A First Look at Perturbation Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A First Look at Perturbation Theory write by James G. Simmonds. This book was released on 2013-07-04. A First Look at Perturbation Theory available in PDF, EPUB and Kindle. Undergraduates in engineering and the physical sciences receive a thorough introduction to perturbation theory in this useful and accessible text. Students discover methods for obtaining an approximate solution of a mathematical problem by exploiting the presence of a small, dimensionless parameter — the smaller the parameter, the more accurate the approximate solution. Knowledge of perturbation theory offers a twofold benefit: approximate solutions often reveal the exact solution's essential dependence on specified parameters; also, some problems resistant to numerical solutions may yield to perturbation methods. In fact, numerical and perturbation methods can be combined in a complementary way. The text opens with a well-defined treatment of finding the roots of polynomials whose coefficients contain a small parameter. Proceeding to differential equations, the authors explain many techniques for handling perturbations that reorder the equations or involve an unbounded independent variable. Two disparate practical problems that can be solved efficiently with perturbation methods conclude the volume. Written in an informal style that moves from specific examples to general principles, this elementary text emphasizes the "why" along with the "how"; prerequisites include a knowledge of one-variable calculus and ordinary differential equations. This newly revised second edition features an additional appendix concerning the approximate evaluation of integrals.
Introduction to Perturbation Methods
Introduction to Perturbation Methods - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to Perturbation Methods write by Mark H. Holmes. This book was released on 2013-12-01. Introduction to Perturbation Methods available in PDF, EPUB and Kindle. This introductory graduate text is based on a graduate course the author has taught repeatedly over the last ten years to students in applied mathematics, engineering sciences, and physics. Each chapter begins with an introductory development involving ordinary differential equations, and goes on to cover such traditional topics as boundary layers and multiple scales. However, it also contains material arising from current research interest, including homogenisation, slender body theory, symbolic computing, and discrete equations. Many of the excellent exercises are derived from problems of up-to-date research and are drawn from a wide range of application areas.
Perturbation theory for linear operators
Perturbation theory for linear operators - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Perturbation theory for linear operators write by Tosio Kato. This book was released on 2013-06-29. Perturbation theory for linear operators available in PDF, EPUB and Kindle.
Perturbations
Perturbations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Perturbations write by James A. Murdock. This book was released on 1999-01-01. Perturbations available in PDF, EPUB and Kindle. 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.
Advanced Mathematical Methods for Scientists and Engineers I
Advanced Mathematical Methods for Scientists and Engineers I - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Advanced Mathematical Methods for Scientists and Engineers I write by Carl M. Bender. This book was released on 1999-10-29. Advanced Mathematical Methods for Scientists and Engineers I available in PDF, EPUB and Kindle. A clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory for obtaining approximate analytical solutions to differential and difference equations. Aimed at teaching the most useful insights in approaching new problems, the text avoids special methods and tricks that only work for particular problems. Intended for graduates and advanced undergraduates, it assumes only a limited familiarity with differential equations and complex variables. The presentation begins with a review of differential and difference equations, then develops local asymptotic methods for such equations, and explains perturbation and summation theory before concluding with an exposition of global asymptotic methods. Emphasizing applications, the discussion stresses care rather than rigor and relies on many well-chosen examples to teach readers how an applied mathematician tackles problems. There are 190 computer-generated plots and tables comparing approximate and exact solutions, over 600 problems of varying levels of difficulty, and an appendix summarizing the properties of special functions.
