Author: Frank W. J. OlverPublisher: World Scientific
ISBN: 9789810249946
Category : Asymptotic expansions
Languages : en
Pages : 548
Book Description
Selected Papers of F.W.J. Olver
Author: Frank W. J. OlverPublisher: World Scientific
ISBN: 9789810249946
Category : Asymptotic expansions
Languages : en
Pages : 548
Book Description
Contributions to the Theory of Nonlinear Oscillations, Volume II
Author: Solomon LefschetzPublisher: Princeton University Press
ISBN: 1400882702
Category : Mathematics
Languages : en
Pages : 128
Book Description
These two new collections, numbers 28 and 29 respectively in the Annals of Mathematics Studies, continue the high standard set by the earlier Annals Studies 20 and 24 by bringing together important contributions to the theories of games and of nonlinear differential equations.
Numerical Methods for Special Functions
Author: Amparo GilPublisher: SIAM
ISBN: 0898716349
Category : Mathematics
Languages : en
Pages : 418
Book Description
An overview that advises when to use specific methods depending upon the function and range.
Asymptotic Expansions for Ordinary Differential Equations
Author: Wolfgang WasowPublisher: Courier Dover Publications
ISBN: 0486824586
Category : Mathematics
Languages : en
Pages : 385
Book Description
This outstanding text concentrates on the mathematical ideas underlying various asymptotic methods for ordinary differential equations that lead to full, infinite expansions. "A book of great value." — Mathematical Reviews. 1976 revised edition.
Linear Turning Point Theory
Author: Wolfgang WasowPublisher: Springer Science & Business Media
ISBN: 1461210909
Category : Mathematics
Languages : en
Pages : 255
Book Description
My book "Asymptotic Expansions for Ordinary Differential Equations" published in 1965 is out of print. In the almost 20 years since then, the subject has grown so much in breadth and in depth that an account of the present state of knowledge of all the topics discussed there could not be fitted into one volume without resorting to an excessively terse style of writing. Instead of undertaking such a task, I have concentrated, in this exposi tion, on the aspects of the asymptotic theory with which I have been particularly concerned during those 20 years, which is the nature and structure of turning points. As in Chapter VIII of my previous book, only linear analytic differential equations are considered, but the inclusion of important new ideas and results, as well as the development of the neces sary background material have made this an exposition of book length. The formal theory of linear analytic differential equations without a parameter near singularities with respect to the independent variable has, in recent years, been greatly deepened by bringing to it methods of modern algebra and topology. It is very probable that many of these ideas could also be applied to the problems concerning singularities with respect to a parameter, and I hope that this will be done in the near future. It is less likely, however, that the analytic, as opposed to the formal, aspects of turning point theory will greatly benefit from such an algebraization.
Uniform Simplification in a Full Neighborhood of a Transition Point
Author: Yasutaka SibuyaPublisher: American Mathematical Soc.
ISBN: 082181849X
Category : Analytic functions
Languages : en
Pages : 114
Book Description
This memoir addresses linear differential equations, asymptotic expansions, and analytic functions.
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables
Author: Milton AbramowitzPublisher:
ISBN:
Category : Functions
Languages : en
Pages : 1072
Book Description
Introduction to Asymptotics and Special Functions
Author: F. W. J. OlverPublisher: Academic Press
ISBN: 1483267083
Category : Mathematics
Languages : en
Pages : 312
Book Description
Introduction to Asymptotics and Special Functions is a comprehensive introduction to two important topics in classical analysis: asymptotics and special functions. The integrals of a real variable are discussed, along with contour integrals and differential equations with regular and irregular singularities. The Liouville-Green approximation is also considered. Comprised of seven chapters, this volume begins with an overview of the basic concepts and definitions of asymptotic analysis and special functions, followed by a discussion on integrals of a real variable. Contour integrals are then examined, paying particular attention to Laplace integrals with a complex parameter and Bessel functions of large argument and order. Subsequent chapters focus on differential equations having regular and irregular singularities, with emphasis on Legendre functions as well as Bessel and confluent hypergeometric functions. A chapter devoted to the Liouville-Green approximation tackles asymptotic properties with respect to parameters and to the independent variable, eigenvalue problems, and theorems on singular integral equations. This monograph is intended for students needing only an introductory course to asymptotics and special functions.
Research in Progress
Author: Journal of Research of the National Bureau of Standards
Author: United States. National Bureau of StandardsPublisher:
ISBN:
Category : Chemistry
Languages : en
Pages : 572
Book Description