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 Calculus written by Gilbert Strang and published by Wellesley-Cambridge Press. This book was released on 2017-09-14 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gilbert Strang's clear, direct style and detailed, intensive explanations make this textbook ideal as both a course companion and for self-study. Single variable and multivariable calculus are covered in depth. Key examples of the application of calculus to areas such as physics, engineering and economics are included in order to enhance students' understanding. New to the third edition is a chapter on the 'Highlights of calculus', which accompanies the popular video lectures by the author on MIT's OpenCourseWare. These can be accessed from math.mit.edu/~gs.

Download or read book Numerical Integration 1 written by W. F. Eberlein and published by . This book was released on 1954 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

Download or read book Numerical Methods in Scientific Computing written by Germund Dahlquist and published by SIAM. This book was released on 2008-09-04 with total page 741 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work addresses the increasingly important role of numerical methods in science and engineering. It combines traditional and well-developed topics with other material such as interval arithmetic, elementary functions, operator series, convergence acceleration, and continued fractions.

Download or read book APEX Calculus written by Gregory Hartman and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).

Download or read book Quadrature Theory written by Helmut Brass and published by American Mathematical Soc.. This book was released on 2011-10-12 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Every book on numerical analysis covers methods for the approximate calculation of definite integrals. The authors of this book provide a complementary treatment of the topic by presenting a coherent theory of quadrature methods that encompasses many deep and elegant results as well as a large number of interesting (solved and open) problems. The inclusion of the word ``theory'' in the title highlights the authors' emphasis on analytical questions, such as the existence and structure of quadrature methods and selection criteria based on strict error bounds for quadrature rules. Systematic analyses of this kind rely on certain properties of the integrand, called ``co-observations,'' which form the central organizing principle for the authors' theory, and distinguish their book from other texts on numerical integration. A wide variety of co-observations are examined, as a detailed understanding of these is useful for solving problems in practical contexts. While quadrature theory is often viewed as a branch of numerical analysis, its influence extends much further. It has been the starting point of many far-reaching generalizations in various directions, as well as a testing ground for new ideas and concepts. The material in this book should be accessible to anyone who has taken the standard undergraduate courses in linear algebra, advanced calculus, and real analysis.

Download or read book Geometric Numerical Integration written by Ernst Hairer and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Numerical Methods that Work written by Forman S. Acton and published by American Mathematical Soc.. This book was released on 2020-07-31 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 218 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.

Download or read book CK 12 Calculus written by CK-12 Foundation and published by CK-12 Foundation. This book was released on 2010-08-15 with total page 603 pages. Available in PDF, EPUB and Kindle. Book excerpt: CK-12 Foundation's Single Variable Calculus FlexBook introduces high school students to the topics covered in the Calculus AB course. Topics include: Limits, Derivatives, and Integration.

Download or read book Introduction To Numerical Computation An Second Edition written by Wen Shen and published by World Scientific. This book was released on 2019-08-28 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book serves as a set of lecture notes for a senior undergraduate level course on the introduction to numerical computation, which was developed through 4 semesters of teaching the course over 10 years. The book requires minimum background knowledge from the students, including only a three-semester of calculus, and a bit on matrices.The book covers many of the introductory topics for a first course in numerical computation, which fits in the short time frame of a semester course. Topics range from polynomial approximations and interpolation, to numerical methods for ODEs and PDEs. Emphasis was made more on algorithm development, basic mathematical ideas behind the algorithms, and the implementation in Matlab.The book is supplemented by two sets of videos, available through the author's YouTube channel. Homework problem sets are provided for each chapter, and complete answer sets are available for instructors upon request.The second edition contains a set of selected advanced topics, written in a self-contained manner, suitable for self-learning or as additional material for an honored version of the course. Videos are also available for these added topics.

Download or read book A First Course in Numerical Analysis written by Anthony Ralston and published by Courier Corporation. This book was released on 2001-01-01 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book An Introduction to Numerical Methods and Analysis written by James F. Epperson and published by John Wiley & Sons. This book was released on 2013-06-06 with total page 579 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the First Edition ". . . outstandingly appealing with regard to its style, contents, considerations of requirements of practice, choice of examples, and exercises." —Zentrablatt Math ". . . carefully structured with many detailed worked examples . . ." —The Mathematical Gazette ". . . an up-to-date and user-friendly account . . ." —Mathematika An Introduction to Numerical Methods and Analysis addresses the mathematics underlying approximation and scientific computing and successfully explains where approximation methods come from, why they sometimes work (or don't work), and when to use one of the many techniques that are available. Written in a style that emphasizes readability and usefulness for the numerical methods novice, the book begins with basic, elementary material and gradually builds up to more advanced topics. A selection of concepts required for the study of computational mathematics is introduced, and simple approximations using Taylor's Theorem are also treated in some depth. The text includes exercises that run the gamut from simple hand computations, to challenging derivations and minor proofs, to programming exercises. A greater emphasis on applied exercises as well as the cause and effect associated with numerical mathematics is featured throughout the book. An Introduction to Numerical Methods and Analysis is the ideal text for students in advanced undergraduate mathematics and engineering courses who are interested in gaining an understanding of numerical methods and numerical analysis.

Download or read book Numerical Computation 1 written by Christoph W. Ueberhuber and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with various aspects of scientific numerical computing. No at tempt was made to be complete or encyclopedic. The successful solution of a numerical problem has many facets and consequently involves different fields of computer science. Computer numerics- as opposed to computer algebra- is thus based on applied mathematics, numerical analysis and numerical computation as well as on certain areas of computer science such as computer architecture and operating systems. Applied Mathemalies I I I Numerical Analysis Analysis, Algebra I I Numerical Computation Symbolic Computation I Operating Systems Computer Hardware Each chapter begins with sample situations taken from specific fields of appli cation. Abstract and general formulations of mathematical problems are then presented. Following this abstract level, a general discussion about principles and methods for the numerical solution of mathematical problems is presented. Relevant algorithms are developed and their efficiency and the accuracy of their results is assessed. It is then explained as to how they can be obtained in the form of numerical software. The reader is presented with various ways of applying the general methods and principles to particular classes of problems and approaches to extracting practically useful solutions with appropriately chosen numerical software are developed. Potential difficulties and obstacles are examined, and ways of avoiding them are discussed. The volume and diversity of all the available numerical software is tremendous.

Download or read book Introduction to Python in Earth Science Data Analysis written by Maurizio Petrelli and published by Springer Nature. This book was released on 2021-09-16 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book A First Course in Numerical Methods written by Uri M. Ascher and published by SIAM. This book was released on 2011-07-14 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers students a practical knowledge of modern techniques in scientific computing.