Asymptotics of Linear Differential Equations

M. H. Lantsman

ISBN 10: 0792371933 / ISBN 13: 9780792371939

Published by Springer Netherlands Sep 2001, 2001

About this Item

This item is printed on demand - it takes 3-4 days longer - Neuware -The asymptotic theory deals with the problern of determining the behaviour of a function in a neighborhood of its singular point. The function is replaced by another known function ( named the asymptotic function) close (in a sense) to the function under consideration. Many problems of mathematics, physics, and other divisions of natural sci ence bring out the necessity of solving such problems. At the present time asymptotic theory has become an important and independent branch of mathematical analysis. The present consideration is mainly based on the theory of asymp totic spaces. Each asymptotic space is a collection of asymptotics united by an associated real function which determines their growth near the given point and (perhaps) some other analytic properties. The main contents of this book is the asymptotic theory of ordinary linear differential equations with variable coefficients. The equations with power order growth coefficients are considered in detail. As the application of the theory of differential asymptotic fields, we also consider the following asymptotic problems: the behaviour of explicit and implicit functions, improper integrals, integrals dependent on a large parameter, linear differential and difference equations, etc . The obtained results have an independent meaning. The reader is assumed to be familiar with a comprehensive course of the mathematical analysis studied, for instance at mathematical departments of universities. Further necessary information is given in this book in summarized form with proofs of the main aspects. 456 pp. Englisch.

Seller Inventory # 9780792371939

Bibliographic Details

• Title: Asymptotics of Linear Differential Equations
• Publisher: Springer Netherlands Sep 2001
• Publication Date: 2001
• Language: English
• ISBN 10: 0792371933
• ISBN 13: 9780792371939
• Binding: Buch
• Condition: Neu
• Dimensions: 241W x 160H x 30D millimeters 241 millimeters width by 160 millimeters height by 30 millimeters depth
• Weight: 846 grams

About this title

Synopsis

The asymptotic theory deals with the problern of determining the behaviour of a function in a neighborhood of its singular point. The function is replaced by another known function ( named the asymptotic function) close (in a sense) to the function under consideration. Many problems of mathematics, physics, and other divisions of natural sci­ ence bring out the necessity of solving such problems. At the present time asymptotic theory has become an important and independent branch of mathematical analysis. The present consideration is mainly based on the theory of asymp­ totic spaces. Each asymptotic space is a collection of asymptotics united by an associated real function which determines their growth near the given point and (perhaps) some other analytic properties. The main contents of this book is the asymptotic theory of ordinary linear differential equations with variable coefficients. The equations with power order growth coefficients are considered in detail. As the application of the theory of differential asymptotic fields, we also consider the following asymptotic problems: the behaviour of explicit and implicit functions, improper integrals, integrals dependent on a large parameter, linear differential and difference equations, etc .. The obtained results have an independent meaning. The reader is assumed to be familiar with a comprehensive course of the mathematical analysis studied, for instance at mathematical departments of universities. Further necessary information is given in this book in summarized form with proofs of the main aspects.