Advanced Mathematical Methods for Scientists and Engineers I : Asymptotic Methods and Perturbation Theory / by Carl M. Bender, Steven A. Orszag.

Format:

Book

Author/Creator:

Bender, Carl M., Author.

Orszag, Steven A., Author.

Language:

English

Subjects (All):

Mathematical analysis.

Engineering mathematics.

Engineering--Data processing.

Engineering.

Mathematical physics.

Analysis.

Mathematical and Computational Engineering Applications.

Mathematical Methods in Physics.

Theoretical, Mathematical and Computational Physics.

Local Subjects:

Analysis.

Mathematical and Computational Engineering Applications.

Mathematical Methods in Physics.

Theoretical, Mathematical and Computational Physics.

Physical Description:

1 online resource (XIV, 593 p.)

Edition:

1st ed. 1999.

Place of Publication:

New York, NY : Springer New York : Imprint: Springer, 1999.

Language Note:

English

Summary:

The triumphant vindication of bold theories-are these not the pride and justification of our life's work? -Sherlock Holmes, The Valley of Fear Sir Arthur Conan Doyle The main purpose of our book is to present and explain mathematical methods for obtaining approximate analytical solutions to differential and difference equations that cannot be solved exactly. Our objective is to help young and also establiShed scientists and engineers to build the skills necessary to analyze equations that they encounter in their work. Our presentation is aimed at developing the insights and techniques that are most useful for attacking new problems. We do not emphasize special methods and tricks which work only for the classical transcendental functions; we do not dwell on equations whose exact solutions are known. The mathematical methods discussed in this book are known collectively as­ asymptotic and perturbative analysis. These are the most useful and powerful methods for finding approximate solutions to equations, but they are difficult to justify rigorously. Thus, we concentrate on the most fruitful aspect of applied analysis; namely, obtaining the answer. We stress care but not rigor. To explain our approach, we compare our goals with those of a freshman calculus course. A beginning calculus course is considered successful if the students have learned how to solve problems using calculus.

Contents:

I Fundamentals

1 Ordinary Differential Equations

2 Difference Equations

II Local Analysis

3 Approximate Solution of Linear Differential Equations

4 Approximate Solution of Nonlinear Differential Equations

5 Approximate Solution of Difference Equations

6 Asymptotic Expansion of Integrals

III Perturbation Methods

7 Perturbation Series

8 Summation of Series

IV Global Analysis

9 Boundary Layer Theory

10 WKB Theory

11 Multiple-Scale Analysis.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and index.

ISBN:

9781475730692

1475730691