Quadrature Formulae
Author | : Aldo Ghizzetti |
Publisher | : |
Total Pages | : 208 |
Release | : 1970 |
Genre | : Numerical integration |
ISBN | : |
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Author | : Aldo Ghizzetti |
Publisher | : |
Total Pages | : 208 |
Release | : 1970 |
Genre | : Numerical integration |
ISBN | : |
Author | : Helmut Brass |
Publisher | : American Mathematical Soc. |
Total Pages | : 376 |
Release | : 2011-10-12 |
Genre | : Mathematics |
ISBN | : 0821853619 |
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.
Author | : Daniel Zwillinger |
Publisher | : CRC Press |
Total Pages | : 927 |
Release | : 2002-11-25 |
Genre | : Mathematics |
ISBN | : 1420035347 |
A perennial bestseller, the 30th edition of CRC Standard Mathematical Tables and Formulae was the first "modern" edition of the handbook - adapted to be useful in the era of personal computers and powerful handheld devices. Now this version will quickly establish itself as the "user-friendly" edition. With a detailed table of contents and an extens
Author | : Meishe Isakovich Levin |
Publisher | : |
Total Pages | : 132 |
Release | : 1979 |
Genre | : Mathematical optimization |
ISBN | : |
Author | : S.L. Sobolev |
Publisher | : Springer Science & Business Media |
Total Pages | : 427 |
Release | : 2013-06-29 |
Genre | : Mathematics |
ISBN | : 9401589135 |
This volume considers various methods for constructing cubature and quadrature formulas of arbitrary degree. These formulas are intended to approximate the calculation of multiple and conventional integrals over a bounded domain of integration. The latter is assumed to have a piecewise-smooth boundary and to be arbitrary in other aspects. Particular emphasis is placed on invariant cubature formulas and those for a cube, a simplex, and other polyhedra. Here, the techniques of functional analysis and partial differential equations are applied to the classical problem of numerical integration, to establish many important and deep analytical properties of cubature formulas. The prerequisites of the theory of many-dimensional discrete function spaces and the theory of finite differences are concisely presented. Special attention is paid to constructing and studying the optimal cubature formulas in Sobolev spaces. As an asymptotically optimal sequence of cubature formulas, a many-dimensional abstraction of the Gregory quadrature is indicated. Audience: This book is intended for researchers having a basic knowledge of functional analysis who are interested in the applications of modern theoretical methods to numerical mathematics.
Author | : Daniel Zwillinger |
Publisher | : CRC Press |
Total Pages | : 792 |
Release | : 2011-06-22 |
Genre | : Mathematics |
ISBN | : 1439835500 |
With over 6,000 entries, CRC Standard Mathematical Tables and Formulae, 32nd Edition continues to provide essential formulas, tables, figures, and descriptions, including many diagrams, group tables, and integrals not available online. This new edition incorporates important topics that are unfamiliar to some readers, such as visual proofs and sequences, and illustrates how mathematical information is interpreted. Material is presented in a multisectional format, with each section containing a valuable collection of fundamental tabular and expository reference material. New to the 32nd Edition A new chapter on Mathematical Formulae from the Sciences that contains the most important formulae from a variety of fields, including acoustics, astrophysics, epidemiology, finance, statistical mechanics, and thermodynamics New material on contingency tables, estimators, process capability, runs test, and sample sizes New material on cellular automata, knot theory, music, quaternions, and rational trigonometry Updated and more streamlined tables Retaining the successful format of previous editions, this comprehensive handbook remains an invaluable reference for professionals and students in mathematical and scientific fields.
Author | : Eleanor Pairman |
Publisher | : |
Total Pages | : 684 |
Release | : 1919 |
Genre | : Gamma functions |
ISBN | : |
Author | : Lloyd N. Trefethen |
Publisher | : SIAM |
Total Pages | : 295 |
Release | : 2013-01-03 |
Genre | : Mathematics |
ISBN | : 9781611972405 |
An original and modern treatment of approximation theory for students in applied mathematics. Includes exercises, illustrations and Matlab code.
Author | : Wen Shen |
Publisher | : World Scientific |
Total Pages | : 339 |
Release | : 2019-08-28 |
Genre | : Mathematics |
ISBN | : 9811204438 |
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.