This book provides a thorough introduction to one of the most efficient approximation methods for the analysis and solution of problems in theoretical physics and applied mathematics. It is written with practical needs in mind and contains a discussion of 50 problems with solutions, of varying degrees of difficulty. The problems are taken from quantum mechanics, but the method has important applications in any field of science involving second order ordinary differential equations. The power of the asymptotic solution of second order differential equations is demonstrated, and in each case the authors clearly indicate which concepts and results of the general theory are needed to solve a particular problem. This book will be ideal as a manual for users of the phase-integral method, as well as a valuable reference text for experienced research workers and graduate students.

Introductory treatment steers a course between simplistic and rigorous approaches to provide a concise overview for advanced undergraduates and graduate students. Topics include Stokes phenomenon, one and two transition points, applications. 1962 edition.

The result of two decades spent developing and refining the phase-integral method to a high level of precision, the authors have applied this method to problems in various fields of theoretical physics. The problems treated are of a mathematical nature, but have important physical applications. This book will thus be of great use to research workers in various branches of theoretical physics, where the problems can be reduced to one-dimensional second-order differential equations of the Schrödinger type for which phase-integral solutions are required. Includes contributions from notable scientists who have already made use of the authors'technique.

The phase-integral method in mathematics, also known as the Wentzel-Kramers-Brillouin (WKB) method, is the focus of this introductory treatment. Author John Heading successfully steers a course between simplistic and rigorous approaches to provide a concise overview for advanced undergraduates and graduate students in mathematics and physics. Since the number of applications is vast, the text considers only a brief selection of topics and emphasizes the method itself rather than detailed applications. The process, once derived, is shown to be one of essential simplicity that involves merely the application of certain well-defined rules. Starting with a historical survey of the problem and its solutions, subjects include the Stokes phenomenon, one and two transition points, and applications to physical problems. An appendix and bibliography conclude the text.

Proceedings of the IABEM Symposium held in Pontignano, Italy, May 28-June 3, 1995

The mathematical modelling of free and moving boundary problems are an important topic in engineering, industry, technology and theoretical sciences. These models allow us to make calculations involved in phase change transitions of materials due to heat transfer. Boundary layer applications are widespread in research and industry. Boundary Element Methods for Heat Transfer with Phase Change Problems: Theory and Application equips the reader with information about heat transfer problems occurring during phase changes. The book covers several boundary element methods, including methods for phase changes, fixed and moving domains and new approaches. The contents are rounded off with chapters on numerical results and industrial applications. Key features: - Simple, didactic presentation of boundary layer problems for heat transfer problems - Covers a wide range of boundary element methods - Includes methods for fixed and moving domains - Explains industrial applications of the methods - Includes solutions to numerical problems The book serves as a textbook for students of advanced mathematics and engineering. It is also a handbook for researchers working on numerical analysis, who require a focused volume on boundary element methods for heat transfer applications.

This volume in the Encyclopedia of Complexity and Systems Science, Second Edition, is devoted to the fundamentals of Perturbation Theory (PT) as well as key applications areas such as Classical and Quantum Mechanics, Celestial Mechanics, and Molecular Dynamics. Less traditional fields of application, such as Biological Evolution, are also discussed. Leading scientists in each area of the field provide a comprehensive picture of the landscape and the state of the art, with the specific goal of combining mathematical rigor, explicit computational methods, and relevance to concrete applications. New to this edition are chapters on Water Waves, Rogue Waves, Multiple Scales methods, legged locomotion, Condensed Matter among others, while all other contributions have been revised and updated. Coverage includes the theory of (Poincare’-Birkhoff) Normal Forms, aspects of PT in specific mathematical settings (Hamiltonian, KAM theory, Nekhoroshev theory, and symmetric systems), technical problems arising in PT with solutions, convergence of series expansions, diagrammatic methods, parametric resonance, systems with nilpotent real part, PT for non-smooth systems, and on PT for PDEs [write out this acronym partial differential equations]. Another group of papers is focused specifically on applications to Celestial Mechanics, Quantum Mechanics and the related semiclassical PT, Quantum Bifurcations, Molecular Dynamics, the so-called choreographies in the N-body problem, as well as Evolutionary Theory. Overall, this unique volume serves to demonstrate the wide utility of PT, while creating a foundation for innovations from a new generation of graduate students and professionals in Physics, Mathematics, Mechanics, Engineering and the Biological Sciences.