Introduction to Random Signals and Applied Kalman Filtering With MATLAB Exercises

This definitive textbook provides a solid introduction to discrete and continuous stochastic processes, tackling a complex field in a way that instils a deep understanding of the relevant mathematical principles, and develops an intuitive grasp of the way these principles can be applied to modelling real-world systems. It includes a careful review of elementary probability and detailed coverage of Poisson, Gaussian and Markov processes with richly varied queuing applications. The theory and applications of inference, hypothesis testing, estimation, random walks, large deviations, martingales and investments are developed. Written by one of the world's leading information theorists, evolving over twenty years of graduate classroom teaching and enriched by over 300 exercises, this is an exceptional resource for anyone looking to develop their understanding of stochastic processes.

Genetic linkage maps are an increasingly important tool in both fundamental and applied research, enabling the study and deployment of genes that determine important biological traits. This concise introduction to genetic mapping in species with disomic inheritance enables life science graduate students and researchers to use mapping software to produce more reliable results. After a brief refresher on meiosis and genetic recombination, the steps in the map construction procedure are described, with explanations of the computations involved. The emphasis throughout is on the practical application of the methods described; detailed mathematical formulae are avoided and exercises are included to help readers consolidate their understanding. A chapter on recognising and solving problems provides valuable guidance for dealing with real-life situations. An extensive chapter dedicated to the more complex situation of outbreeding species offers a unique insight into the approach required for

Genetic linkage maps are an increasingly important tool in both fundamental and applied research, enabling the study and deployment of genes that determine important biological traits. This concise introduction to genetic mapping in species with disomic inheritance enables life science graduate students and researchers to use mapping software to produce more reliable results. After a brief refresher on meiosis and genetic recombination, the steps in the map construction procedure are described, with explanations of the computations involved. The emphasis throughout is on the practical application of the methods described; detailed mathematical formulae are avoided and exercises are included to help readers consolidate their understanding. A chapter on recognising and solving problems provides valuable guidance for dealing with real-life situations. An extensive chapter dedicated to the more complex situation of outbreeding species offers a unique insight into the approach required for

This two-volume text in harmonic analysis introduces a wealth of analytical results and techniques. It is largely self-contained and useful to graduates and researchers in pure and applied analysis. Numerous exercises and problems make the text suitable for self-study and the classroom alike. The first volume starts with classical one-dimensional topics: Fourier series; harmonic functions; Hilbert transform. Then the higher-dimensional Calderón–Zygmund and Littlewood–Paley theories are developed. Probabilistic methods and their applications are discussed, as are applications of harmonic analysis to partial differential equations. The volume concludes with an introduction to the Weyl calculus. The second volume goes beyond the classical to the highly contemporary and focuses on multilinear aspects of harmonic analysis: the bilinear Hilbert transform; Coifman–Meyer theory; Carleson's resolution of the Lusin conjecture; Calderón's commutators and the Cauchy integral on Lipschitz curves. T

This two-volume text in harmonic analysis introduces a wealth of analytical results and techniques. It is largely self-contained and useful to graduates and researchers in pure and applied analysis. Numerous exercises and problems make the text suitable for self-study and the classroom alike. The first volume starts with classical one-dimensional topics: Fourier series; harmonic functions; Hilbert transform. Then the higher-dimensional Calderón–Zygmund and Littlewood–Paley theories are developed. Probabilistic methods and their applications are discussed, as are applications of harmonic analysis to partial differential equations. The volume concludes with an introduction to the Weyl calculus. The second volume goes beyond the classical to the highly contemporary and focuses on multilinear aspects of harmonic analysis: the bilinear Hilbert transform; Coifman–Meyer theory; Carleson's resolution of the Lusin conjecture; Calderón's commutators and the Cauchy integral on Lipschitz curves. T

Bernard Helffer's graduate-level introduction to the basic tools in spectral analysis is illustrated by numerous examples from the Schrödinger operator theory and various branches of physics: statistical mechanics, superconductivity, fluid mechanics and kinetic theory. The later chapters also introduce non self-adjoint operator theory with an emphasis on the role of the pseudospectra. The author's focus on applications, along with exercises and examples, enables readers to connect theory with practice so that they develop a good understanding of how the abstract spectral theory can be applied. The final chapter provides various problems that have been the subject of active research in recent years and will challenge the reader's understanding of the material covered.

Many electronic and acoustic signals can be modelled as sums of sinusoids and noise. However, the amplitudes, phases and frequencies of the sinusoids are often unknown and must be estimated in order to characterise the periodicity or near-periodicity of a signal and consequently to identify its source. This book presents and analyses several practical techniques used for such estimation. The problem of tracking slow frequency changes over time of a very noisy sinusoid is also considered. Rigorous analyses are presented via asymptotic or large sample theory, together with physical insight. The book focuses on achieving extremely accurate estimates when the signal to noise ratio is low but the sample size is large. Each chapter begins with a detailed overview, and many applications are given. Matlab code for the estimation techniques is also included. The book will thus serve as an excellent introduction and reference for researchers analysing such signals.

This two-volume text in harmonic analysis introduces a wealth of analytical results and techniques. It is largely self-contained and will be useful to graduate students and researchers in both pure and applied analysis. Numerous exercises and problems make the text suitable for self-study and the classroom alike. This first volume starts with classical one-dimensional topics: Fourier series; harmonic functions; Hilbert transform. Then the higher-dimensional Calderón–Zygmund and Littlewood–Paley theories are developed. Probabilistic methods and their applications are discussed, as are applications of harmonic analysis to partial differential equations. The volume concludes with an introduction to the Weyl calculus. The second volume goes beyond the classical to the highly contemporary and focuses on multilinear aspects of harmonic analysis: the bilinear Hilbert transform; Coifman–Meyer theory; Carleson's resolution of the Lusin conjecture; Calderón's commutators and the Cauchy integral

Covering point process theory, random geometric graphs and coverage processes, this rigorous introduction to stochastic geometry will enable you to obtain powerful, general estimates and bounds of wireless network performance and make good design choices for future wireless architectures and protocols that efficiently manage interference effects. Practical engineering applications are integrated with mathematical theory, with an understanding of probability the only prerequisite. At the same time, stochastic geometry is connected to percolation theory and the theory of random geometric graphs and accompanied by a brief introduction to the R statistical computing language. Combining theory and hands-on analytical techniques with practical examples and exercises, this is a comprehensive guide to the spatial stochastic models essential for modelling and analysis of wireless network performance.

As with the first edition, this textbook provides a clear introduction to the fundamental theory of structural analysis as applied to vehicular structures such as aircraft, spacecraft, automobiles and ships. The emphasis is on the application of fundamental concepts of structural analysis that are employed in everyday engineering practice. All approximations are accompanied by a full explanation of their validity. In this new edition, more topics, figures, examples and exercises have been added. There is also a greater emphasis on the finite element method of analysis. Clarity remains the hallmark of this text and it employs three strategies to achieve clarity of presentation: essential introductory topics are covered, all approximations are fully explained and many important concepts are repeated.

This textbook provides engineers with the capability, tools and confidence to solve real-world heat transfer problems. It includes many advanced topics, such as Bessel functions, Laplace transforms, separation of variables, Duhamel's theorem and complex combination, as well as high order explicit and implicit numerical integration algorithms. These analytical and numerical solution methods are applied to topics not considered in most textbooks. Examples include heat exchangers involving fluids with varying specific heats or phase changes; heat exchangers in which axial conduction is a concern; and regenerators. Derivations of important results are presented completely, without skipping steps, which reduces student frustration and improves readability and retention. The examples are not trivial 'textbook' exercises; they are rather complex and timely real-world problems that are inherently interesting. This book integrates the computational software packages Maple, MATLAB®, FEHT and Eng

Compressed sensing is an exciting, rapidly growing field, attracting considerable attention in electrical engineering, applied mathematics, statistics and computer science. This book provides the first detailed introduction to the subject, highlighting theoretical advances and a range of applications, as well as outlining numerous remaining research challenges. After a thorough review of the basic theory, many cutting-edge techniques are presented, including advanced signal modeling, sub-Nyquist sampling of analog signals, non-asymptotic analysis of random matrices, adaptive sensing, greedy algorithms and use of graphical models. All chapters are written by leading researchers in the field, and consistent style and notation are utilized throughout. Key background information and clear definitions make this an ideal resource for researchers, graduate students and practitioners wanting to join this exciting research area. It can also serve as a supplementary textbook for courses on compu

The instability of fluid flows is a key topic in classical fluid mechanics because it has huge repercussions for applied disciplines such as chemical engineering, hydraulics, aeronautics, and geophysics. This modern introduction is written for any student, researcher, or practitioner working in the area, for whom an understanding of hydrodynamic instabilities is essential. Based on a decade's experience of teaching postgraduate students in fluid dynamics, this book brings the subject to life by emphasizing the physical mechanisms involved. The theory of dynamical systems provides the basic structure of the exposition, together with asymptotic methods. Wherever possible, Charru discusses the phenomena in terms of characteristic scales and dimensional analysis. The book includes numerous experimental studies, with references to videos and multimedia material, as well as over 150 exercises which introduce the reader to new problems.

The instability of fluid flows is a key topic in classical fluid mechanics because it has huge repercussions for applied disciplines such as chemical engineering, hydraulics, aeronautics, and geophysics. This modern introduction is written for any student, researcher, or practitioner working in the area, for whom an understanding of hydrodynamic instabilities is essential. Based on a decade's experience of teaching postgraduate students in fluid dynamics, this book brings the subject to life by emphasizing the physical mechanisms involved. The theory of dynamical systems provides the basic structure of the exposition, together with asymptotic methods. Wherever possible, Charru discusses the phenomena in terms of characteristic scales and dimensional analysis. The book includes numerous experimental studies, with references to videos and multimedia material, as well as over 150 exercises which introduce the reader to new problems.

Quantum mesoscopic physics covers a whole class in interference effects related to the propagation of waves in complex and random media. These effects are ubiquitous in physics, from the behaviour of electrons in metals and semiconductors to the propagation of electromagnetic waves in suspensions such as colloids, and quantum systems like cold atomic gases. A solid introduction to quantum mesoscopic physics, this book is a modern account of the problem of coherent wave propagation in random media. It provides a unified account of the basic theoretical tools and methods, highlighting the common aspects of the various optical and electronic phenomena involved and presenting a large number of experimental results. With over 200 figures, and exercises throughout, the book was originally published in 2007 and is ideal for graduate students in physics, electrical engineering, applied physics, acoustics and astrophysics. It will also be an interesting reference for researchers.

In this complete introduction to the theory of finding derivatives of scalar-, vector- and matrix-valued functions with respect to complex matrix variables, Hjørungnes describes an essential set of mathematical tools for solving research problems where unknown parameters are contained in complex-valued matrices. The first book examining complex-valued matrix derivatives from an engineering perspective, it uses numerous practical examples from signal processing and communications to demonstrate how these tools can be used to analyze and optimize the performance of engineering systems. Covering un-patterned and certain patterned matrices, this self-contained and easy-to-follow reference deals with applications in a range of areas including wireless communications, control theory, adaptive filtering, resource management and digital signal processing. Over 80 end-of-chapter exercises are provided, with a complete solutions manual available online.

Differential geometry plays an increasingly important role in modern theoretical physics and applied mathematics. This textbook gives an introduction to geometrical topics useful in theoretical physics and applied mathematics, covering: manifolds, tensor fields, differential forms, connections, symplectic geometry, actions of Lie groups, bundles, spinors, and so on. Written in an informal style, the author places a strong emphasis on developing the understanding of the general theory through more than 1000 simple exercises, with complete solutions or detailed hints. The book will prepare readers for studying modern treatments of Lagrangian and Hamiltonian mechanics, electromagnetism, gauge fields, relativity and gravitation. Differential Geometry and Lie Groups for Physicists is well suited for courses in physics, mathematics and engineering for advanced undergraduate or graduate students, and can also be used for active self-study. The required mathematical background knowledge does n

Quantum field theory is the application of quantum mechanics to systems with infinitely many degrees of freedom. This 2007 textbook presents quantum field theoretical applications to systems out of equilibrium. It introduces the real-time approach to non-equilibrium statistical mechanics and the quantum field theory of non-equilibrium states in general. It offers two ways of learning how to study non-equilibrium states of many-body systems: the mathematical canonical way and an easy intuitive way using Feynman diagrams. The latter provides an easy introduction to the powerful functional methods of field theory, and the use of Feynman diagrams to study classical stochastic dynamics is considered in detail. The developed real-time technique is applied to study numerous phenomena in many-body systems. Complete with numerous exercises to aid self-study, this textbook is suitable for graduate students in statistical mechanics and condensed matter physics.

This new, fully-revised edition covers all the major topics of digital signal processing (DSP) design and analysis in a single, all-inclusive volume, interweaving theory with real-world examples and design trade-offs. Building on the success of the original, this edition includes new material on random signal processing, a new chapter on spectral estimation, greatly expanded coverage of filter banks and wavelets, and new material on the solution of difference equations. Additional steps in mathematical derivations make them easier to follow, and an important new feature is the do-it-yourself section at the end of each chapter, where readers get hands-on experience of solving practical signal processing problems in a range of MATLAB experiments. With 120 worked examples, 20 case studies, and almost 400 homework exercises, the book is essential reading for anyone taking DSP courses. Its unique blend of theory and real-world practical examples also makes it an ideal reference for practiti

This 2004 book is an accessible and comprehensive introduction to machine vision. It provides all the necessary theoretical tools and shows how they are applied in actual image processing and machine vision systems. A key feature is the inclusion of many programming exercises that give insights into the development of practical image processing algorithms. The authors begin with a review of mathematical principles and go on to discuss key issues in image processing such as the description and characterization of images, edge detection, restoration and feature extraction, segmentation, texture and shape. They also discuss image matching, statistical pattern recognition, clustering, and syntactic pattern recognition. Important applications are described, including optical character recognition and automatic target recognition. Software and data used in the book can be found at www.cambridge.org/9780521830461. A useful reference for practitioners, the book is aimed at graduate students in

Seismic interferometry is an exciting field in geophysics utilising multiple scattering events to provide unprecedented views of the Earth's subsurface. This is a comprehensive book describing the theory and practice of seismic interferometry with an emphasis on applications in exploration seismology. Exercises are provided at the end of each chapter, and the text is supplemented by online MATLAB codes that illustrate important ideas and allow readers to generate synthetic traces and invert these to determine the Earth's reflectivity structure. Later chapters reinforce these principles by deriving the rigorous mathematics of seismic interferometry. Incorporating examples that apply interferometric imaging to synthetic and field data, from applied geophysics and earthquake seismology, this book is a valuable reference for academic researchers and oil industry professionals. It can also be used to teach a one-semester course for advanced students in geophysics and petroleum engineering.

Since the original publication of this book, available computer power has increased greatly. Today, scientific computing is playing an ever more prominent role as a tool in scientific discovery and engineering analysis. In this second edition, the key addition is an introduction to the finite element method. This is a widely used technique for solving partial differential equations (PDEs) in complex domains. This text introduces numerical methods and shows how to develop, analyse, and use them. Complete MATLAB programs for all the worked examples are now available at www.cambridge.org/Moin, and more than 30 exercises have been added. This thorough and practical book is intended as a first course in numerical analysis, primarily for new graduate students in engineering and physical science. Along with mastering the fundamentals of numerical methods, students will learn to write their own computer programs using standard numerical methods.

Since the original publication of this book, available computer power has increased greatly. Today, scientific computing is playing an ever more prominent role as a tool in scientific discovery and engineering analysis. In this second edition, the key addition is an introduction to the finite element method. This is a widely used technique for solving partial differential equations (PDEs) in complex domains. This text introduces numerical methods and shows how to develop, analyse, and use them. Complete MATLAB programs for all the worked examples are now available at www.cambridge.org/Moin, and more than 30 exercises have been added. This thorough and practical book is intended as a first course in numerical analysis, primarily for new graduate students in engineering and physical science. Along with mastering the fundamentals of numerical methods, students will learn to write their own computer programs using standard numerical methods.

This introduction to some of the principal models in the theory of disordered systems leads the reader through the basics, to the very edge of contemporary research, with the minimum of technical fuss. Topics covered include random walk, percolation, self-avoiding walk, interacting particle systems, uniform spanning tree, random graphs, as well as the Ising, Potts, and random-cluster models for ferromagnetism, and the Lorentz model for motion in a random medium. Schramm–Löwner evolutions (SLE) arise in various contexts. The choice of topics is strongly motivated by modern applications and focuses on areas that merit further research. Special features include a simple account of Smirnov's proof of Cardy's formula for critical percolation, and a fairly full account of the theory of influence and sharp-thresholds. Accessible to a wide audience of mathematicians and physicists, this book can be used as a graduate course text. Each chapter ends with a range of exercises.

This is a one-stop introduction to the methods of ergodic theory applied to holomorphic iteration. The authors begin with introductory chapters presenting the necessary tools from ergodic theory thermodynamical formalism, and then focus on recent developments in the field of 1-dimensional holomorphic iterations and underlying fractal sets, from the point of view of geometric measure theory and rigidity. Detailed proofs are included. Developed from university courses taught by the authors, this book is ideal for graduate students. Researchers will also find it a valuable source of reference to a large and rapidly expanding field. It eases the reader into the subject and provides a vital springboard for those beginning their own research. Many helpful exercises are also included to aid understanding of the material presented and the authors provide links to further reading and related areas of research.

Discover what you can do with R! Introducing the R system, covering standard regression methods, then tackling more advanced topics, this book guides users through the practical, powerful tools that the R system provides. The emphasis is on hands-on analysis, graphical display, and interpretation of data. The many worked examples, from real-world research, are accompanied by commentary on what is done and why. The companion website has code and datasets, allowing readers to reproduce all analyses, along with solutions to selected exercises and updates. Assuming basic statistical knowledge and some experience with data analysis (but not R), the book is ideal for research scientists, final-year undergraduate or graduate-level students of applied statistics, and practising statisticians. It is both for learning and for reference. This third edition expands upon topics such as Bayesian inference for regression, errors in variables, generalized linear mixed models, and random forests.

Presenting a rigorous treatment of the physical and mechanical basis for the modelling of sedimentary basins, this book supplies geoscientists with practical tools for creating their own models. It begins with a thorough grounding in properties of porous media, linear elasticity, continuum mechanics and rock compressibility. Chapters on heat flow, subsidence, rheology, flexure and gravity consider sedimentary basins in the context of the Earth's lithosphere, and the book concludes with coverage of pore space cementation, compaction and fluid flow. The volume introduces basic, state-of-the-art models and demonstrates how to reproduce results using tools like MATLAB® and Octave. Main equations are derived from first principles, and their basic solutions are obtained and then applied. Separate notes sections supply more technical details, and the text is illustrated throughout with real-world examples, applications and test exercises. This is an accessible introduction to quantitative mod

Communication technology has become pervasive in the modern world, and ever more complex. Focusing on the most basic ideas, this carefully paced, logically structured textbook is packed with insights and illustrative examples, making this an ideal introduction to modern digital communication. Examples with step-by-step solutions help with the assimilation of theoretical ideas, and MATLAB exercises develop confidence in applying mathematical concepts to real-world problems. Right from the start the authors use the signal space approach to give students an intuitive feel for the modulation/demodulation process. After a review of signals and random processes, they describe core topics and techniques such as source coding, baseband transmission, modulation, and synchronization. The book closes with coverage of advanced topics such as trellis-coding, CMDA, and space-time codes to stimulate further study. This is an ideal textbook for anyone who wants to learn about modern digital communicat

Seismic interferometry is an exciting field in geophysics utilising multiple scattering events to provide unprecedented views of the Earth's subsurface. This is a comprehensive book describing the theory and practice of seismic interferometry with an emphasis on applications in exploration seismology. Exercises are provided at the end of each chapter, and the text is supplemented by online MATLAB codes that illustrate important ideas and allow readers to generate synthetic traces and invert these to determine the Earth's reflectivity structure. Later chapters reinforce these principles by deriving the rigorous mathematics of seismic interferometry. Incorporating examples that apply interferometric imaging to synthetic and field data, from applied geophysics and earthquake seismology, this book is a valuable reference for academic researchers and oil industry professionals. It can also be used to teach a one-semester course for advanced students in geophysics and petroleum engineering.

This textbook provides engineers with the capability, tools and confidence to solve real-world heat transfer problems. It includes many advanced topics, such as Bessel functions, Laplace transforms, separation of variables, Duhamel's theorem and complex combination, as well as high order explicit and implicit numerical integration algorithms. These analytical and numerical solution methods are applied to topics not considered in most textbooks. Examples include heat exchangers involving fluids with varying specific heats or phase changes; heat exchangers in which axial conduction is a concern; and regenerators. Derivations of important results are presented completely, without skipping steps, which reduces student frustration and improves readability and retention. The examples are not trivial 'textbook' exercises; they are rather complex and timely real-world problems that are inherently interesting. This book integrates the computational software packages Maple, MATLAB®, FEHT and Eng

Low-Dimensional Semiconductor Structures provides a seamless, atoms-to-devices introduction to the latest quantum heterostructures. It covers their fabrication, their electronic, optical and transport properties, their role in exploring physical phenomena, and their utilization in devices. The authors begin with a detailed description of the epitaxial growth of semiconductors. They then deal with the physical behaviour of electrons and phonons in low-dimensional structures. A discussion of localization effects and quantum transport phenomena is followed by coverage of the optical properties of quantum wells. They then go on to discuss non-linear optics in quantum heterostructures. The final chapters deal with semiconductor lasers, mesoscopic devices, and high-speed heterostructure devices. The book contains many exercises and comprehensive references. It is suitable as a textbook for graduate-level courses in electrical engineering and applied physics. It will also be of interest to en

This updated textbook is an excellent way to introduce probability and information theory to new students in mathematics, computer science, engineering, statistics, economics, or business studies. Only requiring knowledge of basic calculus, it starts by building a clear and systematic foundation to the subject: the concept of probability is given particular attention via a simplified discussion of measures on Boolean algebras. The theoretical ideas are then applied to practical areas such as statistical inference, random walks, statistical mechanics and communications modelling. Topics covered include discrete and continuous random variables, entropy and mutual information, maximum entropy methods, the central limit theorem and the coding and transmission of information, and added for this new edition is material on Markov chains and their entropy. Lots of examples and exercises are included to illustrate how to use the theory in a wide range of applications, with detailed solutions to

This updated textbook is an excellent way to introduce probability and information theory to new students in mathematics, computer science, engineering, statistics, economics, or business studies. Only requiring knowledge of basic calculus, it starts by building a clear and systematic foundation to the subject: the concept of probability is given particular attention via a simplified discussion of measures on Boolean algebras. The theoretical ideas are then applied to practical areas such as statistical inference, random walks, statistical mechanics and communications modelling. Topics covered include discrete and continuous random variables, entropy and mutual information, maximum entropy methods, the central limit theorem and the coding and transmission of information, and added for this new edition is material on Markov chains and their entropy. Lots of examples and exercises are included to illustrate how to use the theory in a wide range of applications, with detailed solutions to

This textbook is ideal for a course in engineering systems dynamics and controls. The work is a comprehensive treatment of the analysis of lumped parameter physical systems. Starting with a discussion of mathematical models in general, and ordinary differential equations, the book covers input/output and state space models, computer simulation and modeling methods and techniques in mechanical, electrical, thermal and fluid domains. Frequency domain methods, transfer functions and frequency response are covered in detail. The book concludes with a treatment of stability, feedback control (PID, lead-lag, root locus) and an introduction to discrete time systems. This new edition features many new and expanded sections on such topics as: solving stiff systems, operational amplifiers, electrohydraulic servovalves, using Matlab with transfer functions, using Matlab with frequency response, Matlab tutorial and an expanded Simulink tutorial. The work has 40% more end-of-chapter exercises and 3

Quantum field theory is the application of quantum mechanics to systems with infinitely many degrees of freedom. This 2007 textbook presents quantum field theoretical applications to systems out of equilibrium. It introduces the real-time approach to non-equilibrium statistical mechanics and the quantum field theory of non-equilibrium states in general. It offers two ways of learning how to study non-equilibrium states of many-body systems: the mathematical canonical way and an easy intuitive way using Feynman diagrams. The latter provides an easy introduction to the powerful functional methods of field theory, and the use of Feynman diagrams to study classical stochastic dynamics is considered in detail. The developed real-time technique is applied to study numerous phenomena in many-body systems. Complete with numerous exercises to aid self-study, this textbook is suitable for graduate students in statistical mechanics and condensed matter physics.

Quantum mesoscopic physics covers a whole class in interference effects related to the propagation of waves in complex and random media. These effects are ubiquitous in physics, from the behaviour of electrons in metals and semiconductors to the propagation of electromagnetic waves in suspensions such as colloids, and quantum systems like cold atomic gases. A solid introduction to quantum mesoscopic physics, this book is a modern account of the problem of coherent wave propagation in random media. It provides a unified account of the basic theoretical tools and methods, highlighting the common aspects of the various optical and electronic phenomena involved and presenting a large number of experimental results. With over 200 figures, and exercises throughout, the book was originally published in 2007 and is ideal for graduate students in physics, electrical engineering, applied physics, acoustics and astrophysics. It will also be an interesting reference for researchers.

Optimal Reliability Design, first published in 2000, provides a detailed introduction to systems reliability and reliability optimization. Techniques for maximizing system reliability are described, focusing on component reliability enhancement and redundancy arrangement. The authors present several case studies and show how optimization techniques are applied in practice. They also pay particular attention to finding methods that give the optimal trade-off between reliability and cost. The book begins with a review of key background material, and a discussion of a range of optimization models. The authors go on to cover optimization tools, such as heuristics, discrete optimization, nonlinear programming, mixed integer programming, optimal arrangement, and metaheuristic algorithms. They also describe the computational implementation of these tools. Many numerical examples are included, and the book contains over 180 homework exercises. It is suitable as a textbook for graduate-level co

Differential geometry plays an increasingly important role in modern theoretical physics and applied mathematics. This textbook gives an introduction to geometrical topics useful in theoretical physics and applied mathematics, covering: manifolds, tensor fields, differential forms, connections, symplectic geometry, actions of Lie groups, bundles, spinors, and so on. Written in an informal style, the author places a strong emphasis on developing the understanding of the general theory through more than 1000 simple exercises, with complete solutions or detailed hints. The book will prepare readers for studying modern treatments of Lagrangian and Hamiltonian mechanics, electromagnetism, gauge fields, relativity and gravitation. Differential Geometry and Lie Groups for Physicists is well suited for courses in physics, mathematics and engineering for advanced undergraduate or graduate students, and can also be used for active self-study. The required mathematical background knowledge does n

Free Probability Theory studies a special class of 'noncommutative'random variables, which appear in the context of operators on Hilbert spaces and in one of the large random matrices. Since its emergence in the 1980s, free probability has evolved into an established field of mathematics with strong connections to other mathematical areas, such as operator algebras, classical probability theory, random matrices, combinatorics, representation theory of symmetric groups. Free probability also connects to more applied scientific fields, such as wireless communication in electrical engineering. This 2006 book gives a self-contained and comprehensive introduction to free probability theory which has its main focus on the combinatorial aspects. The volume is designed so that it can be used as a text for an introductory course (on an advanced undergraduate or beginning graduate level), and is also well-suited for the individual study of free probability.

Mathematical modelling is widely used in ecology and evolutionary biology and it is a topic that many biologists find difficult to grasp. In this new textbook Marc Mangel provides a no-nonsense introduction to the skills needed to understand the principles of theoretical and mathematical biology. Fundamental theories and applications are introduced using numerous examples from current biological research, complete with illustrations to highlight key points. Exercises are also included throughout the text to show how theory can be applied and to test knowledge gained so far. Suitable for advanced undergraduate courses in theoretical and mathematical biology, this book forms an essential resource for anyone wanting to gain an understanding of theoretical ecology and evolution.