Asymptotic Expansions for Ordinary Differential Equations

by Wasow, Wolfgang

• ISBN13: 9780486824581
• ISBN10: 0486824586
• Edition: Revised
• Format: Paperback
• Copyright: 2018-03-21
• Publisher: Dover Publications

Summary

"A book of great value ... it should have a profound influence upon future research." —  Mathematical Reviews
In this outstanding text, author Wolfgang Wasow concentrates on the mathematical ideas underlying various asymptotic methods for ordinary differential equations that lead to full, infinite expansions. Starting with some basic properties of linear differential equations in the complex domain, the treatment advances to considerations of regular and irregular singular points, asymptotic power series, generalizations by means of Jordan's canonical form, and some special asymptotic methods.
Subsequent chapters explore asymptotic expansions with respect to a parameter, turning point problems, nonlinear equations, singular perturbations, and integration of differential equations by factorial series. Numerous problems appear throughout the text, which is ideal for course work or self-study.

Author Biography

Wolfgang Wasow (1909–93) was Professor of Mathematics at the University of Wisconsin. His other books include Finite Difference Methods for Partial Differential Equations and Linear Turning Point Theory.

Table of Contents

I. Some Basic Properties of Linear Differential Equations in the Complex Domain.

II. Regular Singular Points.

III. Asymptotic Power Series.

IV. Irregular Singular Points.

V.  Generalizations by Means of Jordan's Canonical Form.

VI.  Some Special Asymptotic Methods.

VII. Asymptotic Expansions with Respect to a Parameter.

VIII. Turning Point Problem.

IX. Nonlinear Equations.

X. Singular Perturbations.

XI. Integration of Differential Equations by Factorial Series.

Appendix: A Brief Summary of Some Recent Research.

Bibliography.

Subject Index.