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Author: Nanny Fröman Publisher: Springer Science & Business Media ISBN: 1461223423 Category : Mathematics Languages : en Pages : 258
Book Description
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.
Author: Nanny Fröman Publisher: Springer Science & Business Media ISBN: 1461223423 Category : Mathematics Languages : en Pages : 258
Book Description
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.
Author: John Heading Publisher: Courier Corporation ISBN: 0486316297 Category : Mathematics Languages : en Pages : 178
Book Description
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.
Author: Nanny Fröman Publisher: Cambridge University Press ISBN: 1139434322 Category : Science Languages : en Pages : 230
Book Description
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.
Author: John Heading Publisher: Courier Corporation ISBN: 0486497429 Category : Mathematics Languages : en Pages : 178
Book Description
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.
Author: Norman Bleistein Publisher: Courier Corporation ISBN: 0486650820 Category : Mathematics Languages : en Pages : 453
Book Description
Excellent introductory text, written by two experts, presents a coherent and systematic view of principles and methods. Topics include integration by parts, Watson's lemma, LaPlace's method, stationary phase, and steepest descents. Additional subjects include the Mellin transform method and less elementary aspects of the method of steepest descents. 1975 edition.
Author: Michiel Hazewinkel Publisher: Springer Science & Business Media ISBN: 9400903650 Category : Mathematics Languages : en Pages : 743
Book Description
This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
Author: David Colton Publisher: SIAM ISBN: 1611973155 Category : Mathematics Languages : en Pages : 286
Book Description
This classic book provides a rigorous treatment of the Riesz?Fredholm theory of compact operators in dual systems, followed by a derivation of the jump relations and mapping properties of scalar and vector potentials in spaces of continuous and H?lder continuous functions. These results are then used to study scattering problems for the Helmholtz and Maxwell equations. Readers will benefit from a full discussion of the mapping properties of scalar and vector potentials in spaces of continuous and H?lder continuous functions, an in-depth treatment of the use of boundary integral equations to solve scattering problems for acoustic and electromagnetic waves, and an introduction to inverse scattering theory with an emphasis on the ill-posedness and nonlinearity of the inverse scattering problem.
Author: K. G. Budden Publisher: Cambridge University Press ISBN: 9780521369527 Category : Science Languages : en Pages : 694
Book Description
This book is concerned with the ionosphere and the magnetosphere, and the theory of their effect on radio waves. It includes accounts of some mathematical topics now widely used in this study, particularly W. K. B. approximations, Airy integral functions and integration by steepest descents. The subject is divided into ray theory and full wave theory. Ray theory is useful for high frequencies when the ionosphere is treated as a horizonally stratified medium. The discussion of the magnetosphere, whose structure is more complicated, includes an account of whistlers and ion cyclotron whistlers. The book has been planned both for final year undergraduates and as a reference book for research. It is suitable as a course book on radio propagation for students of physics or electrical engineering or mathematics. Some of the topics are presented from an elementary viewpoint so as to help undergraduates new to the subject. The later parts are more advanced. Because the subject is so large and has seen many important recent advances, some topics have had to be treated briefly, but there is a full bibliography with about 600 references.
Author: R. J. Rivers Publisher: Cambridge University Press ISBN: 9780521368704 Category : Science Languages : en Pages : 356
Book Description
The applications of functional integral methods introduced in this text for solving a range of problems in quantum field theory will prove useful for students and researchers in theoretical physics and quantum field theory.
Author: Nanny Fröman
Author: Nanny Fröman
Author: John Heading
Author: Nanny Fröman
Author: John Heading
Author: Norman Bleistein
Author: Michiel Hazewinkel
Author: United States. National Bureau of Standards
Author: David Colton
Author: K. G. Budden
Author: R. J. Rivers