Airy Functions And Applications To Physics 2nd Edition
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Airy Functions And Applications To Physics
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Author : Olivier Vallée
language : en
Publisher: World Scientific Publishing Company
Release Date : 2004-09-13
Airy Functions And Applications To Physics written by Olivier Vallée and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-09-13 with Science categories.
The use of special functions, and in particular Airy functions, is rather common in physics. The reason may be found in the need, and even in the necessity, to express a physical phenomenon in terms of an effective and comprehensive analytical form for the whole scientific community. However, for the past twenty years, many physical problems have been resolved by computers. This trend is now becoming the norm as the importance of computers continues to grow. As a last resort, the special functions employed in physics will have to be calculated numerically, even if the analytic formulation of physics is of primary importance. Airy functions have periodically been the subject of many review articles, but no noteworthy compilation on this subject has been published since the 1950s. In this work, we provide an exhaustive compilation of the current knowledge on the analytical properties of Airy functions, developing with care the calculus implying the Airy functions. The book is divided into 2 parts: the first is devoted to the mathematical properties of Airy functions, whilst the second presents some applications of Airy functions to various fields of physics. The examples provided succinctly illustrate the use of Airy functions in classical and quantum physics. Contents:A Historical Introduction: Sir George Biddell AiryDefinitions and PropertiesPrimitives and Integrals of Airy FunctionsTransformations of Airy FunctionsThe Uniform ApproximationGeneralisation of Airy FunctionsApplications to Classical PhysicsApplications to Quantum Physics Readership: Physicists or chemical physicists who use closed and analytical formulae in their field, graduate students in physics and chemical physics.
Airy Functions And Applications To Physics 2nd Edition
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Author :
language : en
Publisher: World Scientific
Release Date : 2010
Airy Functions And Applications To Physics 2nd Edition written by and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Airy functions categories.
"Addressed mainly to physicist and chemical physicist, this textbook is the result of a broad compilation of current knowledge on analytical properties of Airy functions. In particular, the calculus implying the Airy functions is developed with care. In the latter chapters, examples are given to succinctly illustrate the use of Airy functions in classical and quantum physics. The physicist, for instance in fluid mechanics, can find what he is looking for, in the references for works of molecular physics or in physics of surfaces, and vice versa."--Publisher's website
Basics Of Statistical Physics Third Edition
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Author : Harald J W Muller-kirsten
language : en
Publisher: World Scientific
Release Date : 2022-03-16
Basics Of Statistical Physics Third Edition written by Harald J W Muller-kirsten and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-16 with Science categories.
Statistics links microscopic and macroscopic phenomena, and requires for this reason a large number of microscopic elements like atoms. The results are values of maximum probability or of averaging. This introduction to statistical physics concentrates on the basic principles and attempts to explain these in simple terms, supplemented by numerous examples. These basic principles include the difference between classical and quantum statistics, a priori probabilities as related to degeneracies, the vital aspect of indistinguishability as compared with distinguishability in classical physics, the differences between conserved and non-conserved elements, the different ways of counting arrangements in the three statistics (Maxwell-Boltzmann, Fermi-Dirac, Bose-Einstein), the difference between maximization of the number of arrangements of elements, and averaging in the Darwin-Fowler method. Significant applications to solids, radiation and electrons in metals are treated in separate chapters, as well as Bose-Einstein condensation. In this latest edition, apart from a general revision, the topic of thermal radiation has been expanded with a new section on black bodies and an additional chapter on black holes. Other additions are more examples with applications of statistical mechanics in solid state physics and superconductivity. Throughout the presentation, the introduction carries almost all details for calculations.
Dimensional Analysis Across The Landscape Of Physics
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Author : Richard W. Robinett
language : en
Publisher: Oxford University Press
Release Date : 2024-12-24
Dimensional Analysis Across The Landscape Of Physics written by Richard W. Robinett and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-24 with Science categories.
Dimensional Analysis Across the Landscape of Physics introduces readers to the powerful idea that almost all physical quantities in science and engineering can be described using only five base dimensions: mass, length, time, charge, and temperature, and combinations thereof. Starting with the basics of how this foundational intellectual concept arises, it illustrates the use of dimensional analysis in approaching the solutions to textbook-level problems in physics and adjacent fields, ranging from introductory courses, through the advanced undergraduate curriculum, to advanced Physics electives. It covers the core curricular topics of classical mechanics, electricity and magnetism, thermal physics, and quantum mechanics. It includes examples of the use of dimensional analysis applied to topics from other related fields such as geosciences, meteorology, engineering, and biophysics to emphasize the utility of such methods across the proverbial landscape of physics. There is also coverage of more specialized topics, such as advanced quantum mechanics, particle physics, field theory, condensed matter physics, and astrophysics and gravitation. Many worked examples are included, as well as an extensive array of end-of-chapter problems, with a solution manual available to instructors. In addition to covering the standard topics in the undergraduate curriculum, the book explores how dimensional analysis has been used (and continues to be used) in research across all fields of physics, citing examples from the historical literature and from very recent research results. The work includes extensive references to the original papers for further study, as well as useful ancillary material, including a dimensional analysis 'dictionary', brief introductions to data-fitting, and connections to metrology. There is an emphasis throughout on the use of modern symbolic programming to streamline the process of the solving systems of linear equations needed for a dimensional analysis approach, with several Mathematica© templates provided for reader use.
Introduction To Perturbation Methods
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Author : Mark H. Holmes
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-05
Introduction To Perturbation Methods written by Mark H. Holmes and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-05 with Mathematics categories.
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. One hundred new pages added including new material on transcedentally small terms, Kummer's function, weakly coupled oscillators and wave interactions.
Density Functionals For Many Particle Systems Mathematical Theory And Physical Applications Of Effective Equations
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Author : Berthold-georg Englert
language : en
Publisher: World Scientific
Release Date : 2023-02-10
Density Functionals For Many Particle Systems Mathematical Theory And Physical Applications Of Effective Equations written by Berthold-georg Englert and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-10 with Science categories.
Density Functional Theory (DFT) first established it's theoretical footing in the 1960s from the framework of Hohenberg-Kohn theorems. DFT has since seen much development in evaluation techniques as well as application in solving problems in Physics, Mathematics and Chemistry.This review volume, part of the IMS Lecture Notes Series, is a collection of contributions from the September 2019 Workshop on the topic, held in the Institute for Mathematical Sciences, National University of Singapore.With contributions from prominent Mathematicians, Physicists, and Chemists, the volume is a blend of comprehensive review articles on the Mathematical and the Physicochemical aspects of DFT and shorter contributions on particular themes, including numerical implementations.The book will be a useful reference for advanced undergraduate and postgraduate students as well as researchers.
Special Functions And Orthogonal Polynomials
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Author : Diego Dominici
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Special Functions And Orthogonal Polynomials written by Diego Dominici and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
"This volume contains fourteen articles that represent the AMS Special Session on Special Functions and Orthogonal Polynomials, held in Tucson, Arizona in April of 2007. It gives an overview of the modern field of special functions with all major subfields represented, including: applications to algebraic geometry, asymptotic analysis, conformal mapping, differential equations, elliptic functions, fractional calculus, hypergeometric and q-hypergeometric series, nonlinear waves, number theory, symbolic and numerical evaluation of integrals, and theta functions. A few articles are expository, with extensive bibliographies, but all contain original research." "This book is intended for pure and applied mathematicians who are interested in recent developments in the theory of special functions. It covers a wide range of active areas of research and demonstrates the vitality of the field."--BOOK JACKET.
Introduction To Quantum Mechanics Schrodinger Equation And Path Integral Second Edition
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Author : Harald J W Muller-kirsten
language : en
Publisher: World Scientific Publishing Company
Release Date : 2012-07-19
Introduction To Quantum Mechanics Schrodinger Equation And Path Integral Second Edition written by Harald J W Muller-kirsten and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-19 with Science categories.
This text on quantum mechanics begins by covering all the main topics of an introduction to the subject. It then concentrates on newer developments. In particular it continues with the perturbative solution of the Schrödinger equation for various potentials and thereafter with the introduction and evaluation of their path integral counterparts. Considerations of the large order behavior of the perturbation expansions show that in most applications these are asymptotic expansions. The parallel consideration of path integrals requires the evaluation of these around periodic classical configurations, the fluctuation equations about which lead back to specific wave equations. The period of the classical configurations is related to temperature, and permits transitions to the thermal domain to be classified as phase transitions.In this second edition of the text important applications and numerous examples have been added. In particular, the chapter on the Coulomb potential has been extended to include an introduction to chemical bonds, the chapter on periodic potentials has been supplemented by a section on the band theory of metals and semiconductors, and in the chapter on large order behavior a section has been added illustrating the success of converging factors in the evaluation of asymptotic expansions. Detailed calculations permit the reader to follow every step.
Nist Handbook Of Mathematical Functions Hardback And Cd Rom
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Author : Frank W. J. Olver
language : en
Publisher: Cambridge University Press
Release Date : 2010-05-17
Nist Handbook Of Mathematical Functions Hardback And Cd Rom written by Frank W. J. Olver and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-17 with Mathematics categories.
The new standard reference on mathematical functions, replacing the classic but outdated handbook from Abramowitz and Stegun. Includes PDF version.
Lecture Notes On Applied Analysis
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Author :
language : en
Publisher: World Scientific
Release Date : 2009
Lecture Notes On Applied Analysis written by and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with categories.