Kenneth Brakke studies in general dimensions a dynamic system of surfaces of no inertial mass driven by the force of surface tension and opposed by a frictional force proportional to velocity. He formulates his study in terms of varifold surfaces and uses the methods of geometric measure theory to develop a mathematical description of the motion of a surface by its mean curvature. This mathematical description encompasses, among other subtleties, those of changing geometries and instantaneous mass losses.

Originally published in 1978.

The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

]]>Modern electrical power systems are facing complex challenges, arising from distributed generation and intermittent renewable energy. Fuzzy logic is one approach to meeting this challenge and providing reliability and power quality.

The book is about fuzzy logic control and its applications in managing, controlling and operating electrical energy systems. It provides a comprehensive overview of fuzzy logic concepts and techniques required for designing fuzzy logic controllers, and then discusses several applications to control and management in energy systems. The book incorporates a novel fuzzy logic controller design approach in both Matlab® and in Matlab Simulink® so that the user can study every step of the fuzzy logic processor, with the ability to modify the code.

Fuzzy Logic Control in Energy Systems is an important read for researchers and practicing engineers in energy engineering and control, as well as advanced students involved with power system research and operation.

]]>The inverted pendulum is a classic problem in dynamics and control theory and is widely used as a benchmark for testing control algorithms. It is also an area of active study, with many new innovations and applications - for example the problem is solved in the technology of the Segway, a self-balancing transportation device.

This book provides an overall picture of historical and current trends and developments in nonlinear control theory, based on the simple structure and rich nonlinear model of the inverted pendulum. After an introduction to the system and open/current problems, the book covers the topic in four parts: applications of robust state estimation and control to pendulum-cart systems; controllers for under-actuated mechanical systems; nonlinear controllers for mobile inverted pendulum systems; and robust controllers based observers via Takagi-Sugeno or linear approaches.

With contributions from international researchers in the field, The Inverted Pendulum in Control Theory and Robotics is essential reading for researchers, scientists, engineers and students in the field of control theory, robotics and nonlinear systems.

]]>Glocal control, a term coined by Professor Shinji Hara at The University of Tokyo, represents a new framework for studying behaviour of complex dynamical systems from a feedback control perspective. A large number of dynamical components can be interconnected and interact with each other to form an integrated system with certain functionalities. Such complex systems are found in nature and have been created by man, including gene regulatory networks, neuronal circuits for memory, decision making, and motor control, bird flocking, global climate dynamics, central processing units for computers, electrical power grids, the World Wide Web, and financial markets. A common feature of these systems is that a global property or function emerges as a result of local, distributed, dynamical interactions of components. The objective of 'glocal' (global + local) control is to understand the mechanisms underlying this feature, analyze existing complex systems, and to design and create innovative systems with new functionalities. This book is dedicated to Professor Shinji Hara on the occasion of his 60th birthday, collecting the latest results by leading experts in control theories to lay a solid foundation towards the establishment of glocal control theory in the coming decades.

]]>As control systems become more complex and are expected to perform tasks in unknown and extreme environments, they may be subject to various types of faults in their sensors, actuators or other components. It is crucial to be able to diagnose the occurrence of faults and to repair them in order to maintain, guarantee, and improve the overall safety, reliability, and performance of the systems. This book addresses the design challenges of developing and implementing novel integrated fault diagnosis and control technologies for complex linear systems.

Integrated Fault Diagnosis and Control Design of Linear Complex Systems considers linear time-invariant (LTI) systems under both time- and event-triggered frameworks. The book initially develops novel methodologies for the problem of integrated fault diagnosis and control of LTI systems to address current design challenges. The results obtained are then extended to a number of complex linear systems, specifically to Markovian jump systems as well as to cooperative multi-agent systems.

]]>Nonlinear Optimization in Electrical Engineering with Applications in MATLAB® provides an introductory course on nonlinear optimization in electrical engineering, with a focus on applications such as the design of electric, microwave, and photonic circuits, wireless communications, and digital filter design.

Basic concepts are introduced using a step-by-step approach and illustrated with MATLAB® codes that the reader can use and adapt. Topics covered include:

classical optimization methods one dimensional optimization unconstrained and constrained optimization global optimization space mapping optimization adjoint variable methodsNonlinear Optimization in Electrical Engineering with Applications in MATLAB® is essential reading for advanced students in electrical engineering.

]]>The book is concerned with understanding the structure of nonlinear dynamic systems within a control engineering context After a discussion of theoretical foundations, the development moves to specific techniques (describing function method, phase plane portrait, linearisation methods). The treatment then becomes oriented to qualitative analysis and maintains this emphasis to the end of the book. The broad aim is to develop methods that will allow the topology of system behaviour to be visualised. The main tools are Lyapunov methods, extending to include recent work on system decomposition. A bibliography lists both earlier seminal and recent literature to allow the reader to follow up particular aspects.

]]>This book aims to demonstrate the power and breadth of polynomial methods in control and filtering. Direct polynomial methods have previously received little attention compared with the alternative Wiener-Hopf transfer-function method and the statespace methods which rely on Riccati equations.

The book provides a broad coverage of the polynomial equation approach in a range of linear control and filtering problems. The principal feature of the approach is the description of systems in fractional form using transfer functions. This representation leads quite naturally and directly to the parameterisation of all 'acceptable' feedback controllers for a given problem in the form of a Diophantine equation over polynomials. In the polynomial equation approach, this direct parameterisation is explicitly carried through to the synthesis of controllers and filters and, further, to the computer implementation of numerical algorithms.

The book is likely to be of interest to students, researchers and engineers with some control and systems theory or signal processing background. It could be used as the basis of a graduate-level course in optimal control and filtering. The book proceeds from the necessary background material presented at a tutorial level, through recent theoretical and practical developments, to a detailed presentation of numerical algorithms.

]]>'To the surprise of some undergraduates, processes do not carry labels marking their variables nor, alas, are they conveniently classified into linear, nonlinear, stochastic, etc., categories. The ability to come to terms with this situation is a prerequisite for anyone proposing to succeed in an industrial environment.' This quotation from Chapter 1 characterises the viewpoint of the book, which is concerned with the application of control theory to real problems in their industrial context.

The book is structured around the following beliefs:

(a) Economic aspects must be considered at an early stage of any project. (b) Simple techniques and ready-made manufacturer's solutions should be applied wherever possible. (c) More advanced techniques will be received enthusiastically in those applications where they can offer a genuine contribution. (d) Control systems using distributed microprocessor power will have an impact that is difficult to exaggerate. Control engineers must become familiar with the concepts involved. (e) Familiarity with a wide range of applications is indispensable in developing an efficient approach in the field of applied control theory.This second edition includes new material and supporting references on:

robotics control programmable logic controllers self-tuning controllers distributed computer control systems biotechnological controlThe book should be accessible to a wide variety of engineers. Preferably they should have an elementary knowledge of automatic control theory.

]]>Frequency-Domain Control Design for High-Performance Systems serves as a practical guide for the control engineer, and attempts to bridge the gap between industrial and academic control theory. Frequencydomain techniques rooted in classical control theory are presented with new approaches in nonlinear compensation that result in robust, high-performance closed-loop systems. Illustrative examples using data from actual control designs are included.

]]>Parameter estimation is the process of using observations from a system to develop mathematical models that adequately represent the system dynamics. The assumed model consists of a finite set of parameters, the values of which are calculated using estimation techniques. Most of the techniques that exist are based on least-square minimisation of error between the model response and actual system response. However, with the proliferation of highspeed digital computers, elegant and innovative techniques like filter error method, genetic algorithms and artificial neural networks are finding more and more use in parameter estimation problems. Modelling and Parameter Estimation of Dynamic Systems presents a detailed examination of many estimation techniques and modelling problems.

]]>Solve engineering and scientific partial differential equation applications using the PDE2D software developed by the author

Solving Partial Differential Equation Applications with PDE2D derives and solves a range of ordinary and partial differential equation (PDE) applications. This book describes an easy-to-use, general purpose, and time-tested PDE solver developed by the author that can be applied to a wide variety of science and engineering problems. The equations studied include many time-dependent, steady-state and eigenvalue applications such as diffusion, heat conduction and convection, image processing, math finance, fluid flow, and elasticity and quantum mechanics, in one, two, and three space dimensions.

The author begins with some simple "0D" problems that give the reader an opportunity to become familiar with PDE2D before proceeding to more difficult problems. The book ends with the solution of a very difficult nonlinear problem, which requires a moving adaptive grid because the solution has sharp, moving peaks. This important book:

Describes a finite-element program, PDE2D, developed by the author over the course of 40 years Derives the ordinary and partial differential equations, with appropriate initial and boundary conditions, for a wide variety of applications Offers free access to the Windows version of the PDE2D software through the author's website at www.pde2d.com Offers free access to the Linux and MacOSX versions of the PDE2D software also, for instructors who adopt the book for their course and contact the author at www.pde2d.comWritten for graduate applied mathematics or computational science classes, Solving Partial Differential Equation Applications with PDE2D offers students the opportunity to actually solve interesting engineering and scientific applications using the accessible PDE2D.

]]>Introduces the latest developments in forecasting in advanced quantitative data analysis

This book presents advanced univariate multiple regressions, which can directly be used to forecast their dependent variables, evaluate their in-sample forecast values, and compute forecast values beyond the sample period. Various alternative multiple regressions models are presented based on a single time series, bivariate, and triple time-series, which are developed by taking into account specific growth patterns of each dependent variables, starting with the simplest model up to the most advanced model. Graphs of the observed scores and the forecast evaluation of each of the models are offered to show the worst and the best forecast models among each set of the models of a specific independent variable.

Advanced Time Series Data Analysis: Forecasting Using EViews provides readers with a number of modern, advanced forecast models not featured in any other book. They include various interaction models, models with alternative trends (including the models with heterogeneous trends), and complete heterogeneous models for monthly time series, quarterly time series, and annually time series. Each of the models can be applied by all quantitative researchers.

Presents models that are all classroom tested Contains real-life data samples Contains over 350 equation specifications of various time series models Contains over 200 illustrative examples with special notes and comments Applicable for time series data of all quantitative studiesAdvanced Time Series Data Analysis: Forecasting Using EViews will appeal to researchers and practitioners in forecasting models, as well as those studying quantitative data analysis. It is suitable for those wishing to obtain a better knowledge and understanding on forecasting, specifically the uncertainty of forecast values.

]]>A seminal handbook in the field for more than 20 years, this new and updated edition of Mathematics for Dyslexics and Dyscalculics contains the latest research and best practices for helping learners with numerical and mathematical difficulties.

Provides a complete overview of theory and research in the fields of dyslexia and dyscalculia, along with detailed yet pragmatic methods to apply in the classroom Contains enhanced coverage of place value and the role of the decimal point, why fractions can challenge a developed logic for arithmetic, and the complexity of time along with new material on addressing anxiety, fear, motivation, and resilience in the classroom; and links to new resources including standardized tests and recommended reading lists Written by two mathematics teachers with 50 years of teaching experience between them, much of it in specialist settings for students with specific learning difficulties Offers effective teaching strategies for learners of all ages in a structured but accessible format]]>Probability and statistics are increasingly important in a huge range of professions. But many people use data in ways they don't even understand, meaning they aren't getting the most from it. Bayesian Statistics the Fun Way will change that.

This book will give you a complete understanding of Bayesian statistics through simple explanations and un-boring examples. Find out the probability of UFOs landing in your garden, how likely Han Solo is to survive a flight through an asteroid shower, how to win an argument about conspiracy theories, and whether a burglary really was a burglary, to name a few examples.

By using these off-the-beaten-track examples, the author actually makes learning statistics fun. And you'll learn real skills, like how to:

- How to measure your own level of uncertainty in a conclusion or belief

- Calculate Bayes theorem and understand what it's useful for

- Find the posterior, likelihood, and prior to check the accuracy of your conclusions

- Calculate distributions to see the range of your data

- Compare hypotheses and draw reliable conclusions from them

Next time you find yourself with a sheaf of survey results and no idea what to do with them, turn to Bayesian Statistics the Fun Way to get the most value from your data.]]>

The P-NP problem is the most important open problem in computer science, if not all of mathematics. Simply stated, it asks whether every problem whose solution can be quickly checked by computer can also be quickly solved by computer. The Golden Ticket provides a nontechnical introduction to P-NP, its rich history, and its algorithmic implications for everything we do with computers and beyond. Lance Fortnow traces the history and development of P-NP, giving examples from a variety of disciplines, including economics, physics, and biology. He explores problems that capture the full difficulty of the P-NP dilemma, from discovering the shortest route through all the rides at Disney World to finding large groups of friends on Facebook. The Golden Ticket explores what we truly can and cannot achieve computationally, describing the benefits and unexpected challenges of this compelling problem.

]]>Geometry Essentials For Dummies (9781119590446) was previously published as Geometry Essentials For Dummies (9781118068755). While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product.

Just the critical concepts you need to score high in geometry

This practical, friendly guide focuses on critical concepts taught in a typical geometry course, from the properties of triangles, parallelograms, circles, and cylinders, to the skills and strategies you need to write geometry proofs. Geometry Essentials For Dummies is perfect for cramming or doing homework, or as a reference for parents helping kids study for exams.

Get down to the basics -- get a handle on the basics of geometry, from lines, segments, and angles, to vertices, altitudes, and diagonals Conquer proofs with confidence -- follow easy-to-grasp instructions for understanding the components of a formal geometry proof Take triangles in strides -- learn how to take in a triangle's sides, analyze its angles, work through an SAS proof, and apply the Pythagorean Theorem Polish up on polygons -- get the lowdown on quadrilaterals and other polygons: their angles, areas, properties, perimeters, and much more]]>Algebra II Essentials For Dummies (9781119590873) was previously published as Algebra II Essentials For Dummies (9780470618400). While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product.

Passing grades in two years of algebra courses are required for high school graduation. Algebra II Essentials For Dummies covers key ideas from typical second-year Algebra coursework to help students get up to speed. Free of ramp-up material, Algebra II Essentials For Dummies sticks to the point, with content focused on key topics only. It provides discrete explanations of critical concepts taught in a typical Algebra II course, from polynomials, conics, and systems of equations to rational, exponential, and logarithmic functions. This guide is also a perfect reference for parents who need to review critical algebra concepts as they help students with homework assignments, as well as for adult learners headed back into the classroom who just need a refresher of the core concepts.

The Essentials For Dummies Series

Dummies is proud to present our new series, The Essentials For Dummies . Now students who are prepping for exams, preparing to study new material, or who just need a refresher can have a concise, easy-to-understand review guide that covers an entire course by concentrating solely on the most important concepts. From algebra and chemistry to grammar and Spanish, our expert authors focus on the skills students most need to succeed in a subject.

Examines numerical and semi-analytical methods for differential equations that can be used for solving practical ODEs and PDEs

This student-friendly book deals with various approaches for solving differential equations numerically or semi-analytically depending on the type of equations and offers simple example problems to help readers along.

Featuring both traditional and recent methods, Advanced Numerical and Semi Analytical Methods for Differential Equations begins with a review of basic numerical methods. It then looks at Laplace, Fourier, and weighted residual methods for solving differential equations. A new challenging method of Boundary Characteristics Orthogonal Polynomials (BCOPs) is introduced next. The book then discusses Finite Difference Method (FDM), Finite Element Method (FEM), Finite Volume Method (FVM), and Boundary Element Method (BEM). Following that, analytical/semi analytic methods like Akbari Ganji's Method (AGM) and Exp-function are used to solve nonlinear differential equations. Nonlinear differential equations using semi-analytical methods are also addressed, namely Adomian Decomposition Method (ADM), Homotopy Perturbation Method (HPM), Variational Iteration Method (VIM), and Homotopy Analysis Method (HAM). Other topics covered include: emerging areas of research related to the solution of differential equations based on differential quadrature and wavelet approach; combined and hybrid methods for solving differential equations; as well as an overview of fractal differential equations. Further, uncertainty in term of intervals and fuzzy numbers have also been included, along with the interval finite element method. This book:

Discusses various methods for solving linear and nonlinear ODEs and PDEs Covers basic numerical techniques for solving differential equations along with various discretization methods Investigates nonlinear differential equations using semi-analytical methods Examines differential equations in an uncertain environment Includes a new scenario in which uncertainty (in term of intervals and fuzzy numbers) has been included in differential equations Contains solved example problems, as well as some unsolved problems for self-validation of the topics coveredAdvanced Numerical and Semi Analytical Methods for Differential Equations is an excellent text for graduate as well as post graduate students and researchers studying various methods for solving differential equations, numerically and semi-analytically.

]]>The topic of missing data has gained considerable attention in recent decades. This new edition by two acknowledged experts on the subject offers an up-to-date account of practical methodology for handling missing data problems. Blending theory and application, authors Roderick Little and Donald Rubin review historical approaches to the subject and describe simple methods for multivariate analysis with missing values. They then provide a coherent theory for analysis of problems based on likelihoods derived from statistical models for the data and the missing data mechanism, and then they apply the theory to a wide range of important missing data problems.

Statistical Analysis with Missing Data, Third Edition starts by introducing readers to the subject and approaches toward solving it. It looks at the patterns and mechanisms that create the missing data, as well as a taxonomy of missing data. It then goes on to examine missing data in experiments, before discussing complete-case and available-case analysis, including weighting methods. The new edition expands its coverage to include recent work on topics such as nonresponse in sample surveys, causal inference, diagnostic methods, and sensitivity analysis, among a host of other topics.

An updated "classic" written by renowned authorities on the subject Features over 150 exercises (including many new ones) Covers recent work on important methods like multiple imputation, robust alternatives to weighting, and Bayesian methods Revises previous topics based on past student feedback and class experience Contains an updated and expanded bibliography

The authors were awarded The Karl Pearson Prize in 2017 by the International Statistical Institute, for a research contribution that has had profound influence on statistical theory, methodology or applications. Their work "has been no less than defining and transforming." (ISI)

Statistical Analysis with Missing Data, Third Edition is an ideal textbook for upper undergraduate and/or beginning graduate level students of the subject. It is also an excellent source of information for applied statisticians and practitioners in government and industry.]]>

Demonstrates how to solve reliability problems using practical applications of Bayesian models

This self-contained reference provides fundamental knowledge of Bayesian reliability and utilizes numerous examples to show how Bayesian models can solve real life reliability problems. It teaches engineers and scientists exactly what Bayesian analysis is, what its benefits are, and how they can apply the methods to solve their own problems. To help readers get started quickly, the book presents many Bayesian models that use JAGS and which require fewer than 10 lines of command. It also offers a number of short R scripts consisting of simple functions to help them become familiar with R coding.

Practical Applications of Bayesian Reliability starts by introducing basic concepts of reliability engineering, including random variables, discrete and continuous probability distributions, hazard function, and censored data. Basic concepts of Bayesian statistics, models, reasons, and theory are presented in the following chapter. Coverage of Bayesian computation, Metropolis-Hastings algorithm, and Gibbs Sampling comes next. The book then goes on to teach the concepts of design capability and design for reliability; introduce Bayesian models for estimating system reliability; discuss Bayesian Hierarchical Models and their applications; present linear and logistic regression models in Bayesian Perspective; and more.

Provides a step-by-step approach for developing advanced reliability models to solve complex problems, and does not require in-depth understanding of statistical methodology Educates managers on the potential of Bayesian reliability models and associated impact Introduces commonly used predictive reliability models and advanced Bayesian models based on real life applications Includes practical guidelines to construct Bayesian reliability models along with computer codes for all of the case studies JAGS and R codes are provided on an accompanying website to enable practitioners to easily copy them and tailor them to their own applicationsPractical Applications of Bayesian Reliability is a helpful book for industry practitioners such as reliability engineers, mechanical engineers, electrical engineers, product engineers, system engineers, and materials scientists whose work includes predicting design or product performance.

]]>Get a handle on pre-calculus in a pinch!

If you're tackling pre-calculus and want to up your chances of doing your very best, this hands-on workbook is just what you need to grasp and retain the concepts that will help you succeed. Inside, you'll get basic content review for every concept, paired with examples and plenty of practice problems, ample workspace, step-by-step solutions, and thorough explanations for each and every problem.

In Pre-Calculus Workbook For Dummies , you'll also get free access to a quiz for every chapter online! With all of the lessons and practice offered, you'll memorize the most frequently used formulas, see how to avoid common mistakes, understand tricky trig proofs, and get the inside scoop on key concepts such as quadratic equations.

Get ample review before jumping into a calculus course Supplement your classroom work with easy-to-follow guidance Make complex formulas and concepts more approachable Be prepared to further your mathematics studiesWhether you're enrolled in a pre-calculus class or you're looking for a refresher as you prepare for a calculus course, this is the perfect study companion to make it easier.

]]>Probability, Random Variables, Statistics, and Random Processes: Fundamentals & Applications is a comprehensive undergraduate-level textbook. With its excellent topical coverage, the focus of this book is on the basic principles and practical applications of the fundamental concepts that are extensively used in various Engineering disciplines as well as in a variety of programs in Life and Social Sciences. The text provides students with the requisite building blocks of knowledge they require to understand and progress in their areas of interest. With a simple, clear-cut style of writing, the intuitive explanations, insightful examples, and practical applications are the hallmarks of this book.

The text consists of twelve chapters divided into four parts. Part-I, Probability (Chapters 1 - 3), lays a solid groundwork for probability theory, and introduces applications in counting, gambling, reliability, and security. Part-II, Random Variables (Chapters 4 - 7), discusses in detail multiple random variables, along with a multitude of frequently-encountered probability distributions. Part-III, Statistics (Chapters 8 - 10), highlights estimation and hypothesis testing. Part-IV, Random Processes (Chapters 11 - 12), delves into the characterization and processing of random processes. Other notable features include:

Most of the text assumes no knowledge of subject matter past first year calculus and linear algebra With its independent chapter structure and rich choice of topics, a variety of syllabi for different courses at the junior, senior, and graduate levels can be supported A supplemental website includes solutions to about 250 practice problems, lecture slides, and figures and tables from the textGiven its engaging tone, grounded approach, methodically-paced flow, thorough coverage, and flexible structure, Probability, Random Variables, Statistics, and Random Processes: Fundamentals & Applications clearly serves as a must textbook for courses not only in Electrical Engineering, but also in Computer Engineering, Software Engineering, and Computer Science.

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