عنوان

Perturbations

شابک

9781611971095 (electronic bk.)

شابک اشتباه

0898714435 (pbk.)

شابک اشتباه

9780898714432 (pbk.)

شماره

b503370

شماره ناشر

CL27

عنوان اصلي

Perturbations

نام عام مواد

[Book]

ساير اطلاعات عنواني

theory and methods /

نام نخستين پديدآور

James A. Murdock.

محل نشرو پخش و غیره

Philadelphia, Pa. :

نام ناشر، پخش کننده و غيره

Society for Industrial and Applied Mathematics,

تاریخ نشرو بخش و غیره

1999.

نام خاص و کميت اثر

1 online resource (xx, 509 p.) :

ساير جزييات

ill.

عنوان فروست

Classics in applied mathematics ;

مشخصه جلد

27.

متن يادداشت

Includes bibliographical references and indexes.

متن يادداشت

Preface to the Classics edition -- Preface -- Part I. Introduction to perturbation theory. Chapter 1. Root finding -- Chapter 2. Regular perturbations -- Chapter 3. Direct error estimation -- Part II. Oscillatory phenomena. Chapter 4. Periodic solutions and Lindstedt series -- Chapter 5. Multiple scales -- Chapter 6. Averaging -- Part III. Transition layers. Chapter 7. Initial layers -- Chapter 8. Boundary layers -- Chapter 9. Methods of the WKB type -- Appendix A. Taylor's theorem -- Appendix B. The implicit function theorem -- Appendix C. Second order differential equations -- Appendix D. Systems of differential equations -- Appendix E. Fourier series -- Appendix F. Lipschitz constants and vector norms -- Appendix G. Logical quantifiers and uniformity -- Symbol index -- Index.

بدون عنوان

0

متن يادداشت

Perturbations: Theory and Methods gives a thorough introduction to both regular and singular perturbation methods for algebraic and differential equations. Unlike most introductory books on the subject, this one distinguishes between formal and rigorous asymptotic validity, which are commonly confused in books that treat perturbation theory as a bag of heuristic tricks with no foundation. The meaning of "uniformity" is carefully explained in a variety of contexts. All standard methods, such as rescaling, multiple scales, averaging, matching, and the WKB method are covered, and the asymptotic validity (in the rigorous sense) of each method is carefully proved. First published in 1991, this book is still useful today because it is an introduction. It combines perturbation results with those known through other methods. Sometimes a geometrical result (such as the existence of a periodic solution) is rigorously deduced from a perturbation result, and at other times a knowledge of the geometry of the solutions is used to aid in the selection of an effective perturbation method. Dr. Murdock's approach differs from other introductory texts because he attempts to present perturbation theory as a natural part of a larger whole, the mathematical theory of differential equations. He explores the meaning of the results and their connections to other ways of studying the same problems.

شماره استاندارد بين المللي کتاب و موسيقي

9780898714432

موضوع مستند نشده

Perturbation (Mathematics)

شماره

ويراست

شماره رده

نشانه اثر

مستند نام اشخاص تاييد نشده

Murdock, James A.

مستند نام تنالگان تاييد نشده

Society for Industrial and Applied Mathematics.

تاريخ عمليات

20110503173955.0

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y