Methods of Numerical Integration PDF Download
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Author: Philip J. Davis
Publisher: Academic Press
ISBN: 1483264289
Category : Mathematics
Languages : en
Pages : 628
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Book Description
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.
Author: Philip J. Davis
Publisher: Academic Press
ISBN: 1483264289
Category : Mathematics
Languages : en
Pages : 628
Get Book Here
Book Description
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.
Author: Philip J. Davis
Publisher:
ISBN:
Category : Numerical integration
Languages : en
Pages : 0
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Book Description
Author: Ernst Hairer
Publisher: Springer Science & Business Media
ISBN: 3662050188
Category : Mathematics
Languages : en
Pages : 526
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Book Description
This book deals with numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions. A complete self-contained theory of symplectic and symmetric methods, which include Runge-Kutta, composition, splitting, multistep and various specially designed integrators, is presented and their construction and practical merits are discussed. The long-time behaviour of the numerical solutions is studied using a backward error analysis (modified equations) combined with KAM theory. The book is illustrated by numerous figures, treats applications from physics and astronomy, and contains many numerical experiments and comparisons of different approaches.
Author: Sergio Blanes
Publisher: CRC Press
ISBN: 1315354861
Category : Mathematics
Languages : en
Pages : 287
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Book Description
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.
Author: Gregory Hartman
Publisher:
ISBN: 9781514225158
Category : Calculus
Languages : en
Pages : 0
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Book Description
APEX Calculus is a calculus textbook written for traditional college/university calculus courses. It has the look and feel of the calculus book you likely use right now (Stewart, Thomas & Finney, etc.). The explanations of new concepts is clear, written for someone who does not yet know calculus. Each section ends with an exercise set with ample problems to practice & test skills (odd answers are in the back).
Author: Edwin Herman
Publisher:
ISBN: 9781947172838
Category : Calculus
Languages : en
Pages : 0
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Book Description
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.
Author: Anthony Ralston
Publisher: Courier Corporation
ISBN: 9780486414546
Category : Mathematics
Languages : en
Pages : 644
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Book Description
Outstanding text, oriented toward computer solutions, stresses errors in methods and computational efficiency. Problems — some strictly mathematical, others requiring a computer — appear at the end of each chapter.
Author: G.N. Milstein
Publisher: Springer Science & Business Media
ISBN: 9401584559
Category : Computers
Languages : en
Pages : 178
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Book Description
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.
Author: Maurizio Petrelli
Publisher: Springer Nature
ISBN: 3030780554
Category : Science
Languages : en
Pages : 229
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Book Description
This textbook introduces the use of Python programming for exploring and modelling data in the field of Earth Sciences. It drives the reader from his very first steps with Python, like setting up the environment and starting writing the first lines of codes, to proficient use in visualizing, analyzing, and modelling data in the field of Earth Science. Each chapter contains explicative examples of code, and each script is commented in detail. The book is minded for very beginners in Python programming, and it can be used in teaching courses at master or PhD levels. Also, Early careers and experienced researchers who would like to start learning Python programming for the solution of geological problems will benefit the reading of the book.
Author: Qingkai Kong
Publisher: Academic Press
ISBN: 0128195509
Category : Technology & Engineering
Languages : en
Pages : 482
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Book Description
Python Programming and Numerical Methods: A Guide for Engineers and Scientists introduces programming tools and numerical methods to engineering and science students, with the goal of helping the students to develop good computational problem-solving techniques through the use of numerical methods and the Python programming language. Part One introduces fundamental programming concepts, using simple examples to put new concepts quickly into practice. Part Two covers the fundamentals of algorithms and numerical analysis at a level that allows students to quickly apply results in practical settings. - Includes tips, warnings and "try this" features within each chapter to help the reader develop good programming practice - Summaries at the end of each chapter allow for quick access to important information - Includes code in Jupyter notebook format that can be directly run online
