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Methods of Numerical Integration

Author: Philip J. Davis

Publisher: Academic Press

Published: 2014-05-10

Total Pages: 628

ISBN-13: 1483264289

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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.

Book Synopsis Methods of Numerical Integration by : Philip J. Davis

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.

Calculus Volume 3

Author: Edwin Herman

Publisher:

Published: 2016-03-30

Total Pages: 0

ISBN-13: 9781947172838

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Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 3 covers parametric equations and polar coordinates, vectors, functions of several variables, multiple integration, and second-order differential equations.

Book Synopsis Calculus Volume 3 by : Edwin Herman

Download or read book Calculus Volume 3 written by Edwin Herman and published by . This book was released on 2016-03-30 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 3 covers parametric equations and polar coordinates, vectors, functions of several variables, multiple integration, and second-order differential equations.

Numerical Integration III

Author: Helmut Brass

Publisher:

Published: 1988

Total Pages: 0

ISBN-13: 9780081762202

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Book Synopsis Numerical Integration III by : Helmut Brass

Download or read book Numerical Integration III written by Helmut Brass and published by . This book was released on 1988 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Practical Numerical Integration

Author: Gwynne Evans

Publisher:

Published: 1993-08-24

Total Pages: 350

ISBN-13:

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Offers the quadrature user a selection of the most effective algorithms in each of the main areas of the subject. Topics range from Simpson's rule and Gaussian quadrature to recent research on irregular oscillatory and singular quadrature. A full set of test examples is given and implemented for each method discussed, demonstrating its practical limitations.

Book Synopsis Practical Numerical Integration by : Gwynne Evans

Download or read book Practical Numerical Integration written by Gwynne Evans and published by . This book was released on 1993-08-24 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers the quadrature user a selection of the most effective algorithms in each of the main areas of the subject. Topics range from Simpson's rule and Gaussian quadrature to recent research on irregular oscillatory and singular quadrature. A full set of test examples is given and implemented for each method discussed, demonstrating its practical limitations.

Numerical Integration

Author: Philip J. Davis

Publisher:

Published: 1960

Total Pages: 0

ISBN-13:

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Book Synopsis Numerical Integration by : Philip J. Davis

Download or read book Numerical Integration written by Philip J. Davis and published by . This book was released on 1960 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

An Introduction to Element-Based Galerkin Methods on Tensor-Product Bases

Author: Francis X. Giraldo

Publisher: Springer Nature

Published: 2020-10-30

Total Pages: 559

ISBN-13: 3030550699

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This book introduces the reader to solving partial differential equations (PDEs) numerically using element-based Galerkin methods. Although it draws on a solid theoretical foundation (e.g. the theory of interpolation, numerical integration, and function spaces), the book’s main focus is on how to build the method, what the resulting matrices look like, and how to write algorithms for coding Galerkin methods. In addition, the spotlight is on tensor-product bases, which means that only line elements (in one dimension), quadrilateral elements (in two dimensions), and cubes (in three dimensions) are considered. The types of Galerkin methods covered are: continuous Galerkin methods (i.e., finite/spectral elements), discontinuous Galerkin methods, and hybridized discontinuous Galerkin methods using both nodal and modal basis functions. In addition, examples are included (which can also serve as student projects) for solving hyperbolic and elliptic partial differential equations, including both scalar PDEs and systems of equations.

Book Synopsis An Introduction to Element-Based Galerkin Methods on Tensor-Product Bases by : Francis X. Giraldo

Download or read book An Introduction to Element-Based Galerkin Methods on Tensor-Product Bases written by Francis X. Giraldo and published by Springer Nature. This book was released on 2020-10-30 with total page 559 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the reader to solving partial differential equations (PDEs) numerically using element-based Galerkin methods. Although it draws on a solid theoretical foundation (e.g. the theory of interpolation, numerical integration, and function spaces), the book’s main focus is on how to build the method, what the resulting matrices look like, and how to write algorithms for coding Galerkin methods. In addition, the spotlight is on tensor-product bases, which means that only line elements (in one dimension), quadrilateral elements (in two dimensions), and cubes (in three dimensions) are considered. The types of Galerkin methods covered are: continuous Galerkin methods (i.e., finite/spectral elements), discontinuous Galerkin methods, and hybridized discontinuous Galerkin methods using both nodal and modal basis functions. In addition, examples are included (which can also serve as student projects) for solving hyperbolic and elliptic partial differential equations, including both scalar PDEs and systems of equations.

Methods of Numerical Integration

Author: Philip J. Davis

Publisher: Courier Corporation

Published: 2007-01-01

Total Pages: 626

ISBN-13: 0486453391

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Useful to programmers and stimulating for theoreticians, this text offers a balanced presentation accessible to those with a background in calculus. Topics include approximate integration over finite and infinite intervals, error analysis, approximate integration in two or more dimensions, and automatic integration. Includes five helpful appendixes. 1984 edition.

Book Synopsis Methods of Numerical Integration by : Philip J. Davis

Download or read book Methods of Numerical Integration written by Philip J. Davis and published by Courier Corporation. This book was released on 2007-01-01 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: Useful to programmers and stimulating for theoreticians, this text offers a balanced presentation accessible to those with a background in calculus. Topics include approximate integration over finite and infinite intervals, error analysis, approximate integration in two or more dimensions, and automatic integration. Includes five helpful appendixes. 1984 edition.

Numerical Methods in Engineering with Python 3

Author: Jaan Kiusalaas

Publisher: Cambridge University Press

Published: 2013-01-21

Total Pages: 437

ISBN-13: 1107033853

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Provides an introduction to numerical methods for students in engineering. It uses Python 3, an easy-to-use, high-level programming language.

Book Synopsis Numerical Methods in Engineering with Python 3 by : Jaan Kiusalaas

Download or read book Numerical Methods in Engineering with Python 3 written by Jaan Kiusalaas and published by Cambridge University Press. This book was released on 2013-01-21 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides an introduction to numerical methods for students in engineering. It uses Python 3, an easy-to-use, high-level programming language.

Numerical Integration of Stochastic Differential Equations

Author: G.N. Milstein

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 178

ISBN-13: 9401584559

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This book is devoted to mean-square and weak approximations of solutions of stochastic differential equations (SDE). These approximations represent two fundamental aspects in the contemporary theory of SDE. Firstly, the construction of numerical methods for such systems is important as the solutions provided serve as characteristics for a number of mathematical physics problems. Secondly, the employment of probability representations together with a Monte Carlo method allows us to reduce the solution of complex multidimensional problems of mathematical physics to the integration of stochastic equations. Along with a general theory of numerical integrations of such systems, both in the mean-square and the weak sense, a number of concrete and sufficiently constructive numerical schemes are considered. Various applications and particularly the approximate calculation of Wiener integrals are also dealt with. This book is of interest to graduate students in the mathematical, physical and engineering sciences, and to specialists whose work involves differential equations, mathematical physics, numerical mathematics, the theory of random processes, estimation and control theory.

Book Synopsis Numerical Integration of Stochastic Differential Equations by : G.N. Milstein

Download or read book Numerical Integration of Stochastic Differential Equations written by G.N. Milstein and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to mean-square and weak approximations of solutions of stochastic differential equations (SDE). These approximations represent two fundamental aspects in the contemporary theory of SDE. Firstly, the construction of numerical methods for such systems is important as the solutions provided serve as characteristics for a number of mathematical physics problems. Secondly, the employment of probability representations together with a Monte Carlo method allows us to reduce the solution of complex multidimensional problems of mathematical physics to the integration of stochastic equations. Along with a general theory of numerical integrations of such systems, both in the mean-square and the weak sense, a number of concrete and sufficiently constructive numerical schemes are considered. Various applications and particularly the approximate calculation of Wiener integrals are also dealt with. This book is of interest to graduate students in the mathematical, physical and engineering sciences, and to specialists whose work involves differential equations, mathematical physics, numerical mathematics, the theory of random processes, estimation and control theory.

A Concise Introduction to Geometric Numerical Integration

Author: Sergio Blanes

Publisher: CRC Press

Published: 2017-11-22

Total Pages: 233

ISBN-13: 1482263440

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Discover How Geometric Integrators Preserve the Main Qualitative Properties of Continuous Dynamical Systems A Concise Introduction to Geometric Numerical Integration presents the main themes, techniques, and applications of geometric integrators for researchers in mathematics, physics, astronomy, and chemistry who are already familiar with numerical tools for solving differential equations. It also offers a bridge from traditional training in the numerical analysis of differential equations to understanding recent, advanced research literature on numerical geometric integration. The book first examines high-order classical integration methods from the structure preservation point of view. It then illustrates how to construct high-order integrators via the composition of basic low-order methods and analyzes the idea of splitting. It next reviews symplectic integrators constructed directly from the theory of generating functions as well as the important category of variational integrators. The authors also explain the relationship between the preservation of the geometric properties of a numerical method and the observed favorable error propagation in long-time integration. The book concludes with an analysis of the applicability of splitting and composition methods to certain classes of partial differential equations, such as the Schrödinger equation and other evolution equations. The motivation of geometric numerical integration is not only to develop numerical methods with improved qualitative behavior but also to provide more accurate long-time integration results than those obtained by general-purpose algorithms. Accessible to researchers and post-graduate students from diverse backgrounds, this introductory book gets readers up to speed on the ideas, methods, and applications of this field. Readers can reproduce the figures and results given in the text using the MATLAB® programs and model files available online.

Book Synopsis A Concise Introduction to Geometric Numerical Integration by : Sergio Blanes

Download or read book A Concise Introduction to Geometric Numerical Integration written by Sergio Blanes and published by CRC Press. This book was released on 2017-11-22 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discover How Geometric Integrators Preserve the Main Qualitative Properties of Continuous Dynamical Systems A Concise Introduction to Geometric Numerical Integration presents the main themes, techniques, and applications of geometric integrators for researchers in mathematics, physics, astronomy, and chemistry who are already familiar with numerical tools for solving differential equations. It also offers a bridge from traditional training in the numerical analysis of differential equations to understanding recent, advanced research literature on numerical geometric integration. The book first examines high-order classical integration methods from the structure preservation point of view. It then illustrates how to construct high-order integrators via the composition of basic low-order methods and analyzes the idea of splitting. It next reviews symplectic integrators constructed directly from the theory of generating functions as well as the important category of variational integrators. The authors also explain the relationship between the preservation of the geometric properties of a numerical method and the observed favorable error propagation in long-time integration. The book concludes with an analysis of the applicability of splitting and composition methods to certain classes of partial differential equations, such as the Schrödinger equation and other evolution equations. The motivation of geometric numerical integration is not only to develop numerical methods with improved qualitative behavior but also to provide more accurate long-time integration results than those obtained by general-purpose algorithms. Accessible to researchers and post-graduate students from diverse backgrounds, this introductory book gets readers up to speed on the ideas, methods, and applications of this field. Readers can reproduce the figures and results given in the text using the MATLAB® programs and model files available online.