Download or read book Handbook of Computational Methods for Integration written by Prem K. Kythe and published by CRC Press. This book was released on 2004-12-20 with total page 621 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the past 20 years, there has been enormous productivity in theoretical as well as computational integration. Some attempts have been made to find an optimal or best numerical method and related computer code to put to rest the problem of numerical integration, but the research is continuously ongoing, as this problem is still very much open-

Download or read book Handbook of computational methods for integration written by and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Computational Methods in Engineering written by S. P. Venkateshan and published by Springer Nature. This book was released on 2023-05-31 with total page 824 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is designed to serve as a textbook for courses offered to graduate and upper-undergraduate students enrolled in mechanical engineering. The book attempts to make students with mathematical backgrounds comfortable with numerical methods. The book also serves as a handy reference for practicing engineers who are interested in applications. The book is written in an easy-to-understand manner, with the essence of each numerical method clearly stated. This makes it easy for professional engineers, students, and early career researchers to follow the material presented in the book. The structure of the book has been modeled accordingly. It is divided into four modules: i) solution of a system of equations and eigenvalues which includes linear equations, determining eigenvalues, and solution of nonlinear equations; ii) function approximations: interpolation, data fit, numerical differentiation, and numerical integration; iii) solution of ordinary differential equations—initial value problems and boundary value problems; and iv) solution of partial differential equations—parabolic, elliptic, and hyperbolic PDEs. Each section of the book includes exercises to reinforce the concepts, and problems have been added at the end of each chapter. Exercise problems may be solved by using computational tools such as scientific calculators, spreadsheet programs, and MATLAB codes. The detailed coverage and pedagogical tools make this an ideal textbook for students, early career researchers, and professionals.

Download or read book Computational Methods for Numerical Analysis with R written by James P Howard, II and published by CRC Press. This book was released on 2017-07-12 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Methods for Numerical Analysis with R is an overview of traditional numerical analysis topics presented using R. This guide shows how common functions from linear algebra, interpolation, numerical integration, optimization, and differential equations can be implemented in pure R code. Every algorithm described is given with a complete function implementation in R, along with examples to demonstrate the function and its use. Computational Methods for Numerical Analysis with R is intended for those who already know R, but are interested in learning more about how the underlying algorithms work. As such, it is suitable for statisticians, economists, and engineers, and others with a computational and numerical background.

Download or read book The Handbook of Integration written by Daniel Zwillinger and published by CRC Press. This book was released on 1992-11-02 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a compilation of the most important and widely applicable methods for evaluating and approximating integrals. It is an indispensable time saver for engineers and scientists needing to evaluate integrals in their work. From the table of contents: - Applications of Integration - Concepts and Definitions - Exact Analytical Methods - Appro

Download or read book Computational Methods for Numerical Analysis with R written by James P Howard, II and published by CRC Press. This book was released on 2017-07-12 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Methods for Numerical Analysis with R is an overview of traditional numerical analysis topics presented using R. This guide shows how common functions from linear algebra, interpolation, numerical integration, optimization, and differential equations can be implemented in pure R code. Every algorithm described is given with a complete function implementation in R, along with examples to demonstrate the function and its use. Computational Methods for Numerical Analysis with R is intended for those who already know R, but are interested in learning more about how the underlying algorithms work. As such, it is suitable for statisticians, economists, and engineers, and others with a computational and numerical background.

Download or read book Methods of Numerical Integration written by Philip J. Davis and published by Academic Press. This book was released on 2014-05-10 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: Methods of Numerical Integration, Second Edition describes the theoretical and practical aspects of major methods of numerical integration. Numerical integration is the study of how the numerical value of an integral can be found. This book contains six chapters and begins with a discussion of the basic principles and limitations of numerical integration. The succeeding chapters present the approximate integration rules and formulas over finite and infinite intervals. These topics are followed by a review of error analysis and estimation, as well as the application of functional analysis to numerical integration. A chapter describes the approximate integration in two or more dimensions. The final chapter looks into the goals and processes of automatic integration, with particular attention to the application of Tschebyscheff polynomials. This book will be of great value to theoreticians and computer programmers.

Download or read book Computational Methods for Linear Integral Equations written by Prem Kythe and published by Springer Science & Business Media. This book was released on 2002-04-26 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents numerical methods and computational aspects for linear integral equations. Such equations occur in various areas of applied mathematics, physics, and engineering. The material covered in this book, though not exhaustive, offers useful techniques for solving a variety of problems. Historical information cover ing the nineteenth and twentieth centuries is available in fragments in Kantorovich and Krylov (1958), Anselone (1964), Mikhlin (1967), Lonseth (1977), Atkinson (1976), Baker (1978), Kondo (1991), and Brunner (1997). Integral equations are encountered in a variety of applications in many fields including continuum mechanics, potential theory, geophysics, electricity and mag netism, kinetic theory of gases, hereditary phenomena in physics and biology, renewal theory, quantum mechanics, radiation, optimization, optimal control sys tems, communication theory, mathematical economics, population genetics, queue ing theory, and medicine. Most of the boundary value problems involving differ ential equations can be converted into problems in integral equations, but there are certain problems which can be formulated only in terms of integral equations. A computational approach to the solution of integral equations is, therefore, an essential branch of scientific inquiry.

Download or read book Handbook of Analytic Computational Methods in Applied Mathematics written by George Anastassiou and published by CRC Press. This book was released on 2019-06-03 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: Working computationally in applied mathematics is the very essence of dealing with real-world problems in science and engineering. Approximation theory-on the borderline between pure and applied mathematics- has always supplied some of the most innovative ideas, computational methods, and original approaches to many types of problems. The f

Download or read book Generalized Differential and Integral Quadrature written by Francesco Tornabene and published by Società Editrice Esculapio. This book was released on 2023-10-17 with total page 689 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main aim of this book is to analyze the mathematical fundamentals and the main features of the Generalized Differential Quadrature (GDQ) and Generalized Integral Quadrature (GIQ) techniques. Furthermore, another interesting aim of the present book is to shown that from the two numerical techniques mentioned above it is possible to derive two different approaches such as the Strong and Weak Finite Element Methods (SFEM and WFEM), that will be used to solve various structural problems and arbitrarily shaped structures. A general approach to the Differential Quadrature is proposed. The weighting coefficients for different basis functions and grid distributions are determined. Furthermore, the expressions of the principal approximating polynomials and grid distributions, available in the literature, are shown. Besides the classic orthogonal polynomials, a new class of basis functions, which depend on the radial distance between the discretization points, is presented. They are known as Radial Basis Functions (or RBFs). The general expressions for the derivative evaluation can be utilized in the local form to reduce the computational cost. From this concept the Local Generalized Differential Quadrature (LGDQ) method is derived. The Generalized Integral Quadrature (GIQ) technique can be used employing several basis functions, without any restriction on the point distributions for the given definition domain. To better underline these concepts some classical numerical integration schemes are reported, such as the trapezoidal rule or the Simpson method. An alternative approach based on Taylor series is also illustrated to approximate integrals. This technique is named as Generalized Taylor-based Integral Quadrature (GTIQ) method. The major structural theories for the analysis of the mechanical behavior of various structures are presented in depth in the book. In particular, the strong and weak formulations of the corresponding governing equations are discussed and illustrated. Generally speaking, two formulations of the same system of governing equations can be developed, which are respectively the strong and weak (or variational) formulations. Once the governing equations that rule a generic structural problem are obtained, together with the corresponding boundary conditions, a differential system is written. In particular, the Strong Formulation (SF) of the governing equations is obtained. The differentiability requirement, instead, is reduced through a weighted integral statement if the corresponding Weak Formulation (WF) of the governing equations is developed. Thus, an equivalent integral formulation is derived, starting directly from the previous one. In particular, the formulation in hand is obtained by introducing a Lagrangian approximation of the degrees of freedom of the problem. The need of studying arbitrarily shaped domains or characterized by mechanical and geometrical discontinuities leads to the development of new numerical approaches that divide the structure in finite elements. Then, the strong form or the weak form of the fundamental equations are solved inside each element. The fundamental aspects of this technique, which the author defined respectively Strong Formulation Finite Element Method (SFEM) and Weak Formulation Finite Element Method (WFEM), are presented in the book.

Download or read book Anisotropic Doubly Curved Shells written by Francesco Tornabene and published by Società Editrice Esculapio. This book was released on 2019-11-01 with total page 1199 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to present in depth several Higher-order Shear Deformation Theories (HSDTs) by means of a unified approach for the mechanical analysis of doubly-curved shell structures made of anisotropic and composite materials. In particular, the strong and weak formulations of the corresponding governing equations are discussed and illustrated. The approach presented in this volume is completely general and represents a valid tool to investigate the structural behavior of many arbitrarily shaped structures. An isogeometric mapping procedure is also illustrated to this aim. Special attention is given also to advanced and innovative constituents, such as Carbon Nanotubes (CNTs), Variable Angle Tow (VAT) composites and Functionally Graded Materials (FGMs). In addition, several numerical applications are developed to support the theoretical models. Accurate, efficient and reliable numerical techniques able to approximate both derivatives and integrals are presented, which are respectively the Differential Quadrature (DQ) and Integral Quadrature (IQ) methods. Finally, two numerical techniques, named Strong Formulation Finite Element Method (SFEM) and Weak Formulation Finite Element Method (WFEM), are developed to deal with multi-element domains characterized by arbitrary shapes and discontinuities.

Download or read book Hygro Thermo Magneto Electro Elastic Theory of Anisotropic Doubly Curved Shells written by Francesco Tornabene and published by Società Editrice Esculapio. This book was released on 2023-10-13 with total page 1073 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to present in depth several Higher-order Shear Deformation Theories (HSDTs) by means of a unified approach for studying the Hygro-Thermo-Magneto-Electro- Elastic Theory of Anisotropic Doubly-Curved Shells. In particular, a general coupled multifield theory regarding anisotropic shell structures is provided. The three-dimensional multifield problem is reduced in a two-dimensional one following the principles of the Equivalent Single Layer (ESL) approach and the Equivalent Layer-Wise (ELW) approach, setting a proper configuration model. According to the adopted configuration assumptions, several Higher-order Shear Deformation Theories (HSDTs) are obtained. Furthermore, the strong and weak formulations of the corresponding governing equations are discussed and illustrated. The approach presented in this volume is completely general and represents a valid tool to investigate the physical behavior of many arbitrarily shaped structures. An isogeometric mapping procedure is also illustrated to this aim. Special attention is given also to advanced and innovative constituents, such as Carbon Nanotubes (CNTs), Variable Angle Tow (VAT) composites and Functionally Graded Materials (FGMs). In addition, several numerical applications are used to support the theoretical models. Accurate, efficient and reliable numerical techniques able to approximate both derivatives and integrals are considered, which are respectively the Differential Quadrature (DQ) and Integral Quadrature (IQ) methods. The Theory of Composite Thin Shells is derived in a simple and intuitive manner from the theory of thick and moderately thick shells (First-order Shear Deformation Theory or Reissner- Mindlin Theory). In particular, the Kirchhoff-Love Theory and the Membrane Theory for composite shells are shown. Furthermore, the Theory of Composite Arches and Beams is also exposed. In particular, the equations of the Timoshenko Theory and the Euler-Bernoulli Theory are directly deducted from the equations of singly-curved shells of translation and of plates.

Download or read book Handbook of Computational Economics written by Karl Schmedders and published by Newnes. This book was released on 2013-12-31 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Computational Economics summarizes recent advances in economic thought, revealing some of the potential offered by modern computational methods. With computational power increasing in hardware and algorithms, many economists are closing the gap between economic practice and the frontiers of computational mathematics. In their efforts to accelerate the incorporation of computational power into mainstream research, contributors to this volume update the improvements in algorithms that have sharpened econometric tools, solution methods for dynamic optimization and equilibrium models, and applications to public finance, macroeconomics, and auctions. They also cover the switch to massive parallelism in the creation of more powerful computers, with advances in the development of high-power and high-throughput computing. Much more can be done to expand the value of computational modeling in economics. In conjunction with volume one (1996) and volume two (2006), this volume offers a remarkable picture of the recent development of economics as a science as well as an exciting preview of its future potential. - Samples different styles and approaches, reflecting the breadth of computational economics as practiced today - Focuses on problems with few well-developed solutions in the literature of other disciplines - Emphasizes the potential for increasing the value of computational modeling in economics

Download or read book Symbolic Integration I written by Manuel Bronstein and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first volume in the series "Algorithms and Computation in Mathematics", is destined to become the standard reference work in the field. Manuel Bronstein is the number-one expert on this topic and his book is the first to treat the subject both comprehensively and in sufficient detail - incorporating new results along the way. The book addresses mathematicians and computer scientists interested in symbolic computation, developers and programmers of computer algebra systems as well as users of symbolic integration methods. Many algorithms are given in pseudocode ready for immediate implementation, making the book equally suitable as a textbook for lecture courses on symbolic integration.

Download or read book An Introductory Guide to Computational Methods for the Solution of Physics Problems written by George Rawitscher and published by Springer. This book was released on 2018-10-24 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents fundamental aspects of modern spectral and other computational methods, which are not generally taught in traditional courses. It emphasizes concepts as errors, convergence, stability, order and efficiency applied to the solution of physical problems. The spectral methods consist in expanding the function to be calculated into a set of appropriate basis functions (generally orthogonal polynomials) and the respective expansion coefficients are obtained via collocation equations. The main advantage of these methods is that they simultaneously take into account all available information, rather only the information available at a limited number of mesh points. They require more complicated matrix equations than those obtained in finite difference methods. However, the elegance, speed, and accuracy of the spectral methods more than compensates for any such drawbacks. During the course of the monograph, the authors examine the usually rapid convergence of the spectral expansions and the improved accuracy that results when nonequispaced support points are used, in contrast to the equispaced points used in finite difference methods. In particular, they demonstrate the enhanced accuracy obtained in the solutionof integral equations. The monograph includes an informative introduction to old and new computational methods with numerous practical examples, while at the same time pointing out the errors that each of the available algorithms introduces into the specific solution. It is a valuable resource for undergraduate students as an introduction to the field and for graduate students wishing to compare the available computational methods. In addition, the work develops the criteria required for students to select the most suitable method to solve the particular scientific problem that they are confronting.

Download or read book The Routledge Handbook for Advancing Integration in Mixed Methods Research written by John H. Hitchcock and published by Taylor & Francis. This book was released on 2022-05-10 with total page 635 pages. Available in PDF, EPUB and Kindle. Book excerpt: This groundbreaking edited book, The Routledge Handbook for Advancing Integration in Mixed Methods Research, presents an array of different integration ideas, with contributions from scholars across the globe. This handbook represents the first major volume that comprehensively discusses this topic of integration. Perhaps the most fundamental and longstanding question in mixed methods research is: How does one best integrate disparate forms of information to produce the best form of inquiry? Each of the 34 seminal chapters in this handbook accelerates the discussion of integration across a broad range of disciplines, including education, arts-based analyses, and work in the Global South, as well as special topics such as psychometrics and media research. Many of the chapters present new topics that have never been written about before, and all chapters offer cutting-edge approaches to integration. They also offer different perspectives of integration – leading the introductory chapter to offer a new and comprehensive definition for integration, as follows: "referring to the optimal mixing, combining, blending, amalgamating, incorporating, joining, linking, merging, consolidating, or unifying of research approaches, methodologies, philosophies, methods, techniques, concepts, language, modes, disciplines, fields, and/or teams within a single study." The concluding chapter offers a meta-framework that accounts for this definition and is designed to help scholars think more about integration in a way that represents a continuous, dynamic, iterative, interactive, synergistic, and holistic meaning-making process. This handbook will be an essential reference work for all scholars and practitioners using or seeking to use mixed methods in their research.

Download or read book Handbook of Research on Integrating Computer Science and Computational Thinking in K 12 Education written by Keengwe, Jared and published by IGI Global. This book was released on 2019-12-13 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: As technology continues to develop and prove its importance in modern society, certain professions are acclimating. Aspects such as computer science and computational thinking are becoming essential areas of study. Implementing these subject areas into teaching practices is necessary for younger generations to adapt to the developing world. There is a critical need to examine the pedagogical implications of these technological skills and implement them into the global curriculum. The Handbook of Research on Integrating Computer Science and Computational Thinking in K-12 Education is a collection of innovative research on the methods and applications of computer science curriculum development within primary and secondary education. While highlighting topics including pedagogical implications, comprehensive techniques, and teacher preparation models, this book is ideally designed for teachers, IT consultants, curriculum developers, instructional designers, educational software developers, higher education faculty, administrators, policymakers, researchers, and graduate students.