Topic #16 ------------- OP-SF NET 8.6 ------------- November 15, 2001 ~~~~~~~~~~~~~ From: OP-SF NET Editor (muldoon@yorku.ca) Subject: Selected Papers of Frank Olver http://www.wspc.com.sg/books/mathematics/4251.html World Scientific Series in 20th Century Mathematics - Vol. 7 SELECTED PAPERS OF F. W. J. OLVER (In 2 Volumes) edited by Roderick Wong (City University of Hong Kong) 1124pp Pub. date: Jan 2000 ISBN 981-02-4106-2(set) US$236 / £161 This is a collection of selected papers written by Frank W J Olver from 1949 to 1999. It contains his most important contributions to the fields of asymptotic analysis and numerical analysis, including the global existence of uniform asymptotic expansions for solution of ordinary differential equations and construction of error bounds. It is a valuable collection for anyone who works in, or uses, asymptotics, and should be on the shelves of all major libraries. Contents: - The Asymptotic Solution of Linear Differential Equations of the Second Order for Large Values of a Parameter - The Asymptotic Expansion of Bessel Functions of Large Order Uniform Asymptotic Expansions for Weber Parabolic Cylinder Functions of Large Orders - Error Bounds for the Liouville-Green (or WKB) Approximation - Error Analysis of Phase-Integral Methods - Numerical Solution of Second-Order Linear Difference Equations - Unsolved Problems in the Asymptotic Estimation of Special Functions - General Connection Formulae for Liouville-Green Approximations in the Complex Plane - Beyond Floating Point - On Stokes' Phenomenon and Converging Factors - Airy and Bessel Functions by Parallel Integration of ODEs - Hyperasymptotic Solutions of Second-Order Linear Differential Equations - On the Asymptotic and Numerical Solution of Linear Ordinary Differential Equations and 42 other papers Readership: Graduates in asymptotic analysis, differential equations and numerical & computational methods. "These two volumes exemplify a redoubtable mathematical talent, the work of a man who has done more than almost anyone else in the 20th century to bestow on the discipline of applied mathematics the elegance and rigor that its earliest practitioners such as Gauss and Laplace would have wished for it ... the books are beautifully bound and printed ... D S Jones has contributed an intimate and adulatory introduction, and Roderick Wong should be congratulated for bringing the entire effort to fruition." (From the review by Jet Wimp in SIAM Review, Vol 43, 2001)

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