; 20. A spacetime ; 21. Some physics on Minkowski spacetime ; 22. Einstein spacetimes ; 23. Spacetimes near an isolated star ; 24. Nonempty spacetimes ; 25. Lie groups ; 26. Fiber bundles ; 27. Connections on fiber bundles ; 28. Gauge theory

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Book SynopsisThis monograph provides a treatment of the theory of algebraic Riccati equations, an area of increasing interest in the mathematics and engineering communities. A range of applications are covered, demonstrating the use of these equations for providing solutions to complex problems.Table of Contents1. Preliminaries from the theory of matrices ; 2. Indefinite scalar products ; 3. Skew-symmetric scalar products ; 4. Matrix theory and control ; 5. Linear matrix equations ; 6. Rational matrix functions ; 7. Geometric theory: the complex case ; 8. Geometric theory: the real case ; 9. Constructive existence and comparison theorems ; 10. Hermitian solutions and factorizations of rational matrix functions ; 11. Perturbation theory ; 12. Geometric theory for the discrete algebraic Riccati equation ; 13. Constructive existence and comparison theorems ; 14. Perturbation theory for discrete algebraic Riccati equations ; 15. Discrete algebraic Riccati equations and matrix pencils ; 16. Linear-quadratic regulator problems ; 17. The discrete Kalman filter ; 18. The total least squares technique ; 19. Canonical factorization ; 20. Hoo control problems ; 21. Contractive rational matrix functions ; 22. The matrix sign function ; 23. Structured stability radius ; Bibliography ; List of notations ; Index

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Book SynopsisThis book is aimed at those readers who already have some knowledge of mathematical methods and have also been introduced to the basic ideas of quantum optics. It should be attractive to students who have already explored one of the more introductory texts such as Loudon''s The quantum theory of light (2/e, 1983, OUP) and are seeking to acquire the mathematical skills used in real problems. This book is not primarily about the physics of quantum optics but rather presents the mathematical methods widely used by workers in this field. There is no comparable book which covers either the range or the depth of mathematical techniques.Trade Review... the authors are well-known for their work on topics, such as the quantum-phase operator and quasi-probability distribution so theory PhD students will be able to learn these subjects direct from the horse's mouth. The authors have [] included, for pedagogic purposes, extra detail of the mathematical workings that a PhD student would not be able find in the research literature. * New Scientist, 6 June 1998 *The reader will find here a very clear presentation of material not readily found elsewhere. Postgraduate students of quantum optics will find this work to be of the greatest utility... Care has been taken to present quite difficult topics in the simplest and most straightforward way; and yet the treatment is concise and focused... Experienced researchers will find that this text is a most convenient handbook of techniques, and will want it close to their elbow. * Contemporary Physics, 1998, vol. 39, no. 4 *Table of Contents1. Foundations ; 2. Coherent interactions ; 3. Operators and states ; 4. Quantum statistics of fields ; 5. Dissipative processes ; 6. Dressed states ; Appendices ; Selected bibliography ; Index

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Book SynopsisThis monograph explores the equivalence of signal functions with their sets of values taken at discrete points. Beginning with an introduction to the main ideas, and background material on Fourier analysis and Hilbert spaces and their bases, it covers a wide variety of topics.Trade Review...the text is written by use of LATEX and its beautiful graphics reveal the power and the advantages of this system. * Zentralblatt fuer Mathematik 827/97 *Table of Contents1. An introduction to sampling theory ; 1.1 General introduction ; 1.2 Introduction - continued ; 1.3 The seventeenth to the mid twentieth century - a brief review ; 1.4 Interpolation and sampling from the seventeenth century to the mid twentieth century - a brief review ; 1.5 Introduction - concluding remarks ; 2. Background in Fourier analysis ; 2.1 The Fourier Series ; 2.2 The Fourier transform ; 2.3 Poisson's summation formula ; 2.4 Tempered distributions - some basic facts ; 3. Hilbert spaces, bases and frames ; 3.1 Bases for Banach and Hilbert spaces ; 3.2 Riesz bases and unconditional bases ; 3.3 Frames ; 3.4 Reproducing kernel Hilbert spaces ; 3.5 Direct sums of Hilbert spaces ; 3.6 Sampling and reproducing kernels ; 4. Finite sampling ; 4.1 A general setting for finite sampling ; 4.2 Sampling on the sphere ; 5. From finite to infinite sampling series ; 5.1 The change to infinite sampling series ; 5.2 The Theorem of Hinsen and Kloosters ; 6. Bernstein and Paley-Weiner spaces ; 6.1 Convolution and the cardinal series ; 6.2 Sampling and entire functions of polynomial growth ; 6.3 Paley-Weiner spaces ; 6.4 The cardinal series for Paley-Weiner spaces ; 6.5 The space ReH1 ; 6.6 The ordinary Paley-Weiner space and its reproducing kernel ; 6.7 A convergence principle for general Paley-Weiner spaces ; 7. More about Paley-Weiner spaces ; 7.1 Paley-Weiner theorems - a review ; 7.2 Bases for Paley-Weiner spaces ; 7.3 Operators on the Paley-Weiner space ; 7.4 Oscillatory properties of Paley-Weiner functions ; 8. Kramer's lemma ; 8.1 Kramer's Lemma ; 8.2 The Walsh sampling therem ; 9. Contour integral methods ; 9.1 The Paley-Weiner theorem ; 9.2 Some formulae of analysis and their equivalence ; 9.3 A general sampling theorem ; 10. Ireggular sampling ; 10.1 Sets of stable sampling, of interpolation and of uniqueness ; 10.2 Irregular sampling at minimal rate ; 10.3 Frames and over-sampling ; 11. Errors and aliasing ; 11.1 Errors ; 11.2 The time jitter error ; 11.3 The aliasing error ; 12. Multi-channel sampling ; 12.1 Single channel sampling ; 12.3 Two channels ; 13. Multi-band sampling ; 13.1 Regular sampling ; 13.3 An algorithm for the optimal regular sampling rate ; 13.4 Selectively tiled band regions ; 13.5 Harmonic signals ; 13.6 Band-ass sampling ; 14. Multi-dimensional sampling ; 14.1 Remarks on multi-dimensional Fourier analysis ; 14.2 The rectangular case ; 14.3 Regular multi-dimensional sampling ; 15. Sampling and eigenvalue problems ; 15.1 Preliminary facts ; 15.2 Direct and inverse Sturm-Liouville problems ; 15.3 Further types of eigenvalue problem - some examples ; 16. Campbell's generalised sampling theorem ; 16.1 L.L. Campbell's generalisation of the sampling theorem ; 16.2 Band-limited functions ; 16.3 Non band-limited functions - an example ; 17. Modelling, uncertainty and stable sampling ; 17.1 Remarks on signal modelling ; 17.2 Energy concentration ; 17.3 Prolate Spheroidal Wave functions ; 17.4 The uncertainty principle of signal theory ; 17.5 The Nyquist-Landau minimal sampling rate

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

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

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

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

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