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An Introduction to Phase Integral Methods

An Introduction to Phase Integral Methods Author John Heading
ISBN-10 9780486497426
Release 2013
Pages 160
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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.

Asymptotic Expansions of Integrals

Asymptotic Expansions of Integrals Author Norman Bleistein
ISBN-10 9780486650821
Release 1975
Pages 425
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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.

Introduction to Nonlinear Differential and Integral Equations

Introduction to Nonlinear Differential and Integral Equations Author Harold Thayer Davis
ISBN-10 0486609715
Release 1962
Pages 566
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Topics covered include differential equations of the 1st order, the Riccati equation and existence theorems, 2nd order equations, elliptic integrals and functions, nonlinear mechanics, nonlinear integral equations, more. Includes 137 problems.

Ray Tracing and Beyond

Ray Tracing and Beyond Author E. R. Tracy
ISBN-10 9780521768061
Release 2014-02-27
Pages 541
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This complete introduction to the use of modern ray tracing techniques in plasma physics describes the powerful mathematical methods generally applicable to vector wave equations in non-uniform media, and clearly demonstrates the application of these methods to simplify and solve important problems in plasma wave theory. Key analytical concepts are carefully introduced as needed, encouraging the development of a visual intuition for the underlying methodology, with more advanced mathematical concepts succinctly explained in the appendices, and supporting Matlab and Raycon code available online. Covering variational principles, covariant formulations, caustics, tunnelling, mode conversion, weak dissipation, wave emission from coherent sources, incoherent wave fields, and collective wave absorption and emission, all within an accessible framework using standard plasma physics notation, this is an invaluable resource for graduate students and researchers in plasma physics.

Advanced Mathematical Methods for Scientists and Engineers I

Advanced Mathematical Methods for Scientists and Engineers I Author Carl M. Bender
ISBN-10 9781475730692
Release 2013-03-09
Pages 593
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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.

Applied Complex Variables

Applied Complex Variables Author John W. Dettman
ISBN-10 9780486158280
Release 2012-05-07
Pages 512
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Fundamentals of analytic function theory — plus lucid exposition of 5 important applications: potential theory, ordinary differential equations, Fourier transforms, Laplace transforms, and asymptotic expansions. Includes 66 figures.

Historical Encyclopedia of Natural and Mathematical Sciences

Historical Encyclopedia of Natural and Mathematical Sciences Author Ari Ben-Menahem
ISBN-10 9783540688310
Release 2009-03-06
Pages 5983
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This 5,800-page encyclopedia surveys 100 generations of great thinkers, offering more than 2,000 detailed biographies of scientists, engineers, explorers and inventors who left their mark on the history of science and technology. This six-volume masterwork also includes 380 articles summarizing the time-line of ideas in the leading fields of science, technology, mathematics and philosophy.

Asymptotic Analysis of Differential Equations

Asymptotic Analysis of Differential Equations Author R. B. White
ISBN-10 9781848166073
Release 2010
Pages 405
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"This is a useful volume in which a wide selection of asymptotic techniques is clearly presented in a form suitable for both applied mathematicians and Physicists who require an introduction to asymptotic techniques." --Book Jacket.

A Combinatorial Introduction to Topology

A Combinatorial Introduction to Topology Author Michael Henle
ISBN-10 0486679667
Release 1979
Pages 310
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Excellent text covers vector fields, plane homology and the Jordan Curve Theorem, surfaces, homology of complexes, more. Problems and exercises. Some knowledge of differential equations and multivariate calculus required.Bibliography. 1979 edition.

Differential and Integral Equations

Differential and Integral Equations Author Peter J. Collins
ISBN-10 9780198533825
Release 2006-08-03
Pages 372
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Differential & integral equations involve important mathematical techniques, & as such will be encountered by mathematicians, & physical & social scientists, in their undergraduate courses. This text provides a clear, comprehensive guide to first- & second- order ordinary & partial differential equations.

Path Integrals and Quantum Processes

Path Integrals and Quantum Processes Author Mark S. Swanson
ISBN-10 9780486782300
Release 2014-02-19
Pages 464
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Graduate-level, systematic presentation of path integral approach to calculating transition elements, partition functions, and source functionals. Covers Grassmann variables, field and gauge field theory, perturbation theory, and nonperturbative results. 1992 edition.

Linear Differential Operators

Linear Differential Operators Author Cornelius Lanczos
ISBN-10 0486680355
Release 1997
Pages 564
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The basic and characteristic properties of linear differential operators are explored in this graduate-level text. No specific knowledge beyond the usual introductory courses is necessary. Includes 350 problems and solution.

American Scientific Books

American Scientific Books Author
ISBN-10 PSU:000029473489
Release 1962
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American Scientific Books has been writing in one form or another for most of life. You can find so many inspiration from American Scientific Books also informative, and entertaining. Click DOWNLOAD or Read Online button to get full American Scientific Books book for free.

An Introduction to Probability Theory

An Introduction to Probability Theory Author K. Itô
ISBN-10 0521269601
Release 1984-09-28
Pages 213
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One of the most distinguished probability theorists in the world rigorously explains the basic probabilistic concepts while fostering an intuitive understanding of random phenomena.

Existence Theorems for Ordinary Differential Equations

Existence Theorems for Ordinary Differential Equations Author Francis J. Murray
ISBN-10 9780486154954
Release 2013-11-07
Pages 176
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This text examines fundamental and general existence theorems, along with uniqueness theorems and Picard iterants, and applies them to properties of solutions and linear differential equations. 1954 edition.

A Friendly Approach to Complex Analysis

A Friendly Approach to Complex Analysis Author Sara Maad Sasane
ISBN-10 9789814579018
Release 2013-12-24
Pages 964
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The book constitutes a basic, concise, yet rigorous course in complex analysis, for students who have studied calculus in one and several variables, but have not previously been exposed to complex analysis. The textbook should be particularly useful and relevant for undergraduate students in joint programmes with mathematics, as well as engineering students. The aim of the book is to cover the bare bones of the subject with minimal prerequisites. The core content of the book is the three main pillars of complex analysis: the Cauchy–Riemann equations, the Cauchy Integral Theorem, and Taylor and Laurent series expansions. Each section contains several problems, which are not purely drill exercises, but are rather meant to reinforce the fundamental concepts. Detailed solutions to all the exercises appear at the end of the book, making the book ideal also for self-study. There are many figures illustrating the text. Errata(s) Errata (72 KB)

An Introduction to Differential Equations and Their Applications

An Introduction to Differential Equations and Their Applications Author Stanley J. Farlow
ISBN-10 PSU:000058530306
Release 2006-03-11
Pages 640
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Intended for use in a beginning one-semester course in differential equations, this text is designed for students of pure and applied mathematics with a working knowledge of algebra, trigonometry, and elementary calculus. Its mathematical rigor is balanced by complete but simple explanations that appeal to readers' physical and geometric intuition. Starting with an introduction to differential equations, the text proceeds to examinations of first- and second-order differential equations, series solutions, the Laplace transform, systems of differential equations, difference equations, nonlinear differential equations and chaos, and partial differential equations. Numerous figures, problems with solutions, and historical notes clarify the text.