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Books on the topic 'Numerical integration. Integrals'

Author: Grafiati

Published: 4 June 2021

Last updated: 10 February 2022

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1

Nicolas Bourbaki. Integration. Berlin: Springer, 2004.

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2

Nicolas Bourbaki. Integration. Berlin: Springer, 2004.

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3

Introduction to integration. Oxford: Clarendon Press, 1997.

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4

The general theory of integration. Oxford: Clarendon Press, 1991.

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5

Whitney, Hassler. Geometric integration theory. Mineola, N.Y: Dover Publications, 2005.

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6

Thompson, Jeremy Stewart. High speed numerical integration of Fermi Dirac integrals. Monterey, Calif: Naval Postgraduate School, 1996.

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7

Milʹshteĭn, G. N. Numerical integration of stochastic differential equations. Dordrecht: Kluwer Academic Publishers, 1995.

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8

Kythe, Prem K. Handbook of computational methods for integration. Boca Raton: Chapman & Hall/CRC, 2005.

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9

Measure and integration for use. Oxford: Clarendon Press, 1985.

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10

Lastdrager, Boris. Numerical time integration on sparse grids. [S.l: s.n.], 2002.

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11

Numerical analysis: An introduction. Boston: Birkhäuser, 1997.

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12

Homeier, Herbert. Integraltransformationsmethoden und Quadraturverfahren für Molekülintegrale mit B-Funktionen. Regensburg: Roderer, 1990.

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13

Gienger, Gottlob. On convolution quadratures and their applications to Fredholm integral equations of the second kind. Giessen: Selbstverlag des Mathematischen Instituts, 1988.

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14

Zaanen, Adriaan C. Continuity, integration, and Fourier theory. Berlin: Springer-Verlag, 1989.

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15

Dzhamay, Anton, Christopher W. Curtis, Willy A. Hereman, and B. Prinari. Nonlinear wave equations: Analytic and computational techniques : AMS Special Session, Nonlinear Waves and Integrable Systems : April 13-14, 2013, University of Colorado, Boulder, CO. Providence, Rhode Island: American Mathematical Society, 2015.

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16

Spain) UIMP-RSME Lluis Santaló Summer (2012 Santander. Recent advances in real complexity and computation: UIMP-RSME Lluis A. Santaló Summer School, Recent advances in real complexity and computation, July 16-20, 2012, Universidad Internacional Menéndez Pelayo, Santander, Spain. Edited by Montaña, Jose Luis, 1961- editor of compilation and Pardo, L. M. (Luis M.), editor of compilation. Providence, Rhode Island: American Mathematical Society, 2013.

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17

A course in interpolation and numerical integration for the mathematical laboratory. London: G. Bell & sons, ltd., 1992.

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18

Ng, Wee Leng. Nonabsolute Integration on Measure Spaces. World Scientific Publishing Co Pte Ltd, 2017.

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19

Webster, Jonathan Robert. Methods of numerical integration for rapidly oscillatory integrals. 1999.

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20

Handbook of Computational Methods for Integration. Chapman & Hall/CRC, 2004.

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21

The Joys of Haar Measure. American Mathematical Society, 2014.

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22

Boudreau, Joseph F., and Eric S. Swanson. Numerical quadrature. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198708636.003.0005.

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This chapter discusses the numerous applications of numerical quadrature (integration) in classical mechanics, in semiclassical approaches to quantum mechanics, and in statistical mechanics; and then describes several ways of implementing integration in C++, for both proper and improper integrals. Various algorithms are described and analyzed, including simple classical quadrature algorithms as well as those enhanced with speedups and convergence tests. Classical orthogonal polynomials, whose properties are reviewed, are the basis of a sophisticated technique known as Gaussian integration. Practical implementations require the roots of these polynomials, so an algorithm for finding them from three-term recurrence relations is presented. On the computational side, the concept of polymorphism is introduced and exploited (prior to the detailed treatment later in the text). The nondimensionalization of physical problems, which is a common and important means of simplifying a problem, is discussed using Compton scattering and the Schrödinger equation as an example.

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23

Okecha, George Emese. Numerical quadrature involving singular and non-singular integrals: Methods, based on Gaussian and other quadrature formulae, involving complex integration, for numerical approximation of some singular and non-singular integrals, with estimates or bounds for errors incurred. Bradford, 1985.

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24

Silvestru, Dragomir Sever, and Rassias Themistocles M. 1951-, eds. Ostrowski type inequalities and applications in numerical integration. Dordrecht: Kluwer Academic, 2002.

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25

Gautschi, Walter. Orthogonal Polynomials. Oxford University Press, 2004. http://dx.doi.org/10.1093/oso/9780198506720.001.0001.

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This is the first book on constructive methods for, and applications of orthogonal polynomials, and the first available collection of relevant Matlab codes. The book begins with a concise introduction to the theory of polynomials orthogonal on the real line (or a portion thereof), relative to a positive measure of integration. Topics which are particularly relevant to computation are emphasized. The second chapter develops computational methods for generating the coefficients in the basic three-term recurrence relation. The methods are of two kinds: moment-based methods and discretization methods. The former are provided with a detailed sensitivity analysis. Other topics addressed concern Cauchy integrals of orthogonal polynomials and their computation, a new discussion of modification algorithms, and the generation of Sobolev orthogonal polynomials. The final chapter deals with selected applications: the numerical evaluation of integrals, especially by Gauss-type quadrature methods, polynomial least squares approximation, moment-preserving spline approximation, and the summation of slowly convergent series. Detailed historic and bibliographic notes are appended to each chapter. The book will be of interest not only to mathematicians and numerical analysts, but also to a wide clientele of scientists and engineers who perceive a need for applying orthogonal polynomials.

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26

A Course in Interpolation and Numerical Integration for the Mathematical Laboratory. Franklin Classics, 2018.

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27

Campbell, John, Joey Huston, and Frank Krauss. QCD at Fixed Order: Technology. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199652747.003.0003.

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This chapter is devoted to the technology of fixed-order calculations, in particular, in QCD. After a short summary of methods for the efficient evaluation of tree-level scattering amplitudes for multi-particle production, and their integration in phase space, next-to leading order corrections in QCD are addressed. Techniques for the evaluation of loop amplitudes with modern methods, based on the reduction to master integrals, either analytically or with numerical unitarity cut methods, are discussed in some detail. After identifying the problem of infrared divergences and illuminating their treatment with a toy model, Catani-Seymour subtraction is explicitly introduced and exemplified for two cases, namely inclusive hadron production in electron-positron annihilation and inclusive W boson production in hadron collisions. This chapter concludes with some remarks concerning the rapidly developing field of next-to-next-to leading order calculations.

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