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Advanced Mathematical Mathods for Scientists and Engineers Asymptotic Methods and Perturbation Theory by Carl M. Bender, Steven A. Orszag
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Advanced Mathematical Mathods for Scientists and Engineers Asymptotic Methods and Perturbation Theory written by
Carl M. Bender, Steven A. Orszag .
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.
Book Detail :-
Title: Advanced Mathematical Mathods for Scientists and Engineers Asymptotic Methods and Perturbation Theory
Edition:
Author(s): Carl M. Bender, Steven A. Orszag
Publisher: Springer-Verlag New York
Series:
Year: 1999
Pages:
Type: PDF
Language: English
ISBN: 978-1-4419-3187-0,978-1-4757-3069-2
Country: US
Download from Amazon :
About Author :-
Author Carl M. Bender is Professor at Department of Physics, Washington University, St. Louis, MO 63130, United States.
Author Steven A. Orszag is Professor from Department of Mathematics, Yale University, New Haven, CT 06520, United States.
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Advanced Mathematical Mathods for Scientists and Engineers Asymptotic Methods and Perturbation Theory written by
Carl M. Bender, Steven A. Orszag
cover the following topics.
**FUNDAMENTALS
Ordinary Differential Equation
Difference Equations
**LOCAL ANALYSIS
Approximate Solution of Linear Differential Equations
Approximate Solution of Nonlinear Differential Equations
Approximate Solution of Differential Equations
Asymptotic Expansion of Integrals
**PERTURBATION METHODS
Perturbation Series
Summation of Series
**GLOBAL ANALYSIS
Boundary Layer Theory
WKB theory
Mutiple Scale Analysis
Useful Formulas
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