Most available books on computational electrodynamics are focused on FDTD, FEM, or other specific technique developed in microwave engineering. In contrast, Fourier Modal Method and Its Applications in Computational Nanophotonics is a complete guide to the principles and detailed mathematics of the up-to-date Fourier modal method of optical analysis. It takes readers through the implementation of MATLAB (R) codes for practical modeling of well-known and promising nanophotonic structures. The authors also address the limitations of the Fourier modal method. Features Provides a comprehensive guide to the principles, methods, and mathematics of the Fourier modal method Explores the emerging field of computational nanophotonics Presents clear, step-by-step, practical explanations on how to use the Fourier modal method for photonics and nanophotonics applications Includes the necessary MATLAB codes, enabling readers to construct their own code Using this book, graduate students and researchers can learn about nanophotonics simulations through a comprehensive treatment of the mathematics underlying the Fourier modal method and examples of practical problems solved with MATLAB codes.

A Totally Different Outlook on Power Electronic System Analysis Power Electronic Systems: Walsh Analysis with MATLAB (R) builds a case for Walsh analysis as a powerful tool in the study of power electronic systems. It considers the application of Walsh functions in analyzing power electronic systems, and the advantages offered by Walsh domain analysis of power electronic systems. Solves Power Electronic Systems in an Unconventional Way This book successfully integrates power electronics as well as systems and control. Incorporating a complete orthonormal function set very much unlike the sine-cosine functions, it introduces a blending between piecewise constant orthogonal functions and power electronic systems. It explores the background and evolution of power electronics, and discusses Walsh and related orthogonal basis functions. It develops the mathematical foundation of Walsh analysis, and first- and second-order system analyses by Walsh technique. It also describes the Walsh domain operational method and how it is applied to linear system analysis. Introduces Theories Step by Step While presenting the underlying principles of Walsh analysis, the authors incorporate many illustrative examples, and include a basic introduction to linear algebra and MATLAB (R) programs. They also examine different orthogonal piecewise constant basis functions like Haar, Walsh, slant, block pulse functions, and other related orthogonal functions along with their time scale evolution. * Analyzes pulse-fed single input single output (SISO) first- and second-order systems * Considers stepwise and continuously pulse width modulated chopper systems * Describes a detailed analysis of controlled rectifier circuits * Addresses inverter circuits Power Electronic Systems: Walsh Analysis with MATLAB (R) is written for postgraduate students, researchers, and academicians in the area of power electronics as well as systems and control.

Meshless, or meshfree methods, which overcome many of the limitations of the finite element method, have achieved significant progress in numerical computations of a wide range of engineering problems. A comprehensive introduction to meshless methods, Meshless Methods and Their Numerical Properties gives complete mathematical formulations for the most important and classical methods, as well as several methods recently developed by the authors. This book also offers a rigorous mathematical treatment of their numerical properties-including consistency, convergence, stability, and adaptivity-to help you choose the method that is best suited for your needs. Get Guidance for Developing and Testing Meshless Methods Developing a broad framework to study the numerical computational characteristics of meshless methods, the book presents consistency, convergence, stability, and adaptive analyses to offer guidance for developing and testing a particular meshless method. The authors demonstrate the numerical properties by solving several differential equations, which offer a clearer understanding of the concepts. They also explain the difference between the finite element and meshless methods. Explore Engineering Applications of Meshless Methods The book examines how meshless methods can be used to solve complex engineering problems with lower computational cost, higher accuracy, easier construction of higher-order shape functions, and easier handling of large deformation and nonlinear problems. The numerical examples include engineering problems such as the CAD design of MEMS devices, nonlinear fluid-structure analysis of near-bed submarine pipelines, and two-dimensional multiphysics simulation of pH-sensitive hydrogels. Appendices supply useful template functions, flowcharts, and data structures to assist you in implementing meshless methods. Choose the Best Method for a Particular Problem Providing insight into the special features and intricacies of meshless methods, this is a valuable reference for anyone developing new high-performance numerical methods or working on the modelling and simulation of practical engineering problems. It guides you in comparing and verifying meshless methods so that you can more confidently select the best method to solve a particular problem.

This book is written primarily as a text for a course in factor analysis at the advanced undergraduate or graduate level. It is most appropriate for students of the behavioral and social sciences, though colleagues and students in other disciplines also have used preliminary copies.

A photographic exploration of mathematicians' chalkboards "A mathematician, like a painter or poet, is a maker of patterns," wrote the British mathematician G. H. Hardy. In Do Not Erase, photographer Jessica Wynne presents remarkable examples of this idea through images of mathematicians' chalkboards. While other fields have replaced chalkboards with whiteboards and digital presentations, mathematicians remain loyal to chalk for puzzling out their ideas and communicating their research. Wynne offers more than one hundred stunning photographs of these chalkboards, gathered from a diverse group of mathematicians around the world. The photographs are accompanied by essays from each mathematician, reflecting on their work and processes. Together, pictures and words provide an illuminating meditation on the unique relationships among mathematics, art, and creativity. The mathematicians featured in this collection comprise exciting new voices alongside established figures, including Sun-Yung Alice Chang, Alain Connes, Misha Gromov, Andre Neves, Kasso Okoudjou, Peter Shor, Christina Sormani, Terence Tao, Claire Voisin, and many others. The companion essays give insights into how the chalkboard serves as a special medium for mathematical expression. The volume also includes an introduction by the author, an afterword by New Yorker writer Alec Wilkinson, and biographical information for each contributor. Do Not Erase is a testament to the myriad ways that mathematicians use their chalkboards to reveal the conceptual and visual beauty of their discipline-shapes, figures, formulas, and conjectures created through imagination, argument, and speculation.

Mathematical Foundations for Signal Processing, Communications, and Networking describes mathematical concepts and results important in the design, analysis, and optimization of signal processing algorithms, modern communication systems, and networks. Helping readers master key techniques and comprehend the current research literature, the book offers a comprehensive overview of methods and applications from linear algebra, numerical analysis, statistics, probability, stochastic processes, and optimization. From basic transforms to Monte Carlo simulation to linear programming, the text covers a broad range of mathematical techniques essential to understanding the concepts and results in signal processing, telecommunications, and networking. Along with discussing mathematical theory, each self-contained chapter presents examples that illustrate the use of various mathematical concepts to solve different applications. Each chapter also includes a set of homework exercises and readings for additional study. This text helps readers understand fundamental and advanced results as well as recent research trends in the interrelated fields of signal processing, telecommunications, and networking. It provides all the necessary mathematical background to prepare students for more advanced courses and train specialists working in these areas.

A comprehensive overview of nonlinear H control theory for both continuous-time and discrete-time systems, Nonlinear H -Control, Hamiltonian Systems and Hamilton-Jacobi Equations covers topics as diverse as singular nonlinear H -control, nonlinear H -filtering, mixed H2/ H -nonlinear control and filtering, nonlinear H -almost-disturbance-decoupling, and algorithms for solving the ubiquitous Hamilton-Jacobi-Isaacs equations. The link between the subject and analytical mechanics as well as the theory of partial differential equations is also elegantly summarized in a single chapter. Recent progress in developing computational schemes for solving the Hamilton-Jacobi equation (HJE) has facilitated the application of Hamilton-Jacobi theory in both mechanics and control. As there is currently no efficient systematic analytical or numerical approach for solving them, the biggest bottle-neck to the practical application of the nonlinear equivalent of the H -control theory has been the difficulty in solving the Hamilton-Jacobi-Isaacs partial differential-equations (or inequalities). In light of this challenge, the author hopes to inspire continuing research and discussion on this topic via examples and simulations, as well as helpful notes and a rich bibliography. Nonlinear H -Control, Hamiltonian Systems and Hamilton-Jacobi Equations was written for practicing professionals, educators, researchers and graduate students in electrical, computer, mechanical, aeronautical, chemical, instrumentation, industrial and systems engineering, as well as applied mathematics, economics and management.

This book is concerned with the principles of differentiation and integration. The principles are then applied to solve engineering problems. A familiarity with basic algebra and a basic knowledge of common functions, such as polynomials, trigonometric, exponential, logarithmic and hyperbolic is assumed but reference material on these is included in an appendix.

Why are there so many formulas for area and volume, and why do some of them look alike? Why does one quadrilateral have no special name while another has several, like square, rectangle, rhombus, and parallelogram-and why are all these names useful? How much do you know ... and how much do you need to know? Helping your students develop a robust understanding of geometry requires that you understand this mathematics deeply. But what does that mean? This book focuses on essential knowledge for teachers about geometry. It is organized around four big ideas, supported by multiple smaller, interconnected ideas-essential understandings. Taking you beyond a simple introduction to geometry, the book will broaden and deepen your mathematical understanding of one of the most challenging topics for students-and teachers. It will help you engage your students, anticipate their perplexities, avoid pitfalls, and dispel misconceptions. You will also learn to develop appropriate tasks, techniques, and tools for assessing students' understanding of the topic.

Math Education for America? analyzes math education policy through the social network of individuals and private and public organizations that influence it in the United States. The effort to standardize a national mathematics curriculum for public schools in the U.S. culminated in 2010 when over 40 states adopted the Common Core State Standards for Mathematics. Rather than looking at the text of specific policy documents, this book complements existing critical reviews of the national math education curriculum by employing a unique social network analysis. Breaking new ground in detailing and theorizing the politics of math education, Wolfmeyer argues that the private interests of this network are closely tied to a web of interrelated developments: human capital education policy, debates over traditional and reform pedagogy, the assumed content knowledge deficit of math teachers, and the proliferation of profit-driven educational businesses. By establishing the interconnectedness of these interests with the national math education curriculum, he shows how the purported goals of math education reform are aligned with the prevailing political agendas of this social network rather than the national interest.

This book covers many important aspects of applied chemistry and chemical engineering, focusing on three main aspects: principles, methodology and evaluation methods. It presents a selection of chapters on recent developments of theoretical, mathematical, and computational conceptions, as well as chapters on modeling and simulation of specific research themes covering applied chemistry and chemical engineering. This book attempts to bridge the gap between classical analysis and modern applications. Covering a selection of topics within the field of applied chemistry and chemical engineering, the book is divided into several parts: polymer chemistry and technology bioorganic and biological chemistry nanoscale technology selected topics This book is the second of the two-volume series Applied Chemistry and Chemical Engineering. The first volume is Volume 1: Mathematical and Analytical Techniques.

Understanding mathematical modeling is fundamental in chemical engineering. This book reviews, introduces, and develops the mathematical models that are most frequently encountered in sophisticated chemical engineering domains. The volume provides a collection of models illustrating the power and richness of the mathematical sciences in supplying insight into the operation of important real-world systems. It fills a gap within modeling texts, focusing on applications across a broad range of disciplines. The first part of the book discusses the general components of the modeling process and highlights the potential of modeling in the production of nanofibers. These chapters discuss the general components of the modeling process and the evolutionary nature of successful model building in the electrospinning process. Electrospinning is the most versatile technique for the preparation of continuous nanofibers obtained from numerous materials. This section of book summarizes the state-of-the art in electrospinning as well as updates on theoretical aspects and applications. Part 2 of the book presents a selection of special topics on issues in applied chemistry and chemical engineering, including nanocomposite coating processes by electrocodeposition method, entropic factors conformational interactions, and the application of artificial neural network and meta-heuristic algorithms. This volume covers a wide range of topics in mathematical modeling, computational science, and applied mathematics. It presents a wealth of new results in the development of modeling theories and methods, advancing diverse areas of applications and promoting interdisciplinary interactions between mathematicians, scientists, engineers and representatives from other disciplines.

First Published in 1986. Routledge is an imprint of Taylor & Francis, an informa company.

A provocative collection of papers containing comprehensive reviews of previous research, teaching techniques, and pointers for direction of future study. Provides both a comprehensive assessment of the latest research on mathematical problem solving, with special emphasis on its teaching, and an attempt to increase communication across the active disciplines in this area.

What is the relationship between fractions and rational numbers? Can you explain why the product of two fractions between 0 and 1 is less than either factor? How are rational numbers related to irrational numbers, which your students will study in later grades? How much do you know... and how much do you need to know? Helping your upper elementary school students develop a robust understanding of rational numbers requires that you understand this mathematics deeply. But what does that mean? This book focuses on essential knowledge for teachers about rational numbers. It is organised around four big ideas, supported by multiple smaller, interconnected ideas-essential understandings. Taking you beyond a simple introduction to rational numbers, the book will broaden and deepen your mathematical understanding of one of the most challenging topics for students and teachers. It will help you engage your students, anticipate their perplexities, avoid pitfalls and dispel misconceptions. You will also learn to develop appropriate tasks, techniques and tools for assessing students' understanding of the topic. Focus on the ideas that you need to understand thoroughly to teach confidently.

This volume features a complete set of problems, hints, and solutions based on Stanford University's well-known competitive examination in mathematics. It offers high school and college students an excellent mathematics workbook of rigorous problems that will assist in developing and cultivating their logic and probability skills.These 20 sets of intriguing problems test originality and insight rather than routine competence. They involve theorizing and verifying mathematical facts; examining the results of general statements; discovering that highly plausible conjectures can be incorrect; solving sequences of subproblems to reveal theory construction; and recognizing "red herrings," in which obvious relationships among the data prove irrelevant to solutions. Hints for each problem appear in a separate section, and a final section features solutions that outline the appropriate procedures.Ideal for teachers seeking challenging practice math problems for their gifted students, this book will also help students prepare for mathematics, science, and engineering programs. Mathematics buffs of all ages will also find it a source of captivating challenges.

Your logical, linear guide to the fundamentals of data science programming Data science is exploding--in a good way--with a forecast of 1.7 megabytes of new information created every second for each human being on the planet by 2020 and 11.5 million job openings by 2026. It clearly pays dividends to be in the know. This friendly guide charts a path through the fundamentals of data science and then delves into the actual work: linear regression, logical regression, machine learning, neural networks, recommender engines, and cross-validation of models. Data Science Programming All-In-One For Dummies is a compilation of the key data science, machine learning, and deep learning programming languages: Python and R. It helps you decide which programming languages are best for specific data science needs. It also gives you the guidelines to build your own projects to solve problems in real time. Get grounded: the ideal start for new data professionals What lies ahead: learn about specific areas that data is transforming Be meaningful: find out how to tell your data story See clearly: pick up the art of visualization Whether you're a beginning student or already mid-career, get your copy now and add even more meaning to your life--and everyone else's!

This revised and updated third edition offers a range of strategies, activities and ideas to bring mathematics to life in the primary classroom. Taking an innovative and playful approach to maths teaching, this book promotes creativity as a key element of practice and offers ideas to help your students develop knowledge, understanding and enjoyment of the subject. In the creative classroom, mathematics becomes a tool to build confidence, develop problem solving skills and motivate children. The fresh approaches explored in this book include a range of activities such as storytelling, music and construction, elevating maths learning beyond subject knowledge itself to enable students to see mathematics in a new way. Key chapters of this book explore: * Learning maths outdoors - make more noise, make more mess or work on a larger scale * Everyday maths - making sense of the numbers, patterns, shapes and measures children see around them * Music and maths - the role of rhythm in learning, and music and pattern in maths Stimulating, accessible and underpinned by the latest research and theory, this is essential reading for trainee and practising teachers who wish to embed creative approaches to maths teaching in their classroom.

Exam Board: Pearson Edexcel Academic Level: AS level Subject: Mathematics First teaching: September 2017 First Exams: Summer 2018 This Revision Workbook is suitable for classroom and independent study, and is the smart choice for those revising for AS level Mathematics. Organise their revision with the one topic-per-page format Speed up their revision with summary notes in short, memorable chunks Track their revision progress with at-a-glance check boxes Check their understanding with worked examples Develop their exam technique with exam-style practice questions and answers

The amount of data in everyday life has been exploding. This data increase has been especially significant in scientific fields, where substantial amounts of data must be captured, communicated, aggregated, stored, and analyzed. Cloud Computing with e-Science Applications explains how cloud computing can improve data management in data-heavy fields such as bioinformatics, earth science, and computer science. The book begins with an overview of cloud models supplied by the National Institute of Standards and Technology (NIST), and then: Discusses the challenges imposed by big data on scientific data infrastructures, including security and trust issues Covers vulnerabilities such as data theft or loss, privacy concerns, infected applications, threats in virtualization, and cross-virtual machine attack Describes the implementation of workflows in clouds, proposing an architecture composed of two layers-platform and application Details infrastructure-as-a-service (IaaS), platform-as-a-service (PaaS), and software-as-a-service (SaaS) solutions based on public, private, and hybrid cloud computing models Demonstrates how cloud computing aids in resource control, vertical and horizontal scalability, interoperability, and adaptive scheduling Featuring significant contributions from research centers, universities, and industries worldwide, Cloud Computing with e-Science Applications presents innovative cloud migration methodologies applicable to a variety of fields where large data sets are produced. The book provides the scientific community with an essential reference for moving applications to the cloud.

Despite remarkable developments in the field, a detailed treatment of non-Kerr law media has not been published. Introduction to non-Kerr Law Optical Solitons is the first book devoted exclusively to optical soliton propagation in media that possesses non-Kerr law nonlinearities. After an introduction to the basic features of fiber-optic communications, the book outlines the nonlinear Schroedinger equation (NLSE), conserved quantities, and adiabatic dynamics of soliton parameters. It then derives the NLSE for Kerr law nonlinearity from basic principles, the inverse scattering transform, and the 1-soliton solution. The book also explains the variational principle and Lie transform. In each case of non-Kerr law solitons, the authors develop soliton dynamics, evaluated integrals of motion, and adiabatic dynamics of soliton parameters based on multiple-scale perturbation theory. The book explores intra-channel collision of optical solitons in both Hamiltonian and non-Hamiltonian type perturbations. In addition, it examines the stochastic perturbation of optical solitons, the corresponding Langevin equations, and optical couplers, followed by an introduction to optical bullets. Establishing a basis in an important yet insufficiently documented subject, Introduction to non-Kerr Law Optical Solitons will help fuel advances in optical communication systems.

This textbook offers a systematic, self-contained account of the main contributions of modern game theory and its applications to economics. Starting with a detailed description of how to model strategic situations, the discussion proceeds by studying basic solution concepts, their main refinements, games played under incomplete information, and repeated games. For each of these theoretical developments, there is a companion set of applications that cover the most representative instances of game-theoretic analysis in economics, e.g. oligopolistic competition, public goods, coordination failures, bargaining, insurance markets, implementation theory, signaling and auctions. The theory and applications covered in the first part of the book fall under the so-called 'classical' approach to game theory, which is founded on the paradigm of players' unlimited rationality. The second part shifts towards topics that no longer abide by that paradigm. This leads to the study of topics such as the interplay between evolution and rationality.

This third edition of the Handbook of International Research in Mathematics Education provides a comprehensive overview of the most recent theoretical and practical developments in the field of mathematics education. Authored by an array of internationally recognized scholars and edited by Lyn English and David Kirshner, this collection brings together overviews and advances in mathematics education research spanning established and emerging topics, diverse workplace and school environments, and globally representative research priorities. New perspectives are presented on a range of critical topics including embodied learning, the theory-practice divide, new developments in the early years, educating future mathematics education professors, problem solving in a 21st century curriculum, culture and mathematics learning, complex systems, critical analysis of design-based research, multimodal technologies, and e-textbooks. Comprised of 12 revised and 17 new chapters, this edition extends the Handbook's original themes for international research in mathematics education and remains in the process a definitive resource for the field.