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Finite Elements I: Approximation and Interpolation (Texts in Applied Mathematics #72)
by Alexandre Ern Jean-Luc GuermondThis book is the first volume of a three-part textbook suitable for graduate coursework, professional engineering and academic research. It is also appropriate for graduate flipped classes. Each volume is divided into short chapters. Each chapter can be covered in one teaching unit and includes exercises as well as solutions available from a dedicated website. The salient ideas can be addressed during lecture, with the rest of the content assigned as reading material. To engage the reader, the text combines examples, basic ideas, rigorous proofs, and pointers to the literature to enhance scientific literacy. Volume I is divided into 23 chapters plus two appendices on Banach and Hilbert spaces and on differential calculus. This volume focuses on the fundamental ideas regarding the construction of finite elements and their approximation properties. It addresses the all-purpose Lagrange finite elements, but also vector-valued finite elements that are crucial to approximate the divergence and the curl operators. In addition, it also presents and analyzes quasi-interpolation operators and local commuting projections. The volume starts with four chapters on functional analysis, which are packed with examples and counterexamples to familiarize the reader with the basic facts on Lebesgue integration and weak derivatives. Volume I also reviews important implementation aspects when either developing or using a finite element toolbox, including the orientation of meshes and the enumeration of the degrees of freedom.
Finite Elements II: Galerkin Approximation, Elliptic and Mixed PDEs (Texts in Applied Mathematics #73)
by Alexandre Ern Jean-Luc GuermondThis book is the second volume of a three-part textbook suitable for graduate coursework, professional engineering and academic research. It is also appropriate for graduate flipped classes. Each volume is divided into short chapters. Each chapter can be covered in one teaching unit and includes exercises as well as solutions available from a dedicated website. The salient ideas can be addressed during lecture, with the rest of the content assigned as reading material. To engage the reader, the text combines examples, basic ideas, rigorous proofs, and pointers to the literature to enhance scientific literacy.Volume II is divided into 32 chapters plus one appendix. The first part of the volume focuses on the approximation of elliptic and mixed PDEs, beginning with fundamental results on well-posed weak formulations and their approximation by the Galerkin method. The material covered includes key results such as the BNB theorem based on inf-sup conditions, Céa's and Strang's lemmas, and the duality argument by Aubin and Nitsche. Important implementation aspects regarding quadratures, linear algebra, and assembling are also covered. The remainder of Volume II focuses on PDEs where a coercivity property is available. It investigates conforming and nonconforming approximation techniques (Galerkin, boundary penalty, Crouzeix—Raviart, discontinuous Galerkin, hybrid high-order methods). These techniques are applied to elliptic PDEs (diffusion, elasticity, the Helmholtz problem, Maxwell's equations), eigenvalue problems for elliptic PDEs, and PDEs in mixed form (Darcy and Stokes flows). Finally, the appendix addresses fundamental results on the surjectivity, bijectivity, and coercivity of linear operators in Banach spaces.
Finite Elements III: First-Order and Time-Dependent PDEs (Texts in Applied Mathematics #74)
by Alexandre Ern Jean-Luc GuermondThis book is the third volume of a three-part textbook suitable for graduate coursework, professional engineering and academic research. It is also appropriate for graduate flipped classes. Each volume is divided into short chapters. Each chapter can be covered in one teaching unit and includes exercises as well as solutions available from a dedicated website. The salient ideas can be addressed during lecture, with the rest of the content assigned as reading material. To engage the reader, the text combines examples, basic ideas, rigorous proofs, and pointers to the literature to enhance scientific literacy. Volume III is divided into 28 chapters. The first eight chapters focus on the symmetric positive systems of first-order PDEs called Friedrichs' systems. This part of the book presents a comprehensive and unified treatment of various stabilization techniques from the existing literature. It discusses applications to advection and advection-diffusion equations and various PDEs written in mixed form such as Darcy and Stokes flows and Maxwell's equations. The remainder of Volume III addresses time-dependent problems: parabolic equations (such as the heat equation), evolution equations without coercivity (Stokes flows, Friedrichs' systems), and nonlinear hyperbolic equations (scalar conservation equations, hyperbolic systems). It offers a fresh perspective on the analysis of well-known time-stepping methods. The last five chapters discuss the approximation of hyperbolic equations with finite elements. Here again a new perspective is proposed. These chapters should convince the reader that finite elements offer a good alternative to finite volumes to solve nonlinear conservation equations.
Finite Elements Methods in Mechanics
by M. Reza EslamiThis book covers all basic areas of mechanical engineering, such as fluid mechanics, heat conduction, beams and elasticity with detailed derivations for the mass, stiffness and force matrices. It is especially designed to give physical feeling to the reader for finite element approximation by the introduction of finite elements to the elevation of elastic membrane. A detailed treatment of computer methods with numerical examples are provided. In the fluid mechanics chapter, the conventional and vorticity transport formulations for viscous incompressible fluid flow with discussion on the method of solution are presented. The variational and Galerkin formulations of the heat conduction, beams and elasticity problems are also discussed in detail. Three computer codes are provided to solve the elastic membrane problem. One of them solves the Poisson's equation. The second computer program handles the two dimensional elasticity problems and the third one presents the three dimensional transient heat conduction problems. The programs are written in C++ environment.
Finite Form Representations for Meijer G and Fox H Functions: Applied to Multivariate Likelihood Ratio Tests Using Mathematica®, MAXIMA and R (Lecture Notes in Statistics #223)
by Carlos A. Coelho Barry C. ArnoldThis book depicts a wide range of situations in which there exist finite form representations for the Meijer G and the Fox H functions. Accordingly, it will be of interest to researchers and graduate students who, when implementing likelihood ratio tests in multivariate analysis, would like to know if there exists an explicit manageable finite form for the distribution of the test statistics. In these cases, both the exact quantiles and the exact p-values of the likelihood ratio tests can be computed quickly and efficiently.The test statistics in question range from common ones, such as those used to test e.g. the equality of means or the independence of blocks of variables in real or complex normally distributed random vectors; to far more elaborate tests on the structure of covariance matrices and equality of mean vectors. The book also provides computational modules in Mathematica®, MAXIMA and R, which allow readers to easily implement, plot and compute the distributions of any of these statistics, or any other statistics that fit into the general paradigm described here.
Finite Frequency Analysis and Synthesis for Singularly Perturbed Systems
by Chenxiao Cai Zidong Wang Jing Xu Yun ZouThis book is a self-contained collection of recent research findings providing a comprehensive and systematic unified framework for both analysis and synthesis for singularly perturbed systems. It paves the way for the gap between frequency-domain-transfer-function-based results and time-domain-state-space-based results to be bridged. It is divided into three parts focusing on: fundamental background of singular perturbation; general singular perturbation methodologies and time-scale techniques and the theoretical foundation of finite-frequency control; the analysis and synthesis of singularly perturbed systems; and real-world engineering applications implementing the results developed in systems like wind turbines and autonomous-aerial-vehicle hovering. It also presents solutions to analysis and design problems in terms of linear matrix inequalities. Lastly, it provides valuable reference material for researchers who wish to explore the design of controllers for such systems.
Finite Geometries
by Catherine Anne BakerThis book is a compilation of the papers presented at the conference in Winnipeg on the subject of finite geometry in 1984. It covers different fields in finite geometry: classical finite geometry, the geometry of finite planes, geometric structures and the theory of translation planes.
Finite Geometries
by Gyorgy Kiss Tamas SzonyiFinite Geometries stands out from recent textbooks about the subject of finite geometries by having a broader scope. The authors thoroughly explain how the subject of finite geometries is a central part of discrete mathematics. The text is suitable for undergraduate and graduate courses. Additionally, it can be used as reference material on recent works. The authors examine how finite geometries’ applicable nature led to solutions of open problems in different fields, such as design theory, cryptography and extremal combinatorics. Other areas covered include proof techniques using polynomials in case of Desarguesian planes, and applications in extremal combinatorics, plus, recent material and developments. Features: Includes exercise sets for possible use in a graduate course Discusses applications to graph theory and extremal combinatorics Covers coding theory and cryptography Translated and revised text from the Hungarian published version
Finite Geometry and Combinatorial Applications
by Simeon BallThe projective and polar geometries that arise from a vector space over a finite field are particularly useful in the construction of combinatorial objects, such as latin squares, designs, codes and graphs. This book provides an introduction to these geometries and their many applications to other areas of combinatorics. Coverage includes a detailed treatment of the forbidden subgraph problem from a geometrical point of view, and a chapter on maximum distance separable codes, which includes a proof that such codes over prime fields are short. The author also provides more than 100 exercises (complete with detailed solutions), which show the diversity of applications of finite fields and their geometries. Finite Geometry and Combinatorial Applications is ideal for anyone, from a third-year undergraduate to a researcher, who wishes to familiarise themselves with and gain an appreciation of finite geometry.
Finite Markov Processes and Their Applications
by Marius IosifescuA self-contained treatment of finite Markov chains and processes, this text covers both theory and applications. Author Marius Iosifescu, vice president of the Romanian Academy and director of its Center for Mathematical Statistics, begins with a review of relevant aspects of probability theory and linear algebra. Experienced readers may start with the second chapter, a treatment of fundamental concepts of homogeneous finite Markov chain theory that offers examples of applicable models.The text advances to studies of two basic types of homogeneous finite Markov chains: absorbing and ergodic chains. A complete study of the general properties of homogeneous chains follows. Succeeding chapters examine the fundamental role of homogeneous infinite Markov chains in mathematical modeling employed in the fields of psychology and genetics; the basics of nonhomogeneous finite Markov chain theory; and a study of Markovian dependence in continuous time, which constitutes an elementary introduction to the study of continuous parameter stochastic processes.
Finite Math For Dummies
by Mary Jane SterlingUse mathematical analysis in the real world Finite math takes everything you've learned in your previous math courses and brings them together into one course with a focus on organizing and analyzing information, creating mathematical models for approaching business decisions, using statistics principles to understand future states, and applying logic to data organization. Finite Math For Dummies tracks to a typical college-level course designed for business, computer science, accounting, and other non-math majors, and is the perfect supplement to help you score high! Organize and analyze information Apply calculation principles to real-world problems Use models for business calculations Supplement your coursework with step-by-step example problems If you’re not a math person or just want to brush up on your skills to get a better grade, Finite Math For Dummies is your ticket to scoring higher!
Finite Mathematics
by Howard L. RolfGet the background you need and discover the usefulness of mathematics in analyzing and solving problems with FINITE MATHEMATICS, Eighth Edition. The author clearly explains concepts, and the computations demonstrate enough detail to allow you to follow and learn steps in the problem-solving process. Hundreds of examples and exercises, many based on real-world data, illustrate the practical applications of mathematical concepts. <p><p>The book also includes technology guidelines to help you successfully use graphing calculators and Microsoft Excel to solve selected exercises. Available with InfoTrac Student Collections http://gocengage.com/infotrac.
Finite Mathematics
by Robert M. Stark Carla C. MorrisFeatures step-by-step examples based on actual data and connects fundamental mathematical modeling skills and decision making concepts to everyday applicability Featuring key linear programming, matrix, and probability concepts, Finite Mathematics: Models and Applications emphasizes cross-disciplinary applications that relate mathematics to everyday life. The book provides a unique combination of practical mathematical applications to illustrate the wide use of mathematics in fields ranging from business, economics, finance, management, operations research, and the life and social sciences. In order to emphasize the main concepts of each chapter, Finite Mathematics: Models and Applications features plentiful pedagogical elements throughout such as special exercises, end notes, hints, select solutions, biographies of key mathematicians, boxed key principles, a glossary of important terms and topics, and an overview of use of technology. The book encourages the modeling of linear programs and their solutions and uses common computer software programs such as LINDO. In addition to extensive chapters on probability and statistics, principles and applications of matrices are included as well as topics for enrichment such as the Monte Carlo method, game theory, kinship matrices, and dynamic programming. Supplemented with online instructional support materials, the book features coverage including: Algebra Skills Mathematics of Finance Matrix Algebra Geometric Solutions Simplex Methods Application Models Set and Probability Relationships Random Variables and Probability Distributions Markov Chains Mathematical Statistics Enrichment in Finite Mathematics An ideal textbook, Finite Mathematics: Models and Applications is intended for students in fields from entrepreneurial and economic to environmental and social science, including many in the arts and humanities.
Finite Mathematics: An Applied Approach (Tenth edition)
by Michael SullivanThis comprehensive book on finite mathematics covers wide range of topics like linear equations, linear systems, linear programming,basic mathematics of finance, set theory and basic combinatorics, probability and statistics, etc.
Finite Mathematics: For The Managerial, Life, And Social Sciences
by Soo T. TanFINITE MATHEMATICS FOR THE MANAGERIAL, LIFE, AND SOCIAL SCIENCES, Twelfth Edition, is a clear, easy-to-follow text that balances contemporary mathematics applications and the latest technology to help give you the key problem-solving skills you need for your life and career in the 21st century. Real-world applications put math concepts in context and cover topics including social media accounts, corporate fraud, criminal justice, cyber privacy, starting a new job, gas prices, smartphone ownership, mobile ad revenues, and more.
Finite Mathematics, 10th Edition
by Margaret L. Lial Raymond N. Greenwell Nathan P. RitcheyFinite Mathematics is a thorough, application-oriented text for students majoring in business, management, economics, or the life or social sciences.
Finite Mathematics and Calculus with Applications
by Margaret Lial Raymond Greenwell Nathan RitcheyFinite Mathematics and Calculus with Applications, Tenth Edition by Lial, Greenwell, and Ritchey, is our most applied text to date, making the math relevant and accessible for students of business, life science, and social sciences. Current applications, many using real data, are incorporated in numerous forms throughout the book, preparing students for success in their professional careers. With this edition, students will find new ways to help them learn the material, such as Warm-Up Exercises and added “help text” within examples.
Finite Mathematics as the Foundation of Classical Mathematics and Quantum Theory: With Applications to Gravity and Particle Theory
by Felix LevThis book delves into finite mathematics and its application in physics, particularly quantum theory. It is shown that quantum theory based on finite mathematics is more general than standard quantum theory, whilst finite mathematics is itself more general than standard mathematics.As a consequence, the mathematics describing nature at the most fundamental level involves only a finite number of numbers while the notions of limit, infinite/infinitesimal and continuity are needed only in calculations that describe nature approximately. It is also shown that the concepts of particle and antiparticle are likewise approximate notions, valid only in special situations, and that the electric charge and baryon- and lepton quantum numbers can be only approximately conserved.
Finite Mathematics Concepts and Applications
by Tityik WongThis book has been used by the author at the College of Southern Nevada since 2018. It serves as a college freshman level finite mathematics textbook. The major topics in a typical finite mathematics course (mathematics of finance, set theory, linear algebra, counting techniques, probability and statistics) are covered. The book emphasizes the thinking and reasoning aspects of mathematics. The goal is to help students acquire certain amount of useful knowledge, and at the same time become better critical thinkers. Some new approaches to old topics and some new topics are included in the book.
Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences (Thirteenth Edition)
by Raymond A. Barnett Michael R. Ziegler Karl E. ByleenLearn about the math that will help you in many careers and academic disciplines.
Finite Mathematics for the Managerial, Life, and Social Sciences (Tenth Edition)
by Soo T. TanThe text pairs pioneering technology with rock-solid theory, delivering matchless flexibility to both traditional and modern practitioners. The text abounds with helpful examples, exercises, applications, and features to motivate further exploration.
Finite Mathematics & Its Applications (12th Edition)
by Steven M. Hair Larry J. Goldstein David I. Schneider Martha J. SiegelFor Finite Math courses for students majoring in business, economics, life science, or social sciences <p><p> The most relevant choice<p> Finite Mathematics is a comprehensive yet flexible text for students majoring in business, economics, life science, or social sciences. Its varied and relevant applications are designed to pique and hold student interest, and the depth of coverage provides a solid foundation for students’ future coursework and careers. Built-in, optional instruction for the latest technology—graphing calculators, spreadsheets, and WolframAlpha—gives instructors flexibility in deciding how to integrate these tools into their course. Thousands of well-crafted exercises–a hallmark of this text–are available in print and online in MyLab™ Math to enable a wide range of practice in skills, applications, concepts, and technology.<p> In the 12th Edition, new co-author Steve Hair (Pennsylvania State University) brings a fresh eye to the content and MyLab™ Math course based on his experience in the classroom. In addition to its updated applications, exercises, and technology coverage, the revision infuses modern topics such as health statistics and content revisions based on user feedback. The authors relied on aggregated student usage and performance data from MyLab™ Math to improve the quality and quantity of exercises.
Finite Mathematics (Sixth Edition)
by Department of Mathematics NdsuA mathematics textbook for undergraduates.
Finite Mixture of Skewed Distributions (SpringerBriefs in Statistics)
by Víctor Hugo Lachos Dávila Celso Rômulo Cabral Camila Borelli ZellerThis book presents recent results in finite mixtures of skewed distributions to prepare readers to undertake mixture models using scale mixtures of skew normal distributions (SMSN). For this purpose, the authors consider maximum likelihood estimation for univariate and multivariate finite mixtures where components are members of the flexible class of SMSN distributions. This subclass includes the entire family of normal independent distributions, also known as scale mixtures of normal distributions (SMN), as well as the skew-normal and skewed versions of some other classical symmetric distributions: the skew-t (ST), the skew-slash (SSL) and the skew-contaminated normal (SCN), for example. These distributions have heavier tails than the typical normal one, and thus they seem to be a reasonable choice for robust inference. The proposed EM-type algorithm and methods are implemented in the R package mixsmsn, highlighting the applicability of the techniques presented in the book.This work is a useful reference guide for researchers analyzing heterogeneous data, as well as a textbook for a graduate-level course in mixture models. The tools presented in the book make complex techniques accessible to applied researchers without the advanced mathematical background and will have broad applications in fields like medicine, biology, engineering, economic, geology and chemistry.
Finite or Infinite Dimensional Complex Analysis: Proceedings Of The Seventh International Colloquium (Lecture Notes in Pure and Applied Mathematics #Vol. 214)
by Joji Kajiwara Zhong Li Kwang Ho ShonThis volume presents the proceedings of the Seventh International Colloquium on Finite or Infinite Dimensional Complex Analysis held in Fukuoka, Japan. The contributions offer multiple perspectives and numerous research examples on complex variables, Clifford algebra variables, hyperfunctions and numerical analysis.